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 -99 to 99 (50 Questions; All Parentheses)

Integer Resources

lesson 4 homework practice divide 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

lesson 4 homework practice divide 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

lesson 4 homework practice divide 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

lesson 4 homework practice divide 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

lesson 4 homework practice divide 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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Integers: Multiplication and Division Worksheets

This page contains printable worksheets which emphasize integer multiplication and division to 6th grade, 7th grade, and 8th grade students. Practice pages here contain exercises on multiplication squares, in-out boxes, evaluating expressions, filling in missing integers, and more. Procure some of these worksheets for free!

Multiplying Integers

Multiplication of Integers

Multiplication of Integers

Multiply the integers to find the product. A total of 48 problems are given in these integer worksheets for practice.

  • Download the set

Multiplication Squares | 2x2

Multiplication Squares | 2x2

Conceptualize the fundamentals of multiplying integers with this bath of interesting 2x2 squares. Multiply the integers in the rows and columns and write the products in the squares.

Multiplication Squares | 3x3

Multiplication Squares | 3x3

Get students to multiply the positive and negative numbers in each row and column and fill in the empty boxes in each 3x3 square.

Multiplying 3 or 4 Integers

Multiplying 3 or 4 Integers

Find the product of the integers. Apply the multiplication sign rule. Each worksheet consists of ten problems.

Integer Multiplication Table

Integer Multiplication Table

Practice multiplying integers from -10 to +10 with this super simple table. Apply the rules where products turn positive when integers with similar signs are multiplied and negative with differing signs. Get ready to master integer multiplication effortlessly!

Dividing Integers

Integer Division

Integer Division

Perform the division operation on the integers to find the quotient in these three pdf worksheets.

Multiplying and Dividing Integers - Mixed

Multiplying and Dividing Integers

Multiplying and Dividing Integers

Simplify the integer equations by performing multiplication and division operations.

Missing Integers: Multiplication and Division

Missing Integers: Multiplication and Division

Find the missing integer in each equation. There are 16 problems in each worksheet.

In-and-Out boxes: Multiply and Divide

In-and-Out boxes: Multiply and Divide

Fill in the in-and-out boxes according to the rule mentioned in each problem. There are six rules given in each worksheet.

Evaluate: Multiply and Divide

Evaluate: Multiply and Divide

Evaluate the expressions by substituting the values in the variables. Each printable worksheet for grade 7 and grade 8 contains four problems with three expressions each.

Multiplication Chart

Integer Multiplication Charts | Display Charts

Integer Multiplication Charts | Display Charts

Designed to assist 6th grade students with multiplication of integers, this array of charts focuses on multiplication of integers from -5 to +5 and -10 to +10. Explore these visual aids and comprehend the two rules of multiplication of integers.

Related Worksheets

» Adding and Subtracting Integers

» Comparing and Ordering Integers

» Integers on a Number Line

» Multiplication and Division Fact Family

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Division of integers

Integers Workbook

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Negative numbers & division

Division of or by negative numbers can be conceptually difficult; these integer worksheets provide extra practice in both normal and long division form .

lesson 4 homework practice divide integers

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Long division:

lesson 4 homework practice divide integers

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Division of Integers Exercises

Dividing integers practice problems with answers.

There are ten (10) practice questions below about dividing integers . Keep practicing until you master the skill! Good luck!

For your convenience, I included a summary on how to divide integers. The main idea is that if you divide two integers with the same sign , the answer is positive . However, if the signs of the two integers are different , the answer is negative .

rules for dividing integers or integer divisions the quotient of two integers is always positive if the signs are the same. if their signs are different then the quotient is negative.

Problem 1: Divide the integers: [latex]21 \div 7[/latex]

[latex]3[/latex]

Problem 2: Divide the integers: [latex]\left( { – 42} \right) \div 6[/latex]

[latex]-7[/latex]

Problem 3: Divide the integers: [latex]36 \div \left( { – 4} \right)[/latex]

[latex]-9[/latex]

Problem 4: Divide the integers: [latex]\left( { – 54} \right) \div \left( { – 9} \right)[/latex]

[latex]6[/latex]

Problem 5: Divide the integers: [latex]\left( { – 144} \right) \div 6[/latex]

[latex]-24[/latex]

Problem 6: Divide the integers: [latex]\left( { – 19} \right) \div \left( { – 19} \right)[/latex]

