Division

Dividing means sharing something out equally, or finding how many equal groups fit into a number. If 56 sweets are shared by 7 children, each child gets 8. If you have 72 eggs and a box holds 8, you can fill 9 boxes. Division is the opposite of multiplying, so if you know your times tables, you already know how to divide. This page shows how to use them to divide in your head.

What dividing means

We write division with the sign ÷, said "divided by". 56 ÷ 7 = 8 is said "56 divided by 7 is 8". There are two ways to picture it, and both give the same answer:

• Sharing: 56 shared equally between 7 people gives each person 8.
• Grouping: 56 split into groups of 7 makes 8 groups.

The answer to a division is called the quotient. In 56 ÷ 7 = 8, the quotient is 8. Division can also be written as a fraction: 56/7567 means the same as 56 ÷ 7. The line in a fraction means divide.

Division undoes multiplying

Every multiplication fact gives you two division facts for free. These three or four facts belong together, like a family.

So to divide, turn the question around. Instead of "What is 72 divided by 8?", ask "8 times what makes 72?" Then go through the 8 times table until you reach 72.

1. Read the question as a missing number: 8 × ? = 72.
2. Find the number from the times table you know.
3. Check by multiplying back.

Dividing in steps

When you do not remember a fact, you can divide in smaller steps. Dividing by 6 is the same as dividing by 2 and then by 3, because 2 × 3 = 6. Dividing by 4 is halving twice, and dividing by 8 is halving three times.

For a bigger number, split it into parts that are easy to divide, divide each part, and add the answers. The parts must each be in the times table of the number you divide by.

Rules worth knowing

• Any number divided by 1 is the same number: 9 ÷ 1 = 9.
• Any number divided by itself is 1: 9 ÷ 9 = 1.
• Zero divided by any other number is 0: 0 sweets shared by 5 children gives each child 0.
• You can never divide by 0. Sharing 9 sweets among no one has no answer.
• The order matters: 56 ÷ 7 is 8, but 7 ÷ 56 is a small fraction. Always read which number is shared out.

Sometimes a number does not share out exactly. 50 sweets for 7 children gives each child 7, with 1 sweet left over, because 7 × 7 = 49. What is left over is called the remainder. The questions on this site always share out exactly.