Boba Maths

Year 6 · Arithmetic skills · Skill 10B

Skill 10B: Adding and subtracting a mixed number and a proper fraction

Add and subtract a mixed number and a fraction with different denominators.

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Each file is an editable Word document (.docx) with 25 questions in five columns. It opens in Word, Google Docs, Pages and LibreOffice, so you can change questions or add working space before printing.

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Worked examples

A mixed number is a whole number and a fraction together. To add one, deal with the whole number and fraction separately; to subtract, an improper fraction is often safer.

Example 1

Adding: keep the whole number to one side

32⁄3 + 3⁄4

  1. Keep the whole number (3) to one side and add the fractions 2⁄3 + 3⁄4 first.
  2. Find a common denominator. Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. The first number in both lists is 12.
  3. Change both fractions to have 12 as the denominator. Multiply the top and bottom by the same number.
    2⁄3 = 8⁄123⁄4 = 9⁄12
  4. Add the numerators and keep the denominator: 8 + 9 = 17.
    8⁄12 + 9⁄12 = 17⁄12
  5. 17⁄12 is an improper fraction (the top is bigger than the bottom). As a mixed number it is 15⁄12.
  6. Now add the whole number: 3 + 15⁄12 = 45⁄12.

Answer: 45⁄12

Example 2

Subtracting: change to an improper fraction

41⁄6 − 5⁄8

  1. 1⁄6 is smaller than 5⁄8, so we cannot take the fractions straight away. Change 41⁄6 into an improper fraction: 4 × 6 + 1 = 25, so 41⁄6 = 25⁄6.
  2. The common denominator of 6 and 8 is 24. 25⁄6 = 100⁄24 and 5⁄8 = 15⁄24.
    25⁄6 = 100⁄245⁄8 = 15⁄24
  3. Subtract the numerators: 100 − 15 = 85, so the answer is 85⁄24.
  4. 85⁄24 is an improper fraction (the top is bigger than the bottom). As a mixed number it is 313⁄24.
  5. So 41⁄6 − 5⁄8 = 313⁄24.

Answer: 313⁄24

Top tips

  • Adding: add the fractions, then add the whole number.
  • Subtracting when the fraction part is too small: turn the mixed number into an improper fraction.
  • Always change back to a mixed number at the end.

Watch out for

  • Forgetting the whole number at the end.
  • Subtracting the smaller fraction from the larger when the order is the other way round.

Try some questions

These are from the worksheet. Work each one out, then open it to check.

  1. 11⁄2 + 1⁄4 =
    Show the answer

    13⁄4 (or 7⁄4)

  2. 27⁄10 + 1⁄5 =
    Show the answer

    29⁄10 (or 29⁄10)

  3. 17⁄9 + 1⁄6 =
    Show the answer

    117⁄18 (or 35⁄18)

  4. 211⁄14 + 5⁄21 =
    Show the answer

    31⁄