[latex]1[/latex]

Problem 7: Divide the integers: [latex]132 \div 12[/latex]

[latex]11[/latex]

Problem 8: Divide the integers: [latex]189 \div \left( { – 9} \right) \div \left( { – 7} \right)[/latex]

Problem 9: Divide the integers: [latex]120 \div \left( { – 2} \right) \div 5[/latex]

[latex]-12[/latex]

Problem 10: Divide the integers: [latex]\left( { – 96} \right) \div \left( { – 4} \right) \div \left( { – 6} \right)[/latex]

[latex]-4[/latex]

You might also like these tutorials:

  • Dividing Integers

Division of Integers

Related Topics: Lesson Plans and Worksheets for Grade 7 Lesson Plans and Worksheets for all Grades More Lessons for Grade 7 Common Core For Grade 7

Examples, videos, and solutions to help Grade 7 students recognize that division is the reverse process of multiplication, and that integers can be divided provided the divisor is not zero.

New York State Common Core Math Grade 7, Module 2, Lesson 12

Worksheets for Grade 7

Lesson 12 Student Outcomes

  • Students recognize that division is the reverse process of multiplication, and that integers can be divided provided the divisor is not zero.
  • Students understand that every quotient of integers (with a non-zero divisor) is a rational number and divide signed numbers by dividing their absolute values to get the absolute value of the quotient. The quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs.

Lesson 12 Summary

  • The rules for dividing integers are similar to the rules for multiplying integers (when the divisor is not zero). The quotient is positive if the divisor and dividend have the same signs, and negative if they have opposite signs. The quotient of any 2 integers (with a non-zero divisor) will be a rational number.

NYS Math Module 2 Grade 7 Lesson 12 Classwork

Exercise 1: Recalling the Relationship Between Multiplication and Division a. List examples of division problems that produced a quotient that is a negative number. b. If the quotient is a negative number, what must be true about the signs of the dividend and divisor? c. List your examples of division problems that produced a quotient that is a positive number. d. If the quotient is a positive number, what must be true about the signs of the dividend and divisor?

Rules for Dividing Two Integers:

  • A quotient is negative if the divisor and the dividend have _____ signs.
  • A quotient is positive if the divisor and the dividend have ____ signs.

Exercise 2: Is the Quotient of Two Integers Always an Integer Is the quotient of two integers always an integer? Use the work space below to create quotients of integers. Answer the question and use examples or a counterexample to support your claim. Conclusion: Every quotient of two integers is always a rational number, but not always an integer.

Exercise 3: Different Representation of the Same Quotient Are the answers to the three quotients below the same or different? Why or why not? a) -14 ÷ 7 b) 14 ÷ -7 c) -(14 ÷ 7)

Exercise 4: Fact Fluency—Integer Division

Lesson 12 Problem Set

  • Find the missing values in each column:

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lesson 4 homework practice divide integers

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Multiplying and dividing integers

Here you will learn strategies on how to multiply and divide integers, including using visual models as well as using the number line.

Students will first learn about integers in 6th grade math as part of their work with the number system and expand that knowledge to operations with integers in the 7th grade.

What are multiplying and dividing integers?

Multiplying and dividing integers is when you multiply or divide two or more integers together to give a product or quotient that can be either positive or negative.

You can multiply and divide integers using visual models or a rule.

Multiplying and Dividing Integers image 1.1

Do you notice a pattern or rule?

Rule for multiplying integers:

  • If the integers have the same sign , the product will be positive .
  • If the integers have different signs , the product will be negative . Multiply the absolute values and make the answer negative.

Rule for dividing integers:

  • If the integers have the same sign , the quotient will be positive .
  • If the integers have different signs , the quotient will be negative . Divide the absolute values and make the answer negative.

What are multiplying and dividing integers?

Common Core State Standards

How does this apply to 6th grade math and 7th grade math?

  • Grade 6: Number System (6.NS.C.6) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
  • Grade 7: Number System (7.NS.A.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

[FREE] Multiplication and Division Check for Understanding (Grade 4, 5 and 7)

[FREE] Multiplication and Division Check for Understanding (Grade 4, 5 and 7)

Use this quiz to check your grade 4, 5 and 7 students’ understanding of multiplication and division. 10+ questions with answers covering a range of 4, 5 and 7 grade multiplication and division topics to identify areas of strength and support!

