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Dividing decimals

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Decimals

Dividing decimals

Short division works exactly as it does for whole numbers. The only new rule is where the point goes.

The point in the answer sits directly above2.12924.258the two points line up — that is the whole rulerun out of digits? add zeros after the point and keep going
Check it with the inverse: 2.129 × 2 = 4.258 ✓

The method

To divide a decimal by a whole number: 1. Use short division, just as you would for whole numbers. 2. KEEP the decimal point where it is in the question. 3. Write the point in the ANSWER directly above the point in the question.

A worked example

4.258 ÷ 2 4 ÷ 2 = 2, so write 2 above the 4. Now write the decimal point in the answer, above the one in the question. 2 ÷ 2 = 1, write 1 above the 2. 5 ÷ 2 = 2 remainder 1, write 2 above the 5 and carry the 1 onto the 8. 18 ÷ 2 = 9, write 9 above the 8. 4.258 ÷ 2 = 2.129

Adding zeros to finish

41.481 ÷ 18 does not stop neatly. 41 ÷ 18 = 2 r 5, so write 2 and carry the 5. 54 ÷ 18 = 3. 8 ÷ 18 = 0 r 8, so write 0 and carry the 8. 81 ÷ 18 = 4 r 9, carry the 9 onto a NEW zero. 90 ÷ 18 = 5. 41.481 ÷ 18 = 2.3045 When you run out of digits, you may add zeros after the decimal point and keep going — it does not change the value.

Worked examples

4.258 ÷ 2

  1. 4 ÷ 2 = 2.
  2. Put the point in the answer above the point in the question.
  3. 2 ÷ 2 = 1; 5 ÷ 2 = 2 r 1; 18 ÷ 2 = 9.

Answer: 2.129

41.481 ÷ 18

  1. 41 ÷ 18 = 2 r 5; 54 ÷ 18 = 3; 8 ÷ 18 = 0 r 8.
  2. 81 ÷ 18 = 4 r 9 — carry onto a NEW zero.
  3. 90 ÷ 18 = 5.

Answer: 2.3045

Where does the point go?

  1. Keep it where it is in the question.
  2. Write it in the answer directly above.

Answer: Directly above the point in the question

Running out of digits

  1. You may add zeros after the decimal point.
  2. It does not change the value.

Answer: Keep dividing until it finishes

6.4 ÷ 4

  1. 6 ÷ 4 = 1 r 2.
  2. Carry the 2 onto the 4 to make 24.
  3. 24 ÷ 4 = 6.

Answer: 1.6

Checking a division

  1. Multiply the answer back by the divisor.
  2. 1.6 × 4 = 6.4 ✓

Answer: Multiplication is the inverse of division

Where you see this in real life

  • Maggie pays $9.28 for 8 m of ribbon. Per metre that is 9.28 ÷ 8 = $1.16.
  • Splitting a £43.85 bill five ways is 43.85 ÷ 5 = £8.77 each.

Key words

Short division
dividing in a single row, carrying remainders
Inverse calculation
the multiplication that checks a division
Estimation
a rough answer used to check a calculation
Divisor
the number you are dividing by
Remainder
what is left over after a division
Decimal place
a position after the decimal point
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