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      Choose efficient approaches when subtracting mixed numbers

      Lesson details

      Learning outcome

      I can choose efficient approaches when subtracting mixed numbers.

      Key learning points

      1. Partitioning is a strategy that can be used to subtract mixed numbers.
      2. When partitioning, the whole number part and the fractional part of the minuend must be greater than the subtrahend's.
      3. Using number-sense can support us to determine the most efficient method to use when subtracting from mixed numbers.

      Keywords

      • Mixed number - A mixed number is a whole number and a fraction combined.

      • Minuend - The minuend is the first number in a subtraction. The number from which another number is to be subtracted.

      • Subtrahend - The subtrahend is the number that is to be subtracted. The second number in a subtraction.

      Common misconception

      When partitioning to subtract, children may partition correctly but then may subtract incorrectly by swapping the order of the fractional parts being subtracted.

      Is partitioning efficient for this subtraction where the fractional part of the subtrahend is greater than that of the minuend? It may be more efficient to 'find the difference' by counting on.

      Teacher tip

      Children need to have a secure understanding of how to subtract proper fractions and how to convert between mixed numbers and improper fractions. Children also need an understanding of when partitioning can or cannot be used for subtraction.

      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.
      72 − 34 =

      Correct Answer: 38

      Q2.
      $$ {4} \over {5}$$ − $$ {3} \over {5}$$ =

      $$ {7} \over {5}$$
      $$ {7} \over {10}$$
      $$ {1} \over {0}$$
      $$ {1} \over {10}$$
      Correct answer: $$ {1} \over {5}$$

      Q3.
      Match the mixed number to their equivalent improper fraction.

      Correct Answer:$$2{{4} \over {6}}$$,$$ {16} \over {6}$$

      $$ {16} \over {6}$$

      Correct Answer:$$3{{4} \over {7}}$$ ,$$ {25} \over {7}$$

      $$ {25} \over {7}$$

      Correct Answer:$$1{{6} \over {7}}$$ ,$$ {13} \over {7}$$

      $$ {13} \over {7}$$

      Correct Answer:$$2{{1} \over {6}}$$,$$ {13} \over {6}$$

      $$ {13} \over {6}$$

      Correct Answer:$$5{{3} \over {7}}$$,$$ {38} \over {7}$$

      $$ {38} \over {7}$$

      Q4.
      Match the improper fractions to their equivalent mixed number.

      Correct Answer:$$ {10} \over {6}$$,$$1{{4} \over {6}}$$

      $$1{{4} \over {6}}$$

      Correct Answer:$$ {19} \over {6}$$,$$3{{1} \over {6}}$$

      $$3{{1} \over {6}}$$

      Correct Answer:$$ {32} \over {6}$$,$$5{{2} \over {6}}$$

      $$5{{2} \over {6}}$$

      Correct Answer:$$ {35} \over {6}$$ ,$$5{{5} \over {6}}$$

      $$5{{5} \over {6}}$$

      Correct Answer:$$ {41} \over {6}$$,$$6{{5} \over {6}}$$

      $$6{{5} \over {6}}$$

      Q5.
      Use the number line to complete the sentence: the difference between $$3{{2} \over {8}}$$ and $$2{{5} \over {8}}$$ is eighths

      An image in a quiz
      Correct Answer: 5, five

      Q6.
      Complete the missing box to make the equation correct.

      An image in a quiz
      Correct Answer: 6

      6 Questions

      Q1.
      Use counting back (reduction) to solve the calculation $$5{{1} \over {7}}$$ − $$1{{3} \over {7}}$$ equals three and sevenths

      An image in a quiz
      Correct Answer: 5, five

      Q2.
      Use partitioning to solve the calculation $$6{{5} \over {7}}$$ − $$1{{3} \over {7}}$$ equals five and sevenths

      Correct Answer: two, 2

      Q3.
      Use ‘finding the difference’ by counting on to solve $$6{{2} \over {7}}$$ − $$5{{5} \over {7}}$$

      $$11{{7} \over {7}}$$
      $$11{{7} \over {14}}$$
      $$1{{4} \over {7}}$$
      Correct answer: $$ {4} \over {7}$$
      $$1{{3} \over {7}}$$

      Q4.
      By expressing these mixed numbers as improper fractions, calculate this: $$9{{2} \over {8}}$$ - $$3{{5} \over {8}}$$ =

      Correct answer: $$5{{5} \over {8}}$$
      $$12{{7} \over {8}}$$
      $$6{{3} \over {8}}$$
      $$12{{7} \over {16}}$$
      $$6{{5} \over {8}}$$

      Q5.
      In a sequence decreasing by one and one-sixth, what would come next?

      An image in a quiz
      $$5{{5} \over {6}}$$
      $$2{{3} \over {6}}$$
      Correct answer: $$3{{3} \over {6}}$$
      $$4{{3} \over {6}}$$

      Q6.
      In a sequence decreasing by one and three-fifths, what would come next?

      An image in a quiz
      $$7{{5} \over {5}}$$
      $$2{{1} \over {5}}$$
      Correct answer: $$1{{3} \over {5}}$$
      $$1{{4} \over {5}}$$

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