problem solving of integers with answers

Math Problems and Solutions on Integers

Problems related to integer numbers in mathematics are presented along with their solutions.

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.

☛ Check Grade wise Integers Word Problems Worksheets

• 6th Grade Integers Worksheets
• Integers Worksheets for Grade 7
• 8th Grade Integers Worksheets

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

Integer Resources

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

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

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

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

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

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Integer Word Problems

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3.E: Integers (Exercises)

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3.1 - Introduction to Integers

Locate positive and negative numbers on the number line.

In the following exercises, locate and label the integer on the number line.

Order Positive and Negative Numbers

In the following exercises, order each of the following pairs of numbers, using < or >.

• −6__3
• −5__−10
• −9__−4
• 2__−7
• −3__1

Find Opposites

In the following exercises, find the opposite of each number.

In the following exercises, simplify.

• (a) −(8) (b) −(−8)
• (a) −(9) (b) −(−9)

In the following exercises, evaluate.

• −x, when (a) x = 32 (b) x = −32
• −n, when (a) n = 20 (b) n = −20

Simplify Absolute Values

• |−21|
• |−42|
• −|15|
• −|−75|
• |x| when x = −14
• −|r| when r = 27
• −|−y| when y = 33
• |−n| when n = −4

In the following exercises, fill in <, >, or = for each of the following pairs of numbers.

• −|−4|__4
• −2__|−2|
• −|−6|__−6
• −|−9|__|−9|
• −(−55) and − |−55|
• −(−48) and − |−48|
• |12 − 5|
• 6|−9|
• |14−8| − |−2|
• |9 − 3| − |5 − 12|
• 5 + 4|15 − 3|

Translate Phrases to Expressions with Integers

In the following exercises, translate each of the following phrases into expressions with positive or negative numbers.

• the opposite of 16
• the opposite of −8
• 19 minus negative 12
• a temperature of 10 below zero
• an elevation of 85 feet below sea level

3.2 - Add Integers

Model addition of integers.

In the following exercises, model the following to find the sum.

• −2 + 6
• 5 + (−4)
• −3 + (−6)

Simplify Expressions with Integers

In the following exercises, simplify each expression.

• −33 + (−67)
• −75 + 25
• 54 + (−28)
• 11 + (−15) + 3
• −19 + (−42) + 12
• −3 + 6(−1 + 5)
• 10 + 4(−3 + 7)

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

• n + 4 when (a) n = −1 (b) n = −20
• x + (−9) when (a) x = 3 (b) x = −3
• (x + y) 3 when x = −4, y = 1
• (u + v) 2 when u = −4, v = 11

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

• the sum of −8 and 2
• 4 more than −12
• 10 more than the sum of −5 and −6
• the sum of 3 and −5, increased by 18

Add Integers in Applications

In the following exercises, solve.

• Temperature On Monday, the high temperature in Denver was −4 degrees. Tuesday’s high temperature was 20 degrees more. What was the high temperature on Tuesday?
• Credit Frida owed $75 on her credit card. Then she charged $21 more. What was her new balance?

3.3 - Subtract Integers

Model subtraction of integers.

In the following exercises, model the following.

• 6 − 1
• −4 − (−3)
• 2 − (−5)
• −1 − 4
• 24 − 16
• 19 − (−9)
• −31 − 7
• −40 − (−11)
• −52 − (−17) − 23
• 25 − (−3 − 9)
• (1 − 7) − (3 − 8)
• 3 2 − 7 2
• x − 7 when (a) x = 5 (b) x = −4
• 10 − y when (a) y = 15 (b) y = −16
• 2n 2 − n + 5 when n = −4
• −15 − 3u 2 when u = −5

Translate Phrases to Algebraic Expressions

• the difference of −12 and 5
• subtract 23 from −50

Subtract Integers in Applications

In the following exercises, solve the given applications.

• Temperature One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. What was the afternoon temperature?
• Temperature On January 4, the high temperature in Laredo, Texas was 78 degrees, and the high in Houlton, Maine was −28 degrees. What was the difference in temperature of Laredo and Houlton?

