How to Multiply and Divide Integers? (+FREE Worksheet!)

Any number that can be displayed without a fraction is called an integer. For example, the numbers \(-1, -4, 0, 5, 10\) are integers because we can specify them without having to display a regular fraction.

It can be said that integers consist of three categories:

1. Positive integers
2. Zero
3. Negative integers

Multiplying and dividing integers is just like simple multiplying and dividing, the only difference being that you have to specify the answer sign before you do the multiplying or dividing operation.

Here you learn how to multiply and divide integers using integers multiplication and division rules.

Related Topics

• How to Add and Subtract Integers
• How to Order Integers and Numbers
• How to Use Order of Operations
• How to Solve Integers and Absolute Value Problems

Step by step guide to multiplying and dividing integers

To multiply and divide integers, we must do the following 2 steps:

Step 1: Determine the answer sign: When we want to multiply or divide two integers, we first multiply the symbols of the two numbers to determine the answer sign.

• The product of multiplying or dividing two positive numbers is a positive number.
• The product of multiplying or dividing two negative numbers is a positive number.
• The product of multiplying or dividing a positive number and a negative number is a negative number

Use these rules for multiplying and dividing integers:

• \(\color{black}{(negative)} \ × \ \color{ black }{(negative)} = \color{blue}{positive}\)
• \( \color{ black }{(negative)} \ ÷ \ \color{ black }{(negative)} = \color{blue}{positive}\)
• \(\color{ black }{(negative)} \ × \ \color{blue}{(positive)}= \color{ black }{negative}\)
• \( \color{ black }{(negative)} \ ÷ \ \color{blue}{(positive)} = \color{ black }{negative}\)
• \(\color{blue}{(positive)} \ × \ \color{blue}{(positive)}= \color{blue}{positive}\)

Step 2: Once we have found the answer sign, the rest of the work is like a simple multiplication or division: If we have multiplication, we multiply two numbers together. If we have a division, we divide the two numbers.

Multiply and Divide Integers – Example 1:

Solve. \(3 \ \times \ (12 \ – \ 14)=\)

Solution:

First subtract the numbers in brackets, \(12 \ – \ 14= \ – \ 2 → (3) \ \times \ (- \ 2)=\)
Now use this formula: \(\color{ black }{(negative)} \ × \ \color{blue}{(positive)}= \color{ black }{negative}\)
\( (3) \ \times \ (- \ 2)= \ – \ 6\)

Multiply and Divide Integers – Example 2:

Solve. \((- \ 8) \ + \ (12 \ \div \ 4)=\)

Solution:

First divided \( 12\) by \(4\), the numbers in brackets, \(12 \ \div \ 4=3\)
\((-8) \ + \ (3)= -8 \ + \ 3= \ – 5\)

Multiply and Divide Integers – Example 3:

Solve. \((2-5)×(3)=\)

Solution:

First subtract the numbers in brackets, \(2-5=-3 → (-3)×(3)=\)
Now use this rule: \( \color{ black }{(negative)} \ × \ \color{blue}{(positive)} = \color{ black }{negative}\)
\((-3)×(3)= \ -9\)

Multiply and Divide Integers – Example 4:

Solve. \((-12)+(48÷6)=\)

Solution:

First divided \(48\) by \(6\), the numbers in brackets, \(48÷6=8\)
\((-12)+(8)=-12+8= -4\)

Exercises for Multiplying and Dividing Integers

Find each Product and Quotient.

1. \(\color{blue}{(– 8) × (– 2)}\)
2. \(\color{blue}{ – 3 × 6 }\)
3. \(\color{blue}{(– 4) × 5 × (– 6) }\)
4. \(\color{blue}{ – 18 ÷ 3 }\)
5. \(\color{blue}{(– 24) ÷ 4}\)
6. \(\color{blue}{(– 63) ÷ (– 9)}\)

Download Multiplying and Dividing Integers Worksheet

1. \(\color{blue}{16}\)
2. \(\color{blue}{ – 18}\)
3. \(\color{blue}{120}\)
4. \(\color{blue}{ – 6}\)
5. \(\color{blue}{ –6}\)
6. \(\color{blue}{7}\)