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      Use long division with decimal remainders

      Lesson details

      Learning outcome

      I can use long division and give the remainder as a decimal.

      Key learning points

      1. Fraction and decimal equivalence can be used to convert fraction remainders to decimals.
      2. 1 one is equivalent to 10 tenths so a 1 can be exchanged for 10 tenths in the tenths column.
      3. Continue to regroup until the number of the decimal fraction is a multiple of the divisor.

      Keywords

      • Remainder - A remainder is an amount left after a division.

      • Decimal - A decimal number has a decimal point followed by digits that show the fractional part.

      • Equivalent - Equivalent refers to when two or more things have the same value.

      Common misconception

      Pupils do not convert fractions to decimals accurately.

      Take time to remind pupils about key equivalences such as one-half is 0.5 and one-fifth is 0.2 Pupils can use these to check the reasonableness of their answers.

      Teacher tip

      While extending the long division algorithm to include decimal values is shared as a strategy, pupils are more likely to prefer finding a fraction remainder to convert to a decimal.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Use the multiplication facts to derive 31 × 16 =

      An image in a quiz
      Correct Answer: 496

      Q2.
      Match the fractions with an equivalent fraction.

      Correct Answer:$$ {1} \over{2}$$,$$ {32} \over{64}$$

      $$ {32} \over{64}$$

      Correct Answer:$$ {1} \over{5}$$,$$ {13} \over{65}$$

      $$ {13} \over{65}$$

      Correct Answer:$$ {7} \over{8}$$,$$ {49} \over{56}$$

      $$ {49} \over{56}$$

      Q3.
      Match the fractions with an equivalent decimal.

      Correct Answer:$$ {1} \over{2}$$,0.5

      0.5

      Correct Answer:$$ {1} \over{5}$$,0.2

      0.2

      Correct Answer:$$ {3} \over{4}$$,0.75

      0.75

      Q4.
      Match the division equations to their simplified fraction remainders.

      Correct Answer:282 ÷ 4 = 70,$$ {1} \over{2}$$

      $$ {1} \over{2}$$

      Correct Answer:646 ÷ 8 = 80,$$ {3} \over{4}$$

      $$ {3} \over{4}$$

      Correct Answer:543 ÷ 9 = 60,$$ {1} \over{3}$$

      $$ {1} \over{3}$$

      Q5.
      Which of these correctly show the result with a simplified fraction remainder?

      482 ÷ 16 = 31 $$ {2} \over{16}$$
      Correct answer: 482 ÷ 16 = 30 $$ {1} \over{8}$$
      482 ÷ 16 = 32 $$ {1} \over{8}$$

      Q6.
      In June, one giraffe at the zoo ate 1,370kg of acacia leaves. How many kg did the giraffe eat each day? Which of these correctly show the result with a simplified fraction remainder?

      Correct answer: 1,370 ÷ 30 = 45 $$ {2} \over{3}$$
      1,370 ÷ 30 = 45 $$ {1} \over{2}$$
      1,370 ÷ 30 = 45 $$ {4} \over{5}$$

      6 Questions

      Q1.
      Match the different ways to represent a division remainder with their example.

      Correct Answer:As a remainder,282 ÷ 4 = 70 r2

      282 ÷ 4 = 70 r2

      Correct Answer:As a simplified fraction,282 ÷ 4 = 70 $$ {1} \over{2}$$

      282 ÷ 4 = 70 $$ {1} \over{2}$$

      Correct Answer:As a decimal fraction,282 ÷ 4 = 70.5

      282 ÷ 4 = 70.5

      Q2.
      Select the answer which would be best to use for the following question: 283 flamingos need to be shared between 4 different zoos, how many flamingos would there be at each zoo?

      Correct answer: 283 ÷ 4 = 70 r3 Remainder
      283 ÷ 4 = 70.75 Decimal Fraction
      283 ÷ 4 = 70 $$ {3} \over{4}$$ Simplified Fraction

      Q3.
      Select the answer which would be best to use for the following question: It costs £283 per week to feed 4 sea lions at the zoo. How much does it cost to feed one sea lion each week?

      283 ÷ 4 = 70 r3 Remainder
      Correct answer: 283 ÷ 4 = 70.75 Decimal Fraction
      283 ÷ 4 = 70 $$ {3} \over{4}$$ Simplified Fraction

      Q4.
      Select the answer which would be best to use: Some bears have cooked potatoes as part of their diet. 283 potatoes are shared equally between 4 bears, how many potatoes does each each bear have?

      283 ÷ 4 = 70 r3 Remainder
      283 ÷ 4 = 70.75 Decimal Fraction
      Correct answer: 283 ÷ 4 = 70 $$ {3} \over{4}$$ Simplified Fraction

      Q5.
      Buddy’s dog food costs £561 per year. Buddy eats one bag of food each month. How much does one of Buddy’s food bags cost? Give your answer as a decimal in pounds. £ per bag.

      Correct Answer: 46.75

      Q6.
      Pratchett the tortoise walks 3.675km in June. How far did he walk each day? Give your answer as a decimal, in metres. m per day.

      Correct Answer: 122.5

      To help you plan your 6 maths lesson on: Use long division with decimal remainders, download all teaching resources for free and adapt to suit your pupils' needs...