3.4 - Multiply and Divide Integers

Multiply integers.

In the following exercises, multiply.

• −9 • 4
• 5(−7)
• (−11)(−11)
• −1 • 6

Divide Integers

In the following exercises, divide.

• 56 ÷ (−8)
• −120 ÷ (−6)
• −96 ÷ 12
• 96 ÷ (−16)
• 45 ÷ (−1)
• −162 ÷ (−1)
• 5(−9) − 3(−12)
• (−2) 5
• (−3)(4)(−5)(−6)
• 42 − 4(6 − 9)
• (8 − 15)(9 − 3)
• −2(−18) ÷ 9
• 45 ÷ (−3) − 12
• 7x − 3 when x = −9
• 16 − 2n when n = −8
• 5a + 8b when a = −2, b = −6
• x 2 + 5x + 4 when x = −3

In the following exercises, translate to an algebraic expression and simplify if possible.

• the product of −12 and 6
• the quotient of 3 and the sum of −7 and s

3.5 - Solve Equations using Integers; The Division Property of Equality

Determine whether a number is a solution of an equation.

In the following exercises, determine whether each number is a solution of the given equation.

• x = −9
• x = −5
• u = −7
• u = −1

Using the Addition and Subtraction Properties of Equality

• b − 9 = −15
• c + (−10) = −17
• d − (−6) = −26

Model the Division Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.

Solve Equations Using the Division Property of Equality

In the following exercises, solve each equation using the division property of equality and check the solution.

• −12q = 48
• −16r = −64
• −5s = −100

Translate to an Equation and Solve.

In the following exercises, translate and solve.

• The product of −6 and y is −42
• The difference of z and −13 is −18.
• Four more than m is −48.
• The product of −21 and n is 63.

Everyday Math

• Describe how you have used two topics from this chapter in your life outside of your math class during the past month.

PRACTICE TEST

• Locate and label 0, 2, −4, and −1 on a number line.

In the following exercises, compare the numbers, using < or > or =.

• (a) −6__3 (b) −1__−4
• (a) −5__|−5| (b) −|−2|__−2
• (a) −7 (b) 8
• −(−22)
• |4 − 9|
• −8 + 6
• −15 + (−12)
• −7 − (−3)
• 10 − (5 − 6)
• −3 • 8
• −6(−9)
• 70 ÷ (−7)
• (−2) 3
• 16−3(5−7)
• |21 − 6| − |−8|
• 35 − a when a = −4
• (−2r) 2 when r = 3
• 3m − 2n when m = 6, n = −8
• −|−y| when y = 17

In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible.

• the difference of −7 and −4
• the quotient of 25 and the sum of m and n.
• Early one morning, the temperature in Syracuse was −8°F. By noon, it had risen 12°. What was the temperature at noon?
• Collette owed $128 on her credit card. Then she charged $65. What was her new balance?
• p − 11 = −4
• −9r = −54
• The product of 15 and x is 75.
• Eight less than y is −32.

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Integer Word Problems

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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• Word Problems On Integers

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.

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• Word Problems on Integers

Understanding Integers

For solving integer word problems students need the right base of knowledge on integers. Proper practice is required for solving integer questions correctly. In this article, we will help students develop the base required for answering word problems on integers for Class 7.

Let’s start with the fact that an arithmetic operation is an elementary branch of mathematics. Arithmetic operations are subtraction, addition, division, and multiplication. These arithmetic operations are used for solving integer problems. There are also other types of numbers that can be solved with the help of arithmetic operations.

It should also be noted that integers are a special group that does not contain any decimal or fractional part. Integers include positive numbers, negative numbers, and zero . Also, arithmetic operations on integers are similar to whole numbers .

It also makes it a little confusing to solve word problems on integers for class 6 and word problems on integers for class 7 pdf because there are both positive and negative numbers. This is also why integers are different from whole numbers.