How to multiply and divide integers?

In order to add and subtract integers using counters:

  • If the integers have the same sign, the product or quotient is positive.  If not, go to step 2.

If the integers have different signs, the product or quotient is negative.

Find the product or quotient.

Multiplying and dividing integers examples

Example 1: multiplying integers with the same sign.

Multiply: (-4) \times(-12)= \, ?

  • If the integers have the same sign, the product or quotient is positive. If they don’t go to step 2. 

-4 and -12 have the same sign so the product is positive.

2 If the integers have different signs, the product or quotient is negative.

Integers have the same sign.

3 Find the product or quotient.

(-4) \times(-12)=48

Example 2: multiplying integers with different signs

Multiply: (-13) \times 8= \, ?

If the integers have the same sign, the product or quotient is positive.  If not, go to step 2.

-13 and 8 do not have the same sign.

The integers have different signs so the product is negative.

Find the product or the quotient.

(-13) \times 8=-104

Example 3: dividing integers with the same sign

Divide: \cfrac{(-18)}{(-3)}= \, ?

-18 and -3 have the same sign so the quotient will be positive.

\cfrac{(-18)}{(-3)}=6

Example 4: dividing integers with different signs

Divide: -120 \div 3= \, ?

-120 and 3 do not have the same sign.

-120 and 3 have different signs so the quotient will be negative.

-120 \div 3=-40

Example 5: multiplying integers word problem

From sea level, a submarine descends 25 \, ft. per minute (-25 \, ft.).

After 6 minutes, the submarine’s distance can be modeled by (-25) \times 6 = \, d , where d is the submarine in relation to sea level.

How far below sea level is the submarine?

-25 and 6 do not have the same sign.

-25 and 6 have different signs so the product will be negative.

-25 \times 6=-150

Because the submarine is descending, after 6 minutes it will be 150 feet below sea level.

Example 6: dividing integer word problems

On a certain winter day, the temperature changed at a rate of -4 degrees Fahrenheit per hour.

After a specific amount of time, the change in temperature was -36 degrees Fahrenheit, which is modeled by (-36) \div (-4) = \, h, where h represents the amount of hours.

How long did it take for the change in temperature to be -36 degrees Fahrenheit?

-36 and -4 have the same sign so the quotient is positive.

The integers have the same sign.

(-36) \div(-4)=9

Teaching tips for multiplying and dividing integers

  • Multiplying and dividing integers are foundational skills for Algebra 1. Using manipulatives helps students formulate conceptual understanding.
  • Have students identify the patterns with multiplying and dividing integers so that they can figure out the rules on their own.
  • Although practice integer worksheets have their place, have students practice problems through digital games or scavenger hunts around the room to make it engaging.
  • Reinforce essential vocabulary such as dividend, divisor, quotient, factors,  and product.

Easy mistakes to make

  • Mixing up the rules for multiplication and division For example, when multiplying integers with the same sign, you get a negative product, and when dividing integers with the same sign, you get a negative quotient.
  • Mixing up the rules of multiplication and division with addition and subtraction For example, applying the rule of addition of integers to (15) \div(-3)=5 where the absolute value of 15 is greater than the absolute value of 3 so the answer must be positive.

Related multiplication and division lessons

This multiplying and dividing integers topic guide is part of our series on multiplication and division. You may find it helpful to start with the main multiplication and division topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

  • Multiplication and division
  • Multiplication
  • Multiplying multi-digit numbers
  • Long division
  • Negative numbers
  • Negative times negative
  • Multiplying and dividing rational numbers
  • Dividing multi-digit numbers
  • Multiplicative comparison

Practice multiplying and dividing integers

1. Multiply: (6) \times(-2)=\text { ? }

GCSE Quiz False

Using the rule for multiplying integers, 6 and -2 have different signs, so the product is negative.

(6) \times(-2)=-12

You can check your answer with counters.

6 groups of -2 counters is -12 counters

Multiplying and Dividing Integers practice 1

2. Multiply: (-15) \times(-3)= \text { ? }

Using the rule for multiplying integers, -15 and -3 have the same sign, so the product is positive.

(-15) \times(-3)=45

3. Divide: (-52) \div(4)= \text { ? }

Using the rule for dividing integers, -52 and 4 have different signs, so the quotient is negative.

