Long Division

Long division is a written method for dividing a large number (the dividend) by a smaller number (the divisor) when the answer cannot be worked out quickly in your head. It is one of the four basic operations in CBC Mathematics and a permanent feature of every KPSEA paper.

The vocabulary:

• Dividend — the number being divided. (In 96 ÷ 4, the dividend is 96.)
• Divisor — the number we are dividing by. (In 96 ÷ 4, the divisor is 4.)
• Quotient — the answer to a division. (96 ÷ 4 = 24; the quotient is 24.)
• Remainder — what is left over when the division is not exact. (97 ÷ 4 = 24 remainder 1.)

The long division algorithm — five steps that repeat:

The trick to long division is remembering five steps in order:

1. Divide — how many times does the divisor go into the current chunk of the dividend?
2. Multiply — multiply that answer by the divisor.
3. Subtract — take the product from the chunk of the dividend.
4. Bring down — bring down the next digit of the dividend.
5. Repeat — go back to step 1 with the new chunk.

A handy memory trick used in Kenyan classrooms is "Daddy, Mummy, Sister, Brother, Rover" — Divide, Multiply, Subtract, Bring down, Repeat.

Step-by-step example: 936 ÷ 4

1. Look at the first digit of the dividend (9). How many 4s in 9? Two, with 1 left over. Write 2 above the 9. Multiply 2 × 4 = 8. Subtract 9 − 8 = 1.
2. Bring down the next digit (3) to make 13.
3. How many 4s in 13? Three, with 1 left over. Write 3 above the 3. Multiply 3 × 4 = 12. Subtract 13 − 12 = 1.
4. Bring down the next digit (6) to make 16.
5. How many 4s in 16? Four exactly. Write 4 above the 6. Multiply 4 × 4 = 16. Subtract 16 − 16 = 0.

The quotient is 234, with no remainder.

When the division has a remainder:

If at the end of the algorithm there is still a non-zero number left over, that is the remainder. For example, 97 ÷ 4 = 24 r 1. In CBC, remainders can also be written as fractions or decimals:

• 97 ÷ 4 = 24 r 1
• 97 ÷ 4 = 24 ¼
• 97 ÷ 4 = 24.25

Dividing by two-digit divisors:

The same five-step pattern works when the divisor has two digits, but you usually need to estimate. For example, when dividing by 12, ask "how many 12s in 84?" — try 7 × 12 = 84, so the answer is exactly 7.

Common mistakes to avoid:

• Forgetting to write a zero in the quotient. If the divisor doesn't fit into the current chunk, put a 0 in the quotient and bring down the next digit. Example: in 840 ÷ 4, after the first division (2), the next chunk is 04 — divisor 4 fits 1 time. Don't skip writing it.
• Subtracting incorrectly so the leftover is bigger than the divisor. If your leftover is bigger than the divisor, your "how many times" estimate was too low — go back and increase it.
• Bringing down two digits at once. Bring down ONE digit at a time, then repeat the cycle.
• Forgetting the remainder. If you stop before the final subtraction, you may miss leftover digits.

CBC Grade 3 introduces division with one-digit divisors and small dividends; Grade 4 introduces written long division for up to three-digit dividends; Grade 5 covers long division with four-digit dividends and two-digit divisors; Grade 6 extends to using long division within fractions, decimals and word problems — material that appears in KPSEA and KJSEA.