Integers can also be plotted on a number line. A number line might also be used by students when learning how to solve integers questions. These types of questions are more common when it comes to integers word problems Class 7. If you have never seen a number line, then an image of a number line is attached below.

Rules of Integers 

There are several rules that students need for learning how to solve integer word problems. Some of those rules are mentioned below.

The sum of any two positive integers will result in an integer.

The sum of any two negative integers is an integer.

The product of two positive integers will give an integer.

The product of two negative integers will be given an integer.

The sum of any integer and its inverse will be equal to zero.

The product of an integer and its reciprocal will be equal to 1.

Now, let’s look at addition, multiplication, subtraction, and division of signed integer numbers. This will help students to work on story problems with integers answer key.

The Addition of Signed Integer Numbers

As mentioned above, if we add two integers with the same sign, then we have to add the absolute value along with the sign that was provided with the number. For example, (+4) + (+7) = +11 and (-6) + (-4) = -10.

Also, if we add two integers with different signs, then we have to subtract the absolute values and write down the difference. This should be done with the sign of the number that has the largest absolute value. For example, (-4) + (+2) = -2 and (+6) + (-4) = +2.

Subtraction of Signed Integer Numbers

If a student wants to solve integer example problems, then he or she needs to know that while subtracting two integers, we have to change the sign of the second number. The second number should be subtracted and the rules of addition should also be followed. For example, (-7) - (+4) = (-7) + (-4) = -11 and (+8) - (+3) = (+8) + (-3) = +5.

Multiplication and Division of Signed Integer Numbers

When it comes to working on integer word problems with solutions of multiplying and dividing two integer numbers, then the rules are quite straightforward. If both the integers have the same sign, then the final results are positive. If the integers have different signs, then the final result is negative. For example, (+2) x (+3) = +6, (+3) x (-4) = -12, (+6) / (+2) = +3, and (-16) / (+4) = -4.

Properties of Integers

Students should also be familiar with the properties of integers if they want to work on integer word problems grade 6 with solutions. Some of those properties of integers are:

Closure property

Associative property

Commutative property

Distributive property

Additive inverse property

Multiplicative inverse property

Identity property

We also need to look at these properties in detail for solving integer problems in 6th grade. Let’s move on to that discussion.

Closure Property:

According to the closure property of integers, if two integers are added or multiplied together, the final result will be an integer only. This means that if a and b are integers, then:

a + b = integer

a x b = integer

For example, 2 + 5 = 7, which is an integer, and 2 x 5 = 10, which is also an integer.

Commutative Property:

According to this property, if a and b are two integers, then a + b = b + a and a x b = b x a. For example, 3 + 8 = 8 x 3 = 24 and 3 + 8 = 8 + 3 = 11. It should be noted that this property is not followed in the case of subtraction and division.

According to the associative property, if a, b, and c are integers, then:

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

For example, 2 + (3 + 4) = (2 + 3) + 4 = 9 and 2 x (3 x 4) = (2 x 3) x 4 = 24.

This property is only valid when it comes to addition and multiplication.

Distributive Property:

The distributive property states that if a, b, and c are integers, then a x (b + c) = a x b + a x c. For example, if we have to prove that 3 x (5 +1) = 3 x 5 + 3 x 1, then we should be start by finding:

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

Since, LHS = RHS

This proves our example.

Additive Inverse Property:

This additive inverse property states that if a is an integer, then a + (-a) = 0. This means that-a is the additive inverse of integer a.

Multiplicative Inverse Property:

The multiplicative inverse property states that if a is an integer, then a x (1 / a) = 1. This  means that 1 / a is the multiplicative inverse of integer a.

Identity Property of Integers:

The identity property of integers states that a + 0 = a and a x 1 = a. For example, 4 + 0 = 4 and 4 x 1 = 4.

Types of Integers

Earlier, we mentioned that there are three types of integers. In this section, we will look at these types of integers in more depth. The list of those types of integers is mentioned below.

Zero can be characterized as neither a positive nor a negative integer. It can be best defined as a neutral number. This also refers to the fact that zero has no sign (+ or -).

