Division of Single Digits

Division is the reverse of multiplication. If you know your times tables, you already know your division facts. This lesson makes that connection clear.

$12 \div 3$ asks: “How many groups of 3 fit into 12?” or equivalently, “3 times what equals 12?”

$$12 \div 3 = 4 \quad \text{because} \quad 3 \times 4 = 12$$

The $\div$ sign means “divided by.” You can also write it as a fraction: $\frac{12}{3} = 4$.

Key ideas:

• Division is the opposite of multiplication: if $a \times b = c$, then $c \div a = b$
• Dividing by 1 changes nothing: $8 \div 1 = 8$
• A number divided by itself is 1: $6 \div 6 = 1$
• Zero divided by anything is 0: $0 \div 5 = 0$
• You cannot divide by zero: $7 \div 0$ is undefined (it doesn’t work)

The fastest way to divide is to think of the related multiplication fact:

• $18 \div 3 = ?$ → Think: $3 \times ? = 18$ → Answer: 6
• $42 \div 7 = ?$ → Think: $7 \times ? = 42$ → Answer: 6
• $56 \div 8 = ?$ → Think: $8 \times ? = 56$ → Answer: 7

This is why knowing your times tables makes division almost free.

• $8 \div 2 = 4$
• $14 \div 2 = 7$
• $18 \div 2 = 9$

Results come from the 5s times table:

• $25 \div 5 = 5$
• $35 \div 5 = 7$
• $45 \div 5 = 9$

Use the 9s times table backward:

• $27 \div 9 = 3$
• $54 \div 9 = 6$
• $81 \div 9 = 9$

Sometimes a number doesn’t divide evenly. For example:

$14 \div 3 = ?$

$3 \times 4 = 12$ (fits), $3 \times 5 = 15$ (too big). So $14 \div 3 = 4$ remainder $2$.

We write this as $14 \div 3 = 4 \text{ R } 2$.

The remainder is what’s left over: $14 - 12 = 2$.

$48 \div 6$

Think: $6 \times ? = 48$. Since $6 \times 8 = 48$, the answer is 8.

$35 \div 7$

Think: $7 \times ? = 35$. Since $7 \times 5 = 35$, the answer is 5.

$20 \div 3$

$3 \times 6 = 18$ (fits), $3 \times 7 = 21$ (too big). So $20 \div 3 = 6 \text{ R } 2$.