Division on the Abacus, Step by Step

What division means

Division splits a number into equal parts. 12 ÷ 3 is read "12 divided by 3". The number being shared (12) is the dividend, the number you divide by (3) is the divisor, and the answer (4) is the quotient. Children don't need these words at first.

Both give 12 ÷ 3 = 4. Try both with real objects before using the abacus.

Division undoes multiplication

Every division fact comes from a multiplication fact. If your child knows 3 × 4 = 12, they also know 12 ÷ 3 = 4 and 12 ÷ 4 = 3. This is why times tables come first.

Division on the abacus: taking away equal groups

The simplest way to divide on the abacus is to take away the divisor again and again and count how many times you can do it. For 12 ÷ 3, set 12 and take away 3 until nothing is left.

You took away 3 four times, so 12 ÷ 3 = 4. This is slow for big numbers, so next we divide one place at a time.

Step by step for bigger numbers

For bigger numbers, work from the left, one place at a time. Keep the number you are sharing on the abacus and write the answer digits on paper as you find them. In classes the answer is often placed on rods to the left of the number; the steps are the same.

1. Look at the left digit. If it is smaller than the divisor, look at the first two digits together.
2. Ask: how many times does the divisor fit? Use your times tables. Write that digit in the answer.
3. Multiply back and take that amount away on the abacus.
4. Bring down the next digit and repeat.
5. When no digits are left, check: answer × divisor should give the number you started with.

In an exact division nothing is left over: 84 ÷ 4 = 21. Many numbers don't share exactly. 17 ÷ 5 gives 3 groups of 5 (that's 15) with 2 left over. We write 17 ÷ 5 = 3 remainder 2, often shortened to 3 R 2.

Teach exact division first. Most children find remainders easy once exact division is comfortable.

Each example adds one new idea. Keep the abacus for the amount still to share, and the answer on paper.

Common mistakes

• Dividing the wrong way round. 84 ÷ 4 is not the same as 4 ÷ 84. Read it as "84 shared into 4 groups".
• Missing a zero in the answer. In 208 ÷ 2, 2 doesn't fit into 0, so the answer needs a 0: 104, not 14.
• A remainder that is too big. If the remainder is as big as the divisor, or bigger, one more group fits.
• Not checking. Multiply the answer by the divisor and add any remainder. You should get the number you started with.
• Forgetting what was left over. In 96 ÷ 4, the 1 ten left over joins the 6 ones to make 16. Say it out loud.

Tips for parents

• Share real things first: sweets, coins or pencils into equal groups.
• Use the words "shared into" and "groups of" until the ÷ sign makes sense.
• Keep to answers with no remainder at first. ÷ Levels 1 to 4 of the practice never have a remainder.
• Ask your child to check each answer by multiplying back. It builds the habit early.
• Introduce remainders with objects: 7 sweets for 2 children leaves 1 over.

For paper practice, make a division worksheet. To keep skills fresh, play a round of the Practice Game at the Hard level.