problem solving involving addition and subtraction of integers

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Subtracting integers word problems

Here are four great examples about subtracting integers word problems.

Problem #1:

The record high temperature for Massachusetts is 104 degrees Fahrenheit. The record low is -18 degrees Fahrenheit. What is the difference between high and low? Solution The problem has 1 important component. It is the phrase " difference between high and low ." Difference between high and low is the same as subtracting the smaller number from the bigger number.

104 - -18 = 104 + 18 = 122

The difference between high and low is 122 degrees Fahrenheit.

Take a look also at the problem below

Adding integers word problems

Applied math

Calculators.

100 Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius!

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How to Add and Subtract Integers: Word Problems

Mastering the art of tackling word problems involving the addition and subtraction of integers is a vital skill in the mathematical universe. Integers, which include positive, negative, and zero, are more nuanced than their natural number counterparts. To craft a highly detailed, comprehensive, and sophisticated guide, let's dive into the labyrinth of integers, unraveling the mystery of word problems step-by-step.

A Step-by-step Guide to Solve Integers Addition and Subtraction: Word Problems

Here is a step-by-step guide to solving word problems of integers addition and subtraction:

Step 1: Decipher the Problem

The journey begins with an intensive reading of the word problem. Identify the integers involved, noting their signs ($+$ or $-$), and the operations stated or implied (addition or subtraction). Understand the context and constraints of the problem to guide your strategy.

Step 2: Pinpoint the Unknowns

Next, determine what the problem demands you to find. This could be an unknown quantity or a relationship between different quantities. Assign variables to these unknowns, typically ‘$x$’, ‘$y$’, or ‘$z$’.

Step 3: Translate into Mathematical Language

Now, morph the word problem into an equivalent mathematical expression or equation. Expressions such as “increased by” or “more than” often signify addition, while “decreased by” or “less than” hint towards subtraction. This translation serves as a bridge between the narrative of the problem and the mathematical steps to solve it.

Step 4: Construct the Equation(s)

Based on your translation, construct an equation or a system of equations that encapsulate the conditions outlined in the problem. Be vigilant of the signs of the integers; a positive integer added to a negative integer can be treated as subtraction and vice versa.

Step 5: Resolve the Equation(s)

Once your equation(s) are set, deploy your arithmetic and algebraic skills to solve them. Remember the basic rules of integer arithmetic, such as the fact that subtracting a negative integer is equivalent to adding a positive one.

Step 6: Validate Your Solution

Substitute your solution back into the original equation(s) to verify its correctness. If it stands the test, your solution is accurate. If it fails, reexamine your steps to identify potential missteps or miscalculations.

Step 7: Answer the Query

The final act is responding to the original question asked in the problem. Ensure your answer aligns with the question and is phrased appropriately, incorporating units if necessary.

by: Effortless Math Team about 1 year ago (category: Articles )

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Last modified on August 3rd, 2023

Integer Word Problems

We use integers in our everyday life for counting money and measuring the speed of sound and light, height and weight of objects, temperature and pressure of the atmosphere, and depth of a sea. Solving word problems related to the above measurements will help us relate better to the concept with applications.

A submarine was located 600 feet below sea level. Calculate its new position if it ascends 250 feet from its position.

Given, The initial position of the submarine is 600 feet It ascends 250 feet Thus, the new position of the submarine is (600 – 250) feet = 350 feet Thus, the new depth of the submarine is 550 feet

Today’s weather report suggested that the temperature of New York City increased from 10-degree celsius to 20-degree celsius. What is the rise in temperature?

Given, Initial temperature = -10 degree celsius Final temperature = 20 degrees celsius Increase in temperature = 20 – (-10) = 30 degrees celsius Thus, the rise in temperature of New York City is 30 degree Celsius.

Demitri owes her mother \$5.00. He earns \$12.00 doing chores. How much is left with him after he gives his mother what she owes?

Given, Amount to be given to his mother = \$5.00 He earns = \$12.00 Thus, he is left with = \$(12.00 – 5.00) = \$7.00 Thus, Demitri is left with \$7.00.

The local movie theater reported losses of \$475 each day for 3 days. What was the total loss incurred for the 3 days?

Given, Loss incurred by the movie theater per day = \$475 The loss incurred in 3 days = \$(3 × 475) = \$1,425 Thus the total loss incurred by the movie theater in 3 days is \$1,425

The Second World War began in the year 1939 and ended in 1945. How long did it last?

Given, The Second World War began in 1939 and ended in 1945 Thus, it lasted (1945 – 1939) = 6 years

Mt. Everest is 29,028 feet above sea level, and the Dead Sea is 1,312 feet below sea level. Find the difference between the 2 elevations.

Given The height of Mt. Everest is 29,028 feet above sea level The height of the Dead Sea is 1,312 feet below sea level Thus, the difference between the 2 elevations = (29,028 + 1,312) feet = 30,340 feet

Dakota withdrew a total of \$600 over 4 days. If he withdrew the same amount daily, find the amount he withdrew each day.

Given, Total amount Dakota withdrew = \$600 Number of days he withdrew = 4 days Amount withdrawn each day = \$(600 ÷ 4) = \$150 Thus, Dakota withdrew \$150 per day.

Andrew had \$12,000 in his account. He once withdrew \$2,000 and then deposited $6,000. What is the current balance in the account?

Given, Initial balance Andrew had = \$12,000 Amount withdrawn = \$2,000 Amount deposited = \$6,000 Thus, the current balance = \$(12,000 – 2,000 + 6,000) = \$16,000 Thus, the current balance Andrew has currently in his account is \$16,000

A kite rises 100 feet from the ground and then falls back 40 feet. What is the current height of the kite from the ground?

Given, The kite rises = 100 feet and then falls back = 40 feet Thus, the current height of the kite from the ground is (100 – 40) feet = 60 feet

If it is 3°C outside and the temperature drops 15° C in the next 6 hours, how cold will it be after 6 hours?

Initially, the outside temperature was 2°C Then, the temperature drops to = (2 – 15)°C = -13°C Thus, the temperature after 6 hours will be -13°C

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Integers Worksheets

Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

$Adding, Subtracting, Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions)$

Integer Resources

$problem solving involving addition and subtraction of integers$

Coordinate graph paper can be very useful when studying integers. Coordinate geometry is a practical application of integers and can give students practice with using integers while learning another related skill. Coordinate graph paper can be found on the Graph Paper page:

Coordinate Graph Paper

Integer number lines can be used for various math activities including operations with integers, counting, comparing, ordering, etc.

Integer Number Lines Integers Number Lines from -10 to 10 Integers Number Lines from -15 to 15 Integers Number Lines from -20 to 20 Integers Number Lines from -25 to 25 OLD Integer Number Lines

Comparing and Ordering Integers

$problem solving involving addition and subtraction of integers$

For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.

