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Learn Index · Arithmetic and Operations Grade 3–5

Long division

Dividing step by step: divide, multiply, subtract, bring down.

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Dividing big numbers

Long division breaks a large division into small steps, one digit at a time. It uses four repeating steps:

Step Do
1. Divide How many times does the divisor fit?
2. Multiply Multiply that by the divisor.
3. Subtract Take it away.
4. Bring down Bring down the next digit.

A memory trick: "Does McDonald’s Sell Burgers?"

Example: 852 ÷ 4

  • Dividend = 852, divisor = 4.

Hundreds: 4 into 8 goes 2 times. 2 × 4 = 8. 8 − 8 = 0. Bring down 5.

Tens: 4 into 5 goes 1 time. 1 × 4 = 4. 5 − 4 = 1. Bring down 2 → 12.

Ones: 4 into 12 goes 3 times. 3 × 4 = 12. 12 − 12 = 0.

Quotient: 213. Check: 213 × 4 = 852 ✓.

     2 1 3
   -------
 4 ) 8 5 2
     8
     ---
     0 5
       4
     ---
       1 2
       1 2
       ---
         0

When the first digit is too small

Example: 156 ÷ 6

6 doesn’t go into 1, so look at 15. 6 into 15 goes 2 times (12). 15 − 12 = 3. Bring down 6 → 36. 6 into 36 goes 6 times. Quotient: 26.

Zeros in the quotient

Example: 618 ÷ 3

  • 3 into 6 → 2. Subtract: 0. Bring down 1.
  • 3 into 1 → 0. Write 0 in the quotient! 0 × 3 = 0, 1 − 0 = 1. Bring down 8 → 18.
  • 3 into 18 → 6.

Quotient: 206. Forgetting that 0 would give 26, which is far too small.

Remainders

If something is left after the last step, it’s the remainder.

Example: 47 ÷ 5 → 5 into 47 goes 9 times (45), leaving 2. Answer: 9 R2.

Two-digit divisors

The same steps work. For 864 ÷ 24, estimate each step: 24 is about 25, and 25 goes into 86 about 3 times. 3 × 24 = 72, 86 − 72 = 14. Bring down 4 → 144. 24 × 6 = 144. Quotient: 36.

Worked examples

Example 1: 936 ÷ 3 = 312

Example 2: 725 ÷ 5 = 145 (5 into 7 → 1 R2; 22 → 4 R2; 25 → 5)

Example 3: 1,000 ÷ 8 = 125

Common mistakes

  • Forgetting a zero in the quotient when the divisor doesn’t fit.
  • Subtracting wrongly or forgetting to bring down a digit.
  • Getting a "remainder" bigger than the divisor. That means you could have divided one more time.
  • Writing quotient digits in the wrong column. Line each one up above the digit you just divided.

Try it yourself

  1. 584 ÷ 4
  2. 963 ÷ 9
  3. 815 ÷ 5
  4. 1,248 ÷ 12

Answers: 1) 146 2) 107 3) 163 4) 104

Quick recap

  • Long division: divide, multiply, subtract, bring down, repeat.
  • Write a 0 in the quotient when the divisor doesn’t fit.
  • Check: quotient × divisor + remainder = dividend.