(-52) \div(4)=-13

4. Divide: \cfrac{(-72)}{(-9)}= \text { ? }

Using the rule for dividing integers, -72 and -9 have the same sign, so the quotient is positive.

\cfrac{(-72)}{(-9)}=8

5. Multiply: (-190) \times(-10)= \text { ? }

Using the rule for multiplying integers, -190 and -10 have the same sign, so the product is positive.

(-190) \times(-10)=1900

6. A deep sea diver descends at a rate of 10 feet per minute below sea level. The diver descends at this rate for 8 minutes, which can be modeled by 8 \times (-10) = d, where d is how far the diver is below sea level. After 8 minutes, how far did the diver descend?

Using the rule, the signs of the numbers are different, so the product is negative.

8 \times(-10)=-80

The diver descended to -80 feet.

Multiplying and dividing integers FAQs

Multiplying and Dividing Integers FAQS image 1

When it comes to sets of numbers, whole numbers are 0 and positive whole numbers. The set of integers includes all negative whole numbers, 0, and all positive whole numbers.

Multiplication and division of integers help when simplifying algebraic expressions and solving equations.

Yes, positive numbers are to the right of 0 and negative numbers are to the left of 0.

The positive sign does not necessarily need to be written in front of a number. For example, +5 is the same as 5. The positive sign is understood.

The next lessons are

  • Types of numbers
  • Rounding numbers
  • Factors and multiples

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Multiplying and Dividing Integers Lesson Plan

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Multiplying and Dividing Integers Guided Notes & Doodles | Color by Code Lesson

Multiplying and Dividing Integers Guided Notes & Doodles | Color by Code Lesson

Multiplying and Dividing Integers Lesson Plan

Ever wondered how to teach multiplying and dividing integers in an engaging way to your 7th and 8th grade math students?

In this lesson plan, students will learn about integer multiplication and division and their real-life applications. Through artistic, interactive guided notes, checks for understanding, a doodle and color by number activity, and a maze worksheet, students will gain a comprehensive understanding of multiplying and dividing integers.

The lesson culminates with a real-life example that explores how this math concept can be applied to predicting future cost or revenues.

  • Standards : CCSS 7.NS.A.2 , CCSS 7.NS.A.2.a , CCSS 7.NS.A.2.b , CCSS 7.NS.A.2.c
  • Topic : Integers & Rational Numbers
  • Grade : 7th Grade
  • Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to:

Multiply integers, both positive and negative

Divide integers, both positive and negative

Apply multiplication and division of integers to solve real-life problems

Prerequisites

Before this lesson, students should be familiar with:

Understanding of what positive and negative integers are

Multiplying and dividing whole numbers

Colored pencils or markers

Multiplying and Dividing Integers Guided Notes

Key Vocabulary

Multiplication

Introduction

Introduction image

As a hook, ask students why it is important to understand how to multiply and divide integers in real-life situations. You can provide examples such as calculating gains or losses in financial transactions, or finding the total cost of purchases. Refer to the last page of the guided notes as well as the FAQs below for more ideas.

Use the first page of the guided notes to introduce the concept of multiplying integers. Walk through the key points of multiplying positive and negative integers, emphasizing the rules and patterns involved. Explain the concept of a positive number times a positive number resulting in a positive product, a negative number times a negative number resulting in a positive product, and a positive number times a negative number resulting in a negative product. Use examples and visual representations to reinforce the concept. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Use the second page of the guided notes to introduce the concept of dividing integers. Walk through the key points of dividing positive and negative integers, highlighting the rules and patterns. Emphasize the concept of a positive number divided by a positive number resulting in a positive quotient, a negative number divided by a negative number resulting in a positive quotient, and a positive number divided by a negative number resulting in a negative quotient. Provide examples and visual aids to help students grasp the concept. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Practice multiplying and dividing integers image

Have students practice multiplying and dividing integers using the maze activity. Walk around to answer student questions.

Fast finishers can dive into the color by number activity for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

real life application of multiplying and dividing integers

Bring the class back together, and introduce the concept of predicting future cost or revenues using multiplying and dividing integers. Explain that this concept can be applied in real life situations such as budget planning and financial projects.

To illustrate this concept, provide the students with a scenario. For example, imagine a local business owner who wants to predict their future monthly revenue based on their past performance.