Comparing Integers Worksheets Comparing Positive and Negative Integers (-9 to +9) Comparing Positive and Negative Integers (-15 to +15) Comparing Positive and Negative Integers (-25 to +25) Comparing Positive and Negative Integers (-50 to +50) Comparing Positive and Negative Integers (-99 to +99) Comparing Negative Integers (-15 to -1)

By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.

Comparing Integers in Close Proximity Comparing Positive and Negative Integers (-9 to +9) in Close Proximity Comparing Positive and Negative Integers (-15 to +15) in Close Proximity Comparing Positive and Negative Integers (-25 to +25) in Close Proximity Comparing Positive and Negative Integers (-50 to +50) in Close Proximity Comparing Positive and Negative Integers (-99 to +99) in Close Proximity
Ordering Integers Worksheets Ordering Integers on a Number Line Ordering Integers (range -9 to 9) Ordering Integers (range -20 to 20) Ordering Integers (range -50 to 50) Ordering Integers (range -99 to 99) Ordering Integers (range -999 to 999) Ordering Negative Integers (range -9 to -1) Ordering Negative Integers (range -99 to -10) Ordering Negative Integers (range -999 to -100)

Adding and Subtracting Integers

$problem solving involving addition and subtraction of integers$

Two-color counters are fantastic manipulatives for teaching and learning about integer addition. Two-color counters are usually plastic chips that come with yellow on one side and red on the other side. They might be available in other colors, so you'll have to substitute your own colors in the following description.

Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side; then you mash them all together, take out the zeros (if any) and behold, you have your answer! Need further elaboration? Read on!

The correct side means using red to model negative numbers and yellow to model positive numbers. You would model —5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward although, you'll want to caution your students to be less exuberant than usual, so none of the chips get flipped. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You can do this because —1 and 1 when added together equals zero (this is called the zero principle). If you remove the zeros, you don't affect the answer. The benefit of removing the zeros, however, is that you always end up with only one color and as a consequence, the answer to the integer question. If you have no chips left at the end, the answer is zero!

Adding Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (75 Questions) ✎ Adding Integers from -12 to 12 (75 Questions) ✎ Adding Integers from -15 to 15 (75 Questions) ✎ Adding Integers from -20 to 20 (75 Questions) ✎ Adding Integers from -25 to 25 (75 Questions) ✎ Adding Integers from -50 to 50 (75 Questions) ✎ Adding Integers from -99 to 99 (75 Questions) ✎
Adding Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
Adding Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (75 Questions) ✎
Adding Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (50 Questions) ✎ Adding Integers from -12 to 12 (50 Questions) ✎ Adding Integers from -15 to 15 (50 Questions) ✎ Adding Integers from -20 to 20 (50 Questions) ✎ Adding Integers from -25 to 25 (50 Questions) ✎ Adding Integers from -50 to 50 (50 Questions) ✎ Adding Integers from -99 to 99 (50 Questions) ✎
Adding Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
Adding Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (50 Questions) ✎
Adding Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 (Large Print; 25 Questions) ✎
Adding Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
Adding Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (Large Print; 25 Questions) ✎
Vertically Arranged Integer Addition Worksheets 3-Digit Integer Addition (Vertically Arranged) 3-Digit Positive Plus a Negative Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Positive Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Negative Integer Addition (Vertically Arranged)

Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.

Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (75 Questions) ✎ Subtracting Integers from -12 to 12 (75 Questions) ✎ Subtracting Integers from -15 to 15 (75 Questions) ✎ Subtracting Integers from -20 to 20 (75 Questions) ✎ Subtracting Integers from -25 to 25 (75 Questions) ✎ Subtracting Integers from -50 to 50 (75 Questions) ✎ Subtracting Integers from -99 to 99 (75 Questions) ✎
Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (50 Questions) ✎ Subtracting Integers from -12 to 12 (50 Questions) ✎ Subtracting Integers from -15 to 15 (50 Questions) ✎ Subtracting Integers from -20 to 20 (50 Questions) ✎ Subtracting Integers from -25 to 25 (50 Questions) ✎ Subtracting Integers from -50 to 50 (50 Questions) ✎ Subtracting Integers from -99 to 99 (50 Questions) ✎
Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎
Vertically Arranged Integer Subtraction Worksheets 3-Digit Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Negative Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Negative Integer Subtraction (Vertically Arranged)

The worksheets in this section include addition and subtraction on the same page. Students will have to pay close attention to the signs and apply their knowledge of integer addition and subtraction to each question. The use of counters or number lines could be helpful to some students.

Adding and Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (75 Questions) ✎ Adding & Subtracting Integers from -10 to 10 (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (75 Questions) ✎
Adding and Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-5) to (+5) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
Adding and Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
Adding and Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (50 Questions) ✎
Adding and Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
Adding and Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding & Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎

These worksheets include groups of questions that all result in positive or negative sums or differences. They can be used to help students see more clearly how certain integer questions end up with positive and negative results. In the case of addition of negative and positive integers, some people suggest looking for the "heavier" value to determine whether the sum will be positive of negative. More technically, it would be the integer with the greater absolute value. For example, in the question (−2) + 5, the absolute value of the positive integer is greater, so the sum will be positive.

In subtraction questions, the focus is on the subtrahend (the value being subtracted). In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the subtrahend has a greater absolute value, the answer will be positive. Vice-versa for both situations. Alternatively, students can always convert subtraction questions to addition questions by changing the signs (e.g. (−5) − (−7) is the same as (−5) + 7; 3 − 5 is the same as 3 + (−5)).

Scaffolded Integer Addition and Subtraction Positive Plus Negative Integer Addition (Scaffolded) ✎ Negative Plus Positive Integer Addition (Scaffolded) ✎ Mixed Integer Addition (Scaffolded) ✎ Positive Minus Positive Integer Subtraction (Scaffolded) ✎ Negative Minus Negative Integer Subtraction (Scaffolded) ✎

Multiplying and Dividing Integers

$problem solving involving addition and subtraction of integers$

Multiplying integers is very similar to multiplication facts except students need to learn the rules for the negative and positive signs. In short, they are:

In words, multiplying two positives or two negatives together results in a positive product, and multiplying a negative and a positive in either order results in a negative product. So, -8 × 8, 8 × (-8), -8 × (-8) and 8 × 8 all result in an absolute value of 64, but in two cases, the answer is positive (64) and in two cases the answer is negative (-64).

Should you wish to develop some "real-world" examples of integer multiplication, it might be a stretch due to the abstract nature of negative numbers. Sure, you could come up with some scenario about owing a debt and removing the debt in previous months, but this may only result in confusion. For now students can learn the rules of multiplying integers and worry about the analogies later!

