What is long division?

Why it matters

Long division is the first time most kids do a multi-step math procedure on paper. It builds on multiplication facts and place value, and it sets up later work with decimals, fractions, and algebra.

Worked example

Divide 845 by 5.

1. 1

   Set it up: write 845 inside the long-division bracket with 5 outside.

   The 5 is the divisor (how many groups). The 845 is the dividend (what you’re splitting up).

2. 2

   Look at the first digit: 8. Ask "how many 5s fit into 8?" Answer: 1. Write 1 above the 8.

   You’re splitting the 800 into 5 equal piles — each pile gets one 100.

3. 3

   Multiply: 1 × 5 = 5. Write 5 under the 8 and subtract: 8 − 5 = 3.

   That 3 is the leftover hundreds you haven’t shared out yet.

4. 4

   Bring down the next digit (4) to make 34.

   Now you’re working with 340 — the leftover 300 plus the 40.

5. 5

   How many 5s fit into 34? Answer: 6 (because 6 × 5 = 30). Write 6 above the 4.

   Each pile gets six more 10s.

6. 6

   Multiply: 6 × 5 = 30. Subtract: 34 − 30 = 4.

7. 7

   Bring down the last digit (5) to make 45.

8. 8

   How many 5s fit into 45? Answer: 9. Write 9 above the 5.

9. 9

   Multiply: 9 × 5 = 45. Subtract: 45 − 45 = 0. No remainder.

Common mistakes

• •Forgetting to write a 0 in the quotient when the divisor doesn’t fit (e.g. 1206 ÷ 6 — kids skip the 0 and write 21 instead of 201).
• •Bringing down the next digit before subtracting.
• •Mixing up which number goes inside vs outside the bracket.
• •Stopping too early and leaving a remainder when the problem expected decimals or further division.

How Briveli teaches long division

Briveli’s Grade 4 and Grade 5 curriculums walk kids through long division with single-digit and two-digit divisors, starting with no-remainder problems and building up to long division with decimals.