Ask the students to think about what factors could affect the business's revenue. Discuss with the class possible factors such as seasonality, economic conditions, marketing efforts, and customer trends. Next, explain that the business owner has collected data on their monthly revenue over the past year and wants to use this data to forecast their revenue for the next year.

Using the guided notes and the concepts they have learned about multiplying and dividing integers, instruct the students to brainstorm other scenarios in real life where multiplying and dividing integers can be used.

Finally, facilitate a class discussion on how the business owner could use this forecasted revenue to make informed decisions about budgeting, marketing strategies, and resource allocation. Encourage the students to think critically about the importance of understanding and applying integer operations in real-life situations.

Refer to the FAQ section of the lesson plan for more ideas and examples on how to teach real-life applications of multiplying and dividing integers.

Additional Self-Checking Digital Practice

If you’re looking for digital practice for multiplying and dividing integers, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are 2 activities for you to explore:

Multiplying and Dividing Integers Digital Pixel Art

Multiplying and Dividing Integers (Minecraft themed)

What are integers? Open

Integers are whole numbers that can be positive, negative, or zero. They do not have any fractional or decimal parts.

How do you multiply integers? Open

To multiply integers, you multiply the numbers as usual but pay attention to the signs. If the signs are the same (both positive or both negative), the product is positive. If the signs are different, the product is negative.

How do you divide integers? Open

To divide integers, divide the numbers as usual but again, pay attention to the signs. If the signs are the same, the quotient is positive. If the signs are different, the quotient is negative.

Can you give an example of multiplying positive and negative integers? Open

Sure! For example, if you multiply 3 and -4, since the signs are different, the product is negative. Therefore, 3 times -4 equals -12.

How can I practice multiplying and dividing integers? Open

You can practice multiplying and dividing integers by using the worksheets and color by code activity included in the Multiplying and Dividing Integers Guided Notes & Doodles resource. These activities provide opportunities to apply the concepts and strengthen your skills.

How are integers used in real life? Open

Integers are used in a variety of real-life situations. For example, they can be used to represent temperatures above and below zero, gains and losses in money, and positions on a number line.

Can I use this resource for different grade levels? Open

The Multiplying and Dividing Integers Guided Notes & Doodles resource is designed for 7th and 8th-grade students (or advanced 6th grade). However, it can also be used for reteaching or reviewing the topic for other grade levels.

Is there an answer key provided for the worksheets? Open

Yes, there is an answer key included in the resource for all of the worksheets. It will help you check your work and provide a better understanding of the concepts.

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Division of Integers Worksheets

We have previously learned to divide whole numbers that had positive values at a large scale. In this section we explore how to work this same operation with integers that may have positive and/or negative values. This is not as difficult as it sounds. The basic structure and function of the math is the same, the signed value is where most of our focus lies on this topic. There are three rules that we need to focus on here and have down pat. If you need a refresher on how to perform operations either check the lesson just below or the full tutorial that we have created for you on the bottom of this page.

Aligned Standard: Grade 7 Number Systems - 7.NS.A.2b

  • Negative Division Step-by-step Lesson - Divide two negatives and work on a cookie based word problem.
  • Guided Lesson - We align division problems for you in many different ways. See if you fit that cake into containers.
  • Guided Lesson Explanation - The cake calculation is something I find myself doing at dinner time almost everyday. Just not with cake.
  • Practice Worksheet - We arrange these problems in every way imaginable and throw in a few word problems to boot.
  • Multiplying and Dividing Integers Five Worksheet Pack - Complete the problems by plugging in the missing numbers.
  • Matching Worksheet - The threes might throw your students here. This one may not be an easy "A" for them.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

We hit these from all levels: straight division, word problems, and implied division.

  • Homework 1 - There are certain rules for dividing integers. We will explore the two core rules over this series of homework sheets.
  • Homework 2 - Rule 1: The quotient of a positive integer and a negative integer or vice versa is a negative integer.
  • Homework 3 - Rule 2: The quotient of two negative integers or two positive integers is a positive integer.

Practice Worksheets

Why not throw a little fraction division in there too!

  • Practice 1 - Miley purchased 2/4 of a pound of coffee for her family. She has to divide it equally among 6 family members. How many pounds of coffee did Miley give to each member?
  • Practice 2 - A painter use 5/8 of a can of acrylic colors to paint 10 canvases. How much acrylic colors did he use to paint each canvas, assuming he used the paint equally?
  • Practice 3 - Taylor wants to eat peanuts. He purchases 3/5 of a pound of peanuts. He wants to share them equally between 12 friends. How many pounds of peanuts did Taylor gave to each friend?