Positive Integers:

As the name indicates, positive integers are those numbers that are positive in their nature. These numbers are represented by a positive or plus (+) sign. The positive integers lie on the right side of the zero on the number line. This also means that all positive integers are greater than zero. For example, 122, 54, and 9087268292.

Negative Integers:

Negative integers, on the other hand, are numbers that are represented by a minus (-) or negative sign. These numbers are present on the left side of the zero on a number line. For example, -182, -8292, and -2927225.

Fun Facts About Integers

The word integer comes from the Latin word “ integer ” which literally means whole. 

You might find it interesting to note that integers are not just simple numbers on paper. Instead, these numbers have real-life applications! Both positive and negative integers are used to symbolize two contradicting situations in the real world. For example, if the temperature is above zero, then positive integers are used for denoting the temperature. But if the temperature is less than zero, then negative integers are used for denoting the temperature.

Integers can also help an individual in comparing and measuring two things like how small or big or few or more things are. These integers help in quantifying things. For example, in games like cricket and soccer, integers are used for keeping a track of scores. Movies and songs can also be rated by using integers!

FAQs on Word Problems on Integers

1. What are integers and what is their importance? 

An integer is usually defined as a number that can be written without any type of fractional component. These numbers tend to consist of zero, positive natural numbers or whole numbers, and their additive inverses. For example, 2, -56, 98, -302, etc. A set of integers is always denoted by the letter “Z”. 

The concept of integers is quite an important one to learn in mathematics. This is mainly because integers tend to help us compute the efficiency in both negative as well as positive numbers in a wide range of fields. They also help us to facilitate a number of calculations that are imperative to our daily lives. For example, we use integers to describe the temperature above or below the freezing point, to debit or credit money, etc. 

2. What are the rules for adding and subtracting integers?

There are some rules to be noted while adding two or more integers. They are as follows: 

The sum of an integer and its additive inverse is always zero. 

When you add two positive integers, the result will always be a positive number which will be greater than the two integers. 

When you add two negative integers, the result will always be a negative number which will be smaller than the two integers you added.

By finding the difference between the absolute value of a positive integer and a negative one, you can add both of them. And the sign of the greater number out of the two will be attached to the end product. 

When you add an integer with zero, you will get the same number as the answer. 

There are some rules to be noted while subtracting two or more integers. They are as follows: 

When you subtract any integer from zero, the answer will be either the additive inverse or the opposite of the integer. And when you subtract zero from any integer, then the result will always be the integer itself. 

If you want to subtract two integers that have the same sign, you ought to perform a subtraction operation on the absolute values of those numbers. 

If you want to subtract two integers that have different signs, you ought to add the absolute values. 

3. State the principles that the addition and subtraction of integers on a number line is based on. 

The principles upon which the addition of integers on a number line is based are as follows: 

Moving towards the right or the positive side of the number line will lead to the addition of a positive integer. 

Moving towards the left or the negative side of the number line will lead to the addition of a negative integer. 

Any of the integers can be taken as the base point (the point from where you start to move on the number line). 

The principles upon which the subtraction of integers on a number line is based are as follows: 

Every subtraction fact can also be written as an addition fact. 

Moving towards the left or the negative side of the number line will lead to the subtraction of a positive integer. 

Moving towards the right or the positive side of the number line will lead to the subtraction of a negative integer. 

4. Is multiplying rational numbers just like multiplying integers? If so, how?

To a certain extent, multiplying rational numbers is just like multiplying integers because the rules that are applicable to the latter, are also the same for the former. Rational numbers are just numbers that can be written in the fraction form of two given integers. So, if both the divisor and the dividend have the same signs, then the quotient will be positive. And if the divisor and the dividend have different signs, then the quotient will be negative. 

5. Can integers be decimals?

No. Just like whole numbers, integers can neither be fractions, nor can they be decimals. All integers can be expressed as a decimal, however, most of the numbers that are decimals cannot be expressed as integers. If there are any digits after the decimal point, and all of them are zeroes, only then can the number be identified as an integer. 

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