Performing a division

Euclidean division

Dividing a number a (the dividend) by a number b (the divisor) amounts to finding how many times b fits into a. This yields a quotient q and, often, a remainder r, with the relationship: a = b × q + r, where r < b.

The steps of written division

1. Take the first digits of the dividend, starting from the left, until you obtain a number greater than or equal to the divisor.
2. Work out how many times the divisor fits into this number (the quotient).
3. Multiply this figure by the divisor, subtract, and obtain a partial remainder.
4. Bring down the next digit of the dividend next to the remainder, and repeat the process.

Example: 156 ÷ 4

• Look at 15 (as 1 < 4). How many times does 4 go into 15? 3 times (3 × 4 = 12). Write 3 in the quotient; the remainder is 15 – 12 = 3.
• Bring down the 6: this gives 36. How many times does 4 go into 36? 9 times (9 × 4 = 36). Write 9 as the quotient; the remainder is 0.

Result: 156 ÷ 4 = 39, remainder 0 (exact division).

Example with a remainder: 47 ÷ 5

• How many times does 5 go into 47? 9 times (9 × 5 = 45), with a remainder of 47 – 45 = 2.

Result: 47 = 5 × 9 + 2, so the quotient is 9 and the remainder is 2.

Pitfalls to avoid

• Choosing a quotient that is too large or too small (the remainder at each step must always be strictly less than the divisor).
• Forgetting to bring down a digit from the dividend at each step.
• Confusing the quotient and the remainder in the final answer.