Math Skill Quizzes

In your progression through the year, these quizzes should fit perfectly!

  • Quiz 1 - Example problem: 3 x 4 + 5 x 6 = 6 (5 + _____ ). You are tasked with finding the missing value.
  • Quiz 2 - Rex throws party at his house. He invited 200 guests. He ordered pizza. If each guest can eat 2/4 of the pizza how many people will 10 pizzas feed?
  • Quiz 3 - The easy problem: Divide the integers: 100 ÷ 4. The more difficult problems will require up to three steps. A great overview of basic algebra skills.

How to Determine if a Quotient's Value is Negative

Surprisingly, many students struggle to identify whether the end value of the quotient is negative or positive. It is one of the most basic of principles of mathematics but is not often discussed or debated among the students. The sign of the quotient depends on the signed value of the integers, which is similar to the whole number division (both positive). Except, the sign of the quotient should be determined.

A quick review of the parts of a division operation, the anatomy of it is: dividend ÷ divisor = quotient.

There are three rules you can refer to when you are determining the end signed value of a quotient:

Both Positive - If both the dividend and the divisor are of positive value, the quotient, in that case, will be positive as well.

Both Negative - If both the dividend and the divisor are of negative value, the quotient, in that case, will be positive.

One Negative and One Positive - If one of them is negative and the other one is positive, then the quotient, in that case, will be negative.

While this may seem like just a simple math operation that does not have much worth in your daily life, this skill is used in many different walks of life. We use this we schedule payments or credits in many different financial situations. Once you get your first bankcard you will quickly come across this.

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Multiplying and Dividing Integers: Advanced Lesson

With this lesson, students will learn about positive and negative numbers and learn the rules for multiplying and dividing by them.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to add another activity. For this activity, students will flip over two playing cards and multiply (red for negative, black for positive). Students collect the cards if they get the right answer, and the student with the most cards at the end wins.

Description

Additional information, what our multiplying and dividing integers lesson plan includes.

Lesson Objectives and Overview: Multiplying and Dividing Integers introduces students to working with positive and negative integers. The included manipulative is a great way for students to visualize the concept and practice solving problems. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the orange box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. There are no supplies needed for this lesson. To prepare for this lesson ahead of time, you can copy the handouts.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. An optional addition to this lesson is to add another activity. For this activity, students will flip over two playing cards and multiply (red for negative, black for positive). Students collect the cards if they get the right answer, and the student with the most cards at the end wins. If some of your students have trouble multiplying or dividing, they can use a calculator.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

MULTIPLYING AND DIVIDING INTEGERS LESSON PLAN CONTENT PAGES

Integers (multiplying and dividing).

The Multiplying and Dividing Integers lesson plan includes one page of content. The lesson begins by explaining how to multiply or divide integers with the same sign. To do this, you multiply or divide the number regularly. The answer will always be positive. Next, the lesson explains how to multiply or divide integers with different signs. You also multiply the integers regularly, but in this case, the answer will always be negative. The lesson includes an example for each scenario.

MULTIPLYING AND DIVIDING INTEGERS LESSON PLAN WORKSHEETS

The Multiplying and Dividing Integers lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

TIC-TAC-TOE ACTIVITY WORKSHEET

The activity worksheet asks students to use a tic-tac-toe table to reinforce the rules for multiplying or dividing integers. They will use the table included on the worksheet and will place positive signs on one diagonal and fill in the rest of the places with negative signs. They will then use the table to fill in various statements related to the lesson material.

SOLVING PROBLEMS PRACTICE WORKSHEET

For the practice worksheet, students will solve multiplication and division problems using what they learned during the lesson.

MULTIPLYING AND DIVIDING INTEGERS HOMEWORK ASSIGNMENT

The homework assignment asks students to fill in the tic tac toe board and answer question about it. They will also solve 12 multiplication and division problems.

Worksheet Answer Keys

This lesson plan includes answer keys for the activity worksheet, the practice worksheet, and the homework assignment.  If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

grade-level

6th Grade

subject

Math

State Educational Standards

LB.MATH.CONTENT.6-Advanced Lesson

Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.

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