Multiplying Integers with 100 Questions Per Page Multiplying Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Mixed Integers from -20 to 20 (100 Questions) ✎ Multiplying Mixed Integers from -50 to 50 (100 Questions) ✎
Multiplying Integers with 50 Questions Per Page Multiplying Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (50 Questions) ✎
Multiplying Integers with 25 Large Print Questions Per Page Multiplying Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

Luckily (for your students), the rules of dividing integers are the same as the rules for multiplying:

Dividing a positive by a positive integer or a negative by a negative integer will result in a positive integer. Dividing a negative by a positive integer or a positive by a negative integer will result in a negative integer. A good grasp of division facts and a knowledge of the rules for multiplying and dividing integers will go a long way in helping your students master integer division. Use the worksheets in this section to guide students along.

Dividing Integers with 100 Questions Per Page Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (100 Questions) ✎
Dividing Integers with 50 Questions Per Page Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (50 Questions) ✎
Dividing Integers with 25 Large Print Questions Per Page Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

This section includes worksheets with both multiplying and dividing integers on the same page. As long as students know their facts and the integer rules for multiplying and dividing, their sole worry will be to pay attention to the operation signs.

Multiplying and Dividing Integers with 100 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (100 Questions) ✎
Multiplying and Dividing Integers with 75 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (75 Questions) ✎
Multiplying and Dividing Integers with 50 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (50 Questions) ✎
Multiplying and Dividing Integers with 25 Large Print Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

All Operations with Integers

$problem solving involving addition and subtraction of integers$

In this section, the integers math worksheets include all of the operations. Students will need to pay attention to the operations and the signs and use mental math or another strategy to arrive at the correct answers. It should go without saying that students need to know their basic addition, subtraction, multiplication and division facts and rules regarding operations with integers before they should complete any of these worksheets independently. Of course, the worksheets can be used as a source of questions for lessons, tests or other learning activities.

All Operations with Integers with 50 Questions Per Page (Some Parentheses) All operations with integers from -9 to 9 (50 Questions) ✎ All operations with integers from -12 to 12 (50 Questions) ✎ All operations with integers from -15 to 15 (50 Questions) ✎ All operations with integers from -20 to 20 (50 Questions) ✎ All operations with integers from -25 to 25 (50 Questions) ✎ All operations with integers from -50 to 50 (50 Questions) ✎ All operations with integers from -99 to 99 (50 Questions) ✎
All Operations with Integers with 50 Questions Per Page (All Parentheses) All operations with integers from (-9) to (+9) All Parentheses (50 Questions) ✎ All operations with integers from (-12) to (+12) All Parentheses (50 Questions) ✎ All operations with integers from (-15) to (+15) All Parentheses (50 Questions) ✎ All operations with integers from (-20) to (+20) All Parentheses (50 Questions) ✎ All operations with integers from (-25) to (+25) All Parentheses (50 Questions) ✎ All operations with integers from (-50) to (+50) All Parentheses (50 Questions) ✎ All operations with integers from (-99) to (+99) All Parentheses (50 Questions) ✎
All Operations with Integers with 50 Questions Per Page (No Parentheses) All operations with integers from -9 to 9 No Parentheses (50 Questions) ✎ All operations with integers from -12 to 12 No Parentheses (50 Questions) ✎ All operations with integers from -15 to 15 No Parentheses (50 Questions) ✎ All operations with integers from -20 to 20 No Parentheses (50 Questions) ✎ All operations with integers from -25 to 25 No Parentheses (50 Questions) ✎ All operations with integers from -50 to 50 No Parentheses (50 Questions) ✎ All operations with integers from -99 to 99 No Parentheses (50 Questions) ✎

Order of operations with integers can be found on the Order of Operations page:

Order of Operations with Integers

Integer Word Problems Worksheets

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication . Integer word problems worksheets provide a variety of word problems associated with the use and properties of integers.

Benefits of Integers Word Problems Worksheets

We use integers in our day-to-day life like measuring temperature, sea level, and speed limit. Translating verbal descriptions into expressions is an essential initial step in solving word problems. Deposits are normally represented by a positive sign and withdrawals are denoted by a negative sign. Negative numbers are used in weather forecasting to show the temperature of a region. Solving these integers word problems will help us relate the concept with practical applications.

Download Integers Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

Integers Word Problems Worksheet - 1
Integers Word Problems Worksheet - 2
Integers Word Problems Worksheet - 3
Integers Word Problems Worksheet - 4

☛ Check Grade wise Integers Word Problems Worksheets

6th Grade Integers Worksheets
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Integer Word Problems

problem solving involving addition and subtraction of integers

Welcome to the fascinating world of integer word problems! Don’t let the fancy name scare you off; these problems might be easier and more fun than you think. Simplifying them is handy in daily life, and they’ll reappear in various forms throughout your academic journey. Let’s dive into the fundamental components.

What are Integer Word Problems?

In essence, integer word problems are mathematical problems involving number-related questions in the form of a story or practical situation. Specifically, these problems use integers — whole numbers that can be positive, negative, or zero. For instance, you might be asked how many more books Mike read than Sarah if Mike reads 15 and Sarah reads 7. Since you’re subtracting 7 from 15, you’re dealing with an integer word problem.

Importance of Solving Integer Word Problems

Mastering integer word problems plays a significant role in building your mathematical expertise. They help improve your problem-solving skills and enhance your ability to think logically and critically. Moreover, these problems are a cornerstone of real-world situations. Whether you are calculating the distance between two cities, determining profit and loss in business, or even figuring out temperature changes, integers and their problems come into play.

How to Solve Integer Word Problems

Are you ready to tackle integer word problems? Here are a few steps:

Understand the Problem: Breaking the problem into smaller parts makes it less daunting. Take your time to understand what the problem is about.
Identify the Key Information: Highlight or underline important facts or figures in the problem. Look for clues indicating whether you’re dealing with addition, subtraction, or a combination.
Formulate a Plan: Write down your actions to arrive at the solution.
Execute Your Plan: Apply the actions you’ve mapped out to solve the problem.
Verify Your Answer: Always double-check your outcome. Does it make sense in terms of the problem?

In dealing with integer word problems, practice is critical. The more problems you tackle, the more proficient you become. Happy problem-solving!

Basic Concepts of Integers

As a student or math enthusiast, knowing and mastering the basic concepts of integers will help you understand and tackle integer word problems better. In this section, we’ll delve into the definitions of integers, further distinguishing between positive and negative integers.

Defining Integers

Integers are a number category that includes all the whole numbers, their opposites (negative counterparts), and zero. They are distinct from fractions, decimals, and percents. An integer can be a zero, a positive, or a negative whole number. The set of integers is denoted mathematically as {…, -3, -2, -1, 0, 1, 2, 3}. These numbers form the backbone of many mathematical operations and concepts, especially in algebra.

