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