How to Multiply and Divide Integers

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

Step by step guide to multiplying and dividing integers

Use these rules for multiplying and dividing integers:

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

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. $$\color{blue}{(– 63) ÷ (– 9)}$$

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

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