Positive and Negative Integers

Positive and negative integers make understanding and calculating many real-world situations better and more efficient.

Positive integers , often natural numbers , are numbers greater than zero. They are frequently used to denote weight, distance, or money values. However, not all situations can be expressed with positive numbers; sometimes, we must resort to negative ones.

Negative integers are the opposites of natural numbers, excluding zero, and fall below zero on the number line. They are typically used when something is decreased, removed, or lost. An excellent example of using negative integers is in banking, where they represent debt. Or in meteorology, where they represent temperatures below zero.

Understanding the concept of positive and negative integers is paramount because they are central to successfully dealing with integer word problems. In the next segment, we will dive deeper into strategies for solving these problems, so tighten your seatbelts as we explore a fun section of the mathematical world.

Addition and Subtraction Word Problems

When it comes to integers, understanding how to add and subtract these numbers is crucial, taking center stage in everyday mathematical operations. While learning, students begin grappling with word problems – mathematical problems presented in the form of a narrative or story – which include real-world scenarios. These serve as a bridge for children and adults to apply theoretical knowledge practically.

Adding and Subtracting Integers

In terms of adding integers , there are a few rules to remember. If the integers have the same sign, add their absolute values and keep the standard sign. On the flip side, when the integers have different signs, subtract the smaller absolute value from the larger one and give the solution the sign of the number with the more considerable absolute value.

Subtracting integers , however, involves an additional step. More specifically, any subtraction can be reinterpreted as an addition. To subtract an integer, add its opposite. For example, to subtract -3 from 5 (5 – -3), we add 3 to 5 (5 + 3), with the sum coming to 8.

Real-life Examples of Addition and Subtraction Word Problems

Let’s explore a few word problems that imitate daily life scenarios. Suppose a child has £5 and they want to buy a toy that costs £10. How many more pounds do they need? The problem here is 10 – 5, which equals 5. Thus, the child needs five more pounds.

In another situation, imagine the temperature was 5 degrees Celsius in the morning and dropped 3 degrees by the afternoon. What’s the temperature now? Here, we have 5 – 3 = 2. The answer is 2 degrees Celsius.

These examples illustrate how adding and subtracting integers can help us solve practical problems and better understand the world. We encourage you to find your examples and practice to enhance your understanding and mastery of this fundamental mathematical skill.

Multiplication and Division Word Problems

As the journey of discovery with integers continues, multiplication and division of these numbers become an integral part of our everyday mathematical activities. Understanding how to tackle word problems – mathematical problems in narrative form – becomes critical. Specifically, multiplication and division integer word problems provide the groundwork for applying knowledge practically in real-world situations.

Multiplying and Dividing Integers

Multiplying integers might initially seem complex , but it becomes straightforward once you grasp the core concept. When multiplying two integers, the result will be positive if the signs are the same (positive or negative). However, if the signs are different (positive and negative), the result will be a negative integer.

Dividing integers follows a similar concept. If the integers have the same sign, the quotient is positive, and if they have different signs, it is negative.

Application of Multiplication and Division Word Problems

Now, let’s see how these concepts apply in real-world scenarios. Suppose a person has $20 and wants to buy as many chocolates as possible, with each chocolate bar costing $4. In this case, they’d need to divide 20 by 4. The question boils down to 20 ÷ 4, which equals 5. So, they can buy five chocolate bars.

Considering multiplication, imagine a scenario where a store sells packages of bottled drinking water. Each package contains six bottles, and the store has twenty packages. To calculate the total number of bottles, you would multiply 6 (bottles per package) by 20 (number of packages), getting 6 x 20 = 120. So, the store has 120 bottled water.

These real-world examples show how multiplication and division word problems offer practical ways to understand and apply mathematical knowledge. Engaging with these problems enhances understanding of fundamental math concepts and promotes problem-solving skills crucial for daily life.

Multi-Step Word Problems

In a journey through mathematics, we commonly encounter complex multi-step word problems. These problems often involve multiple operations using integers , such as addition, subtraction, multiplication, and division. Solving these tasks enhances problem-solving skills, logical thinking, and mathematical proficiency. This part will delve into complex integer word problems and introduce strategies for solving multi-step problems.

Complex Integer Word Problems

Complex integer word problems involve more than one mathematical operation, often requiring a systematic approach to reach the solution. For instance, imagine a scenario where a garden filled with 120 roses and petunias is being prepared for a garden show. There are twice as many roses as there are petunias. The question is, “How many petunias are there?”

Here, the problem will be solved in two steps. First, understanding that the number of roses is twice that of petunias. That means, if we denote the number of petunias as ‘p,’ then the number of roses is ‘2p’. The total quantity of flowers (120) is the sum of roses and petunias, leading to the equation 2p + p = 120. Solving this equation provides the number of petunias. Since multi-step word problems rely heavily on integers, understanding their operation rules is essential.

Strategies for Solving Multi-Step Word Problems

Solving multi-step word problems can seem daunting, but a systematic approach simplifies the task. Below are vital strategies:

Understand the Problem: Read the problem carefully, ensure you understand what it’s asking, and identify the operations needed.
Develop a Plan: Break down the problem into smaller, manageable steps. Form equations if needed.
Solve: Carry out each operation. Ensure your calculations are correct at each step.
Check Your Answer: Review your solution, ensuring you answered the initial question correctly. Doing this validates that your solution aligns with the problem’s conditions.

Remember, practice significantly improves problem-solving skills and the ability to tackle complex multi-step word problems involving integers. Happy problem-solving!

Common Mistakes and Tips for Success

In particular, integer word problems can sometimes throw you off course. Like every journey, it is customary to make mistakes along the way. However, understanding and learning from these common errors can help you avoid detours and get you on the fast track to mastery.

Common Errors in Solving Integer Word Problems

Misinterpretation is one of the most common mistakes when handling integer word problems. Often, students need to understand the operations required or interpret the relationship between the integers presented in the problem.

Inaccurate Calculations – Integers include both positive and negative numbers, and it is easy to miscalculate when it comes to subtraction, addition, or other operations involving such numbers. For example, subtracting a negative integer leads to an addition instead.

Helpful Tips and Tricks for Solving Integer Word Problems

Once you’re aware of common pitfalls, arm yourself with the right strategies to navigate your way through complex integer word problems adeptly.

Thorough Understanding: Read the integer word problem carefully and understand what is being asked. It can be helpful to jot down essential information or even draw diagrams to visualize the problem.

Plan: Make a plan. Break the problem down into smaller, solvable parts and create equations representing each step of the problem.

