Multiplying and Dividing 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:

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

Example 1:

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

Solution:

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

Example 2:

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

Solution:

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

Example 3:

Solve. $$(2-5)×(3)=$$

Solution:

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

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

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. $$\color{blue}{7}$$