Check Your Work: After solving, double-check your calculations to ensure accuracy. Compare your answer with the original question to see if it makes sense.

Practice: Just like anything, practice makes perfect. The more problems you solve, the more comfortable you become with integers and their operations.

Always remember making mistakes is part of the learning process. By staying aware and utilizing strategies, you’ll soon find yourself an expert at solving integer word problems. Happy Practicing!

Practice Exercises

Knowing the common errors and tips for solving integer word problems, it is time to put that knowledge into practice. With the right amount of practice, anyone can enhance their skills in solving such problems. With that in mind, let’s tackle some practice exercises to understand integer word problems further.

Practice Problems for Integer Word Problems

Here are some various types of integer word problems. Remember to read carefully, understand what’s asked, and plan your solution before jumping into the problem.

Maria has $15 in her pocket. She spends $7 on a movie and $6 on snacks. Write an integer to represent Maria’s money situation and calculate how much she has left.
At the start of the week, the temperature is 5 degrees. The temperature then drops by 7 degrees the next day. What is the temperature now?
A company lost $2000 this year, 3 times the amount they lost last year. How much did the company lose last year?

Step-by-Step Solutions for Practice Exercises

Let’s walk through the solutions together to help you understand how these problems are solved.

Maria has $15. She spent $7 and $6. This expenditure is a loss, so we represent it with negative integers. So, the situation becomes: 15 + (-7) + (-6) = 2. Maria has $2 left.
The temperature is 5 degrees initially. Then, it drops by 7 degrees (a decrease is a negative operation). So, the situation is 5 + (-7) = -2 degrees. The temperature is now -2 degrees.
Let’s denote the amount of money the company lost last year as x. We know that 3x = $2000. So, x = $2000 / 3 = $666.67. The company lost around $666.67 last year.

Do more exercises and get comfortable with solving integer word problems. It may take some time, but you will get there with consistent practice. Remember, avoiding rushing and breaking the problem into smaller parts can be very helpful. Practicing will make you better at solving integer word problems effectively and efficiently. Happy learning!

Emerging victorious in integer word problems opens up an exciting facet of mathematical knowledge. After all, these problems translate mathematical concepts into real-world scenarios, thereby cultivating critical thinking skills. Let’s explore the benefits of mastering integer word problems and round off with a few parting thoughts.

Benefits of Mastering Integer Word Problems

Boosts Problem-solving Skills: Integer word problems are an ideal way to sharpen problem-solving skills. They compel one to think logically and systematically about how to apply mathematical operations accurately.

Enhances Numerical Literacy: With a firm grasp of integers, people can better comprehend numerical information daily. For instance, understanding debt and assets or gain and loss in finance becomes clearer.

Encourages Diversity of Thought: Integer word problems offer multiple ways to find a solution, fostering creativity. It encourages diverse approaches to problem-solving.

Promotes Practical Application: Integers have ubiquitous applications in diverse fields, including science, engineering, and information technology. Being comfortable with integer word problems equips one with skills applicable to these areas.

Final Thoughts on Integer Word Problems

Integer word problems seem daunting initially, but their mastery is a matter of regular practice and strategy. Break down the problem, identify what operation is warranted, and then move towards a solution progressively. Remember to cross-check the answer, as it ensures correctness.

Remember, it’s perfectly fine to make mistakes while learning. They are merely stepping stones to success. So, stay patient, persist in your efforts, and remember the tips shared. You will soon gain a commendable prowess over integer word problems. The confidence and skills you gain here will be beneficial throughout your mathematical journey.

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Subtraction of Integers Exercises

Subtracting integers practice problems with answers.

The following ten (10) practice problems are all about subtracting integers . Keep practicing and you will get better in no time! Have fun!

Note: To subtract integers, change the operation from subtraction to addition but take the opposite sign of the second integer. Then proceed with regular integer addition as usual.

Case 1: [latex]a – b \to a {\color{red}+} \left( { {\color{red}-} b} \right)[/latex]

Case 2: [latex]a – \left( { – b} \right) \to a {\color{red}+} \left( { {\color{red}+} b} \right)[/latex]

Problem 1: Subtract the integers: [latex]8 – 5[/latex]

[latex]3[/latex]

Problem 2: Subtract the integers: [latex]12 – \left( { – 3} \right)[/latex]

[latex]15[/latex]

Problem 3: Subtract the integers: [latex] – 7 – 4[/latex]

[latex]-11[/latex]

Problem 4: Subtract the integers: [latex] – 13 – \left( { – 17} \right)[/latex]

[latex]4[/latex]

Problem 5: Subtract the integers: [latex]9 – \left( { – 1} \right)[/latex]

[latex]10[/latex]

Problem 6: Subtract the integers: [latex]1 – \left( { – 2} \right) – 3[/latex]

[latex]0[/latex]

Problem 7: Subtract the integers: [latex] – 4 – 2 – \left( { – 9} \right)[/latex]

Problem 8: Subtract the integers: [latex] – 8 – \left( { – 1} \right) – \left( { – 5} \right)[/latex]

[latex]-2[/latex]

Problem 9: Subtract the integers: [latex] – 6 – \left( { – 4} \right) – \left( { – 1} \right) – 3[/latex]

[latex]-4[/latex]

Problem 10: Subtract the integers: [latex]11 – 16 – \left( { – 2} \right) – \left( { – 10} \right)[/latex]

[latex]7[/latex]

Integers: Word Problems On Integers

An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types of numbers including integers.

Integers are a special group of numbers that do not have a fractional or a decimal part. It includes positive numbers, negative numbers and zero. Arithmetic operations on integers are similar to that of whole numbers. Since integers can be positive or negative numbers i.e. as these numbers are preceded either by a positive (+) or a negative sign (-), it makes them a little confusing concept. Therefore, they are different from whole numbers . Let us now see how various arithmetical operations can be performed on integers with the help of a few word problems. Solve the following word problems using various rules of operations of integers.

Word problems on integers Examples:

Example 1: Shyak has overdrawn his checking account by Rs.38. The bank debited him Rs.20 for an overdraft fee. Later, he deposited Rs.150. What is his current balance?

Solution: Given,

Total amount deposited= Rs. 150

Amount overdrew by Shyak= Rs. 38

Amount charged by bank= Rs. 20

⇒ Debit amount= -20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

Hence, the current balance is Rs. 92.

Example 2: Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?

Solution: Given,

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

⇒ (-31) – (-56)

Hence, temperature difference is 25˚C.

Example 3: A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

Initial position = 20 m (above sea level)

Final position = 250 m (below sea level)

Total depth it submerged = (250+20) = 270 m

Thus, the submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = 1/5 minutes

Time taken to submerge 270 m = 270 (1/5) = 54 min

Hence, the submarine will reach 250 m below sea level in 54 minutes.

To solve more problems on the topic, download BYJU’S – The Learning App and watch interactive videos. Also, take free tests to practice for exams.

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Mastering Integer Operations: From Basics to Real-World Applications Unlock the power of integer operations! Learn to add, subtract, and solve problems with multiple integers. Discover practical applications in finance, science, and everyday life.

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Introduction to applications of integer operations
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A rocket countdown is at -11 s. In how many seconds will the rocket be 22 seconds into the flight?
At a particular school, there are 138 students in grade 10, 126 students in grade 11 and 92 students in grade 12. If all senior students are sent to the hall for an assembly, how many students are there in the hall?
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Introduction to Integer Operations and Their Real-World Applications

Integer operations form the foundation of mathematical calculations in our daily lives. These operations, including addition, subtraction, multiplication, and division, are essential for solving a wide range of practical problems. From managing personal finances to calculating distances for travel, integer operations play a crucial role. The introduction video provided offers a comprehensive overview of these operations, serving as a vital resource for understanding their fundamental principles. By watching this video, learners can grasp the core concepts and their applications more effectively. Integer operations are not just abstract mathematical concepts; they have significant relevance in real-world scenarios. Whether you're budgeting for groceries, measuring ingredients for cooking, or analyzing data at work, these operations are indispensable. Understanding integer operations enhances problem-solving skills and numerical literacy, which are valuable in various aspects of life, from education to professional careers. This topic's importance extends beyond the classroom, making it a fundamental skill for everyday decision-making and practical problem-solving.

Q1: What are the basic integer operations? A1: The basic integer operations are addition, subtraction, multiplication, and division. These operations form the foundation for working with whole numbers, both positive and negative, including zero.

Q2: How do you add three integers with different signs? A2: To add three integers with different signs, first add the positive numbers together and the negative numbers together separately. Then, subtract the smaller sum from the larger sum. The result takes the sign of the larger sum. For example, to add 5, -3, and 2: Add positive numbers (5 + 2 = 7), then subtract the absolute value of the negative number (7 - 3 = 4). The result is 4.

Q3: What is the correct order of operations when working with multiple integers? A3: The correct order of operations is given by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). When dealing with only addition and subtraction, perform the operations from left to right.

Q4: How can I avoid common mistakes when working with integer operations? A4: To avoid common mistakes, always pay attention to signs, use parentheses for clarity, follow the order of operations, and double-check your calculations. Practice regularly with various problem types, and use estimation to verify if your answer makes sense.

Q5: How are integer operations applied in real-world scenarios? A5: Integer operations are applied in many real-world scenarios, such as managing finances (calculating income and expenses), tracking temperature changes, measuring altitude differences, and analyzing data in various fields like science and economics. Understanding these operations helps in solving practical problems in daily life and professional settings.

Understanding the application of integer operations is crucial in mathematics, but it requires a solid foundation in several prerequisite topics. One of the most fundamental skills is introduction to integer addition , which lays the groundwork for more complex operations. Mastering integer addition steps is essential before moving on to more advanced concepts.

Equally important is the ability to perform integer subtraction . Grasping integer subtraction examples helps students understand how positive and negative numbers interact, which is crucial for applying integer operations in various contexts.

To effectively work with integers, students must be proficient in comparing and ordering numbers . This skill is particularly important when combining positive and negative numbers, as it helps in determining the final result of integer operations.

The order of operations (PEMDAS) is a critical concept that governs how integer operations should be performed in complex expressions. Understanding PEMDAS ensures that students can correctly solve multi-step problems involving integers.

While not directly related to integers, adding and subtracting decimals builds a strong foundation for working with different number types. This skill often comes into play when applying integer operations in real-world scenarios.

For more advanced applications, students should be familiar with multiplying and dividing radicals . This topic includes understanding the concept of multiplying two negatives, which is crucial in integer operations.

As students progress, they'll encounter more complex problems. Solving two-step linear equations using addition and subtraction is an excellent example of how integer operations are applied in algebra. This skill demonstrates the practical use of integer operations in equation solving.

Another important skill is simplifying rational expressions and restrictions . This topic often involves simplifying algebraic expressions, which frequently requires the application of integer operations.

For those advancing to higher-level mathematics, understanding matrix operations in linear algebra becomes relevant. Integer operations form the basis of many matrix calculations, highlighting the far-reaching applications of these fundamental skills.

By mastering these prerequisite topics, students will be well-equipped to tackle the application of integer operations with confidence and proficiency. Each of these building blocks contributes to a comprehensive understanding of how integers behave and interact, paving the way for success in more advanced mathematical concepts.

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Grade 7 - The Number System

Standard 7.NS.A.1b - Find the missing number in addition and subtraction equations with integers.

Included Skills:

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

If you notice any problems, please let us know .

APPLYING ADDITION AND SUBTRACTION OF INTEGERS

Solving a multistep problem.

You can use what you know about adding and subtracting integers to solve a multistep problem.

Example :

A seal is swimming in the ocean 5 feet below sea level. It dives down 12 feet to catch some fish. Then, the seal swims 8 feet up towards the surface with its catch. What is the seal’s final elevation relative to sea level ?

applyingadditionandsubtractionofintegers1

Step 1 :

The seal starts at 5 feet below the surface, so its initial position is -5 ft.

Write an expression.

Starts - Dives down + Swims up

-5 - 12 + 8

Step 2 :

Add or subtract from left to right to find the value of the expression.

-5 - 12 + 8 = -17 + 8

The seal’s final elevation is 9 feet below sea level.

Applying Properties to Solve Problems

You can use properties of addition to solve problems involving integers.

Jack has a checking account. On Monday he writes a $160 check for groceries. Then he deposits $125. Finally he writes another check for $40. What was the total change in the amount in Jack’s account ?

Analyze Information :

When Jack deposits money, he adds that amount to the account. When he writes a check, that money is deducted from the account.

Formulate a Plan :

Use a positive integer for the amount Jack added to the account. Use negative integers for the checks he wrote. Find the sum.

-160 + 125 + (-40)

Solve :

Add the amounts to find the total change in the account. Use properties of addition to simplify calculations.

Commutative Property :

-160 + 125 + (-40) = -160 + (-40) + 125

Associative Property :

= -200 + 125

= -75

The amount in the account decreased by $75.

Justify and Evaluate :

Jack's account has $75 less than it did before Monday. This is reasonable because he wrote checks for $200 but only deposited $125.

Solved Problems

Problem 1 :

Anna is in a cave 40 feet below the cave entrance. She descends 13 feet, then ascends 18 feet. Find her new position relative to the cave entrance.

Solution :

Anna starts at 40 feet below cave entrance, so her initial position is -40 ft.

Starts - Descends + Ascends

-40 - 13 + 18

-40 - 13 + 18 = -53 + 18

= -35

Anna's new position is 35 feet below the cave entrance.

Problem 2 :

Tomas works as an underwater photographer. He starts at a position that is 15 feet below sea level. He rises 9 feet, then descends 12 feet to take a photo of a coral reef. Write and evaluate an expression to find his position relative to sea level when he took the photo.

Tomas starts at 15 feet below sea level, so his initial position is -15 ft.

Starts + Rises - Descends

-15 + 9 - 12

-15 + 9 - 12 = -6 - 12

= -18

When Tomas takes photo, his position is 18 feet below the sea level.

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Solving word problems both rely the development of reading and language skills. Addition means “putting together” groups of objects and finding how many they are in total while subtraction tells “how many are left” or “how many more or less”.

Steps in Problem Solving:

Identify the Problem. Understand what is asked.
Encircle important numbers.
Underline the keywords. Analyze if it is for addition or subtraction .
Solve the problem.
Present the answer.

Addition: in all, sum, total, more than, plus, altogether, increased by add

Subtraction: fewer, left, less than, take away, minus, difference, remain, decreased

There are 6 surfboards and the surfer bought another 8 pieces. How many surfboards are there in all?

There were 8 beach balls but 5 of them were damaged. How many beach balls were left?

8 – 5 = 3

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Addition and Subtraction of Integers

Adding two positive integers results in positive integers, whereas adding two negative integers will result in the sum with a negative sign. But the addition of two different signed integers will result in subtraction only and the sign of the result will be the same as the larger number.

Table of Content

What are Integers?

Addition of integers, subtraction of integers, rules for adding and subtracting integers, addition and subtraction of integers on number line.

Solved Examples

Integers are whole numbers that can be either positive, negative, or zero. They are represented by the symbol Z and are written as:

Z = \{ \dots, -3, -2, -1, 0, 1, 2, 3, \dots \}

Positive integers: 1, 2, 3
Negative integers: -1, -2, -3
Zero: 0 (neither positive nor negative)

The addition of integers is based on the sign of the integers to be added.

Same Signs: If both integers have the same sign, add their absolute values, and the result takes the common sign.

(+a) + (+b) = + (a + b)
(-a) + (-b) = – (a + b)

For Example:

(+3) + (+5) = +8 (-4) + (-7) = -11

Different Signs: If the integers have different signs, subtract the smaller absolute value from the larger absolute value, and take the sign of the larger absolute value.

(+a) + (-b) = (+ \text{or} -)(a – b)

(+8) + (-5) = +3 (-9) + (+4) = -5

Properties of Addition of Integers

Some properties of addition of integers are:

Closure Property: The sum of any two integers is always an integer. Example: 3 + (-5) = -2
Commutative Property: Changing the order of the addends does not change the sum. Example: 4 + (-7) = -7 + 4 = -3.
Associative Property: The way in which integers are grouped does not affect their sum. Example: (2 + 3) + (-4) = 2 + (3 + (-4))
Additive Identity: Adding zero to any integer does not change its value. Example: 6 + 0 = 6

Subtracting an integer is the same as adding its opposite.

a – b = a + (-b)

7 – 4 = 7 + (-4) = 3 -3 – 5 = -3 + (-5) = -8

Properties of Subtraction of Integers

Some properties of subtraction of integers are:

Non-Commutative Property: Changing the order of the numbers changes the result. Example: 5 – 3 \neq 3 – 5 .
Subtraction as the Addition of the Opposite: Subtracting an integer is the same as adding its opposite. Example: 7 – 4 = 7 + (-4) = 3
Subtraction of Zero: Subtracting zero from an integer does not change its value. Example: 9 – 0 = 9

The table below represents the rules for adding and subtracting integers.

The addition and subtraction of integers on number line are given below.

Addition of Integers on a Number Line

Steps to add integers on number line.

To add a positive integer, move right.
To add a negative integer, move left.

Example: 2 + 3 = 5 (move 3 units right from 2).

Subtraction of Integers on a Number Line

Steps to subtract integers on number line.

To subtract a positive integer, move left.
To subtract a negative integer, move right.

Example: 4 – 6 = -2 (move 6 units left from 4).

Solved Examples on Addition and Subtraction of Integers

Example 1: Add integers 12 and 8.

(+12) + (+8) = +20 Since both integers are positive, we simply add them.

Example 2: Add Integers (+6) + (-9)

(+6) + (-9) = -3 Here, subtract 6 from 9, and since 9 has the larger absolute value and is negative, the result is -3

Example 3: Subtract Integers 10 – (-5)

10 – (-5) = 10 + 5 = 15 We change subtraction to addition and change the sign of -5 to +5

Example 4: Subtract: -7 – (-2)

-7 – (-2) = -7 + 2 = -5 Here, subtract 2 is the same as adding +2, which results in -5

Example 5: Solve (+14) – (+5) + (-8)

(+14) – (+5) + (-8) = 14 – 5 – 8 = 1 First, subtract 5 from 14 to get 9, then subtract 8, resulting in +1

Practice Problems

Q1. (-7) + (+12) =?

Q2. (+20) + (-13) =?

Q3. (-11) – (+6) =?

Q4. 18 – (-9) =?

Q5. (-22) + (+14) =?

Q6. (-4) – (-6) + (+2) =?

Q7. (+5) + (-10) – (-3) =?

(-7) + (+12) = +5
(+20) + (-13) = +7
(-11) – (+6) = -17
18 – (-9) = +27
(-22) + (+14) = -8
(-4) – (-6) + (+2) = +4
(+5) + (-10) – (-3) = -2

From the above discussion we can conclude that in addition of integers if both the integers have same sign, we add the integers, and the resultant sign is the sign of both the integers and if both the signs are different the subtract both integers and resultant sign is of the larger number sign. In subtraction of integers, we subtract both integers and the resultant sign is of larger integer.

Subtraction
Multiplication

FAQs on Addition and Subtraction of Integers

How to solve addition of integers.

To solve the addition of integers, use the rules: If the two int are positive, we add the absolute values of the two int and retain their like sign. Notice that the numbers differ in sign, subtract the sign to the number with the lesser absolute value from the number with the greatest absolute value while accepting the sign from the number bearing the greatest absolute value. Example: 5 + (-3) = 2

What is the rule for adding and subtracting integers?

There is no single formula, but the rules are as follows: For addition: a + b . For subtraction: a – b = a + (-b) .

What are 3 steps in subtraction of integers?

To make the subtraction equal to addition, replace the second integer with the + opposite. Add two integers, if they are both positive or if they are both negative, if one integer is positive and the other is negative subtract the second integer from the first integer. Simplify and write the final result of the equation below.

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PDF 7. Word PROBLEMS WITH INTEGERS
12. The temperature was -3o C last night. It is now -4o C. What was the change in temperature? 13. While watching a football game, Lin Chow decided to list yardage gained as positive integers and yardage lost as negative integers. After these plays, Lin recorded 14, -7, and 9.
Subtracting integers word problems
Solution The problem has 1 important component. It is the phrase "difference between high and low." Difference between high and low is the same as subtracting the smaller number from the bigger number. 104 - -18 = 104 + 18 = 122. The difference between high and low is 122 degrees Fahrenheit. More subtracting integers word problems Problem #2:
How to Solve Word Problems with Addition or Subtraction of Integers
The equation becomes: total candy = 47 + 32 + (51 - 19) Step 2: Solve for the unknown variable in the equation. First, let's perform the subtraction of 51 - 19 for Ellen's candy so that we just ...
How to Add and Subtract Integers: Word Problems
Here is a step-by-step guide to solving word problems of integers addition and subtraction: Step 1: Decipher the Problem. The journey begins with an intensive reading of the word problem. Identify the integers involved, noting their signs ($+$ or $-$), and the operations stated or implied (addition or subtraction).
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Integer Word Problems
Learn how to solve word problems involving addition, subtraction, multiplication, and division of integers with examples ... We use integers in our everyday life for counting money and measuring the speed of sound and light, height and weight of objects, temperature and pressure of the atmosphere, and depth of a sea. ... Solving word problems ...
Integers Worksheets
This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers. If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand.
Adding Integers Practice Problems With Answers
We simply add the absolute values of the integers then copy the common negative sign. There are more than two integers to add so we are going to add them two at a time. We will add the integers two at a time because there are more than two to add. \left [ {\left ( { - 7} \right) + \left ( { - 2} \right)} \right] + 5.
Integer Word Problems Worksheets
Integers are closed under the operations of addition and multiplication. Integer word problems worksheets provide a variety of word problems associated with the use and properties of integers. Benefits of Integers Word Problems Worksheets. We use integers in our day-to-day life like measuring temperature, sea level, and speed limit.
Integer Word Problems
Subtracting integers, however, involves an additional step. More specifically, any subtraction can be reinterpreted as an addition. To subtract an integer, add its opposite. For example, to subtract -3 from 5 (5 - -3), we add 3 to 5 (5 + 3), with the sum coming to 8. Real-life Examples of Addition and Subtraction Word Problems
PDF Adding Integers
You park in a garage 3 floors below ground level. Then you get. located? rise 525 feet and descend again 350 feet. Where are they currently. descends 1,500 feet beneath the surface of the water. They then. 5.) A research team aboard an underwater research vessel.
Subtracting Integers Practice Problems with Answers
The following ten (10) practice problems are all about subtracting integers. Keep practicing and you will get better in no time! Have fun! Note: To subtract integers, change the operation from subtraction to addition but take the opposite sign of the second integer. Then proceed with regular integer addition as usual.
7th Grade Math 1.4a, Add and Subtract Integers, Solving a ...
We can solve multi-step problems involving addition and subtraction of integers by using a problem-solving plan. We identify important information, decide wh...
Addition and Subtraction of Integers (Rules and Examples)
FAQs. Adding two positive integers results in positive integers, whereas adding two negative integers will result in the sum with a negative sign. But, the addition of two different signed integers will result in subtraction only and the sign of the result will be the same as the larger number has. See a few examples below: 2+2 = 4. 2 + (-2) = 0.
Integers: Word Problems On Integers involving operations
An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types of numbers including integers. Integers are a special group of numbers that do not have a fractional or a decimal part.
Master Integer Operations: Addition, Subtraction & Real ...
A2: To add three integers with different signs, first add the positive numbers together and the negative numbers together separately. Then, subtract the smaller sum from the larger sum. The result takes the sign of the larger sum. For example, to add 5, -3, and 2: Add positive numbers (5 + 2 = 7), then subtract the absolute value of the ...
Complete Addition and Subtraction Sentences with Integers
Grade 7 - The Number System. Standard - Find the missing number in addition and subtraction equations with integers. Included Skills: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are ...
APPLYING ADDITION AND SUBTRACTION OF INTEGERS
Applying Properties to Solve Problems. You can use properties of addition to solve problems involving integers. Example : Jack has a checking account. On Monday he writes a $160 check for groceries. Then he deposits $125. Finally he writes another check for $40. What was the total change in the amount in Jack's account ? Analyze Information :
PDF Mathematics 7 Unit 1: Integers
N06.04 Subtract two given integers, using concrete materials and/or pictorial representations, and record the process symbolically. N06.05 Illustrate the relationship between adding integers and subtracting integers. N06.06 Solve a given problem involving the addition and subtraction of integers.
PDF Planning Guide: Grade 7 Addition and Subtraction of Integers
• Illustrate the relations between adding integers and subtracting integers. • Solve a given problem involving the addition and subtraction of integers. Some sample behaviours to look for in relation to these indicators are suggested for many of the instructional activities in Step 3, Section C, Choosing Learning Activities.
Integer Word Problems Practice 0125
Integer Word Problems Practice Integer Word Problems Practice. jbaines Member for 3 years 1 month ... Country code: US. Country: United States. School subject: Math ... Integers (2012528) From worksheet author: Integer Word Problems. Loading ad... Share / Print Worksheet. Google Classroom
Solving Word Problems involving Addition and Subtraction of numbers
This is a fantastic bundle which includes everything you need to know about Solving Word Problems Involving Addition and Subtraction of Numbers within 120 across 15+ in-depth pages. These are ready-to-use Common core aligned Grade 1 Math worksheets. Each ready to use worksheet collection includes 10 activities and an answer guide.
Addition Practice Questions
The Corbettmaths Practice Questions and Answers on Addition. Next: Changing the Subject (advanced) Practice Questions
Addition and Subtraction of Integers
To solve the addition of integers, use the rules: If the two int are positive, we add the absolute values of the two int and retain their like sign. Notice that the numbers differ in sign, subtract the sign to the number with the lesser absolute value from the number with the greatest absolute value while accepting the sign from the number ...

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How to Add and Subtract Integers: Word Problems

A Step-by-step Guide to Solve Integers Addition and Subtraction: Word Problems

Step 1: Decipher the Problem

Step 2: Pinpoint the Unknowns

Step 3: Translate into Mathematical Language

Step 4: Construct the Equation(s)

Step 5: Resolve the Equation(s)

Step 6: Validate Your Solution

Step 7: Answer the Query

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Adding and Subtracting Integers

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Integers: Word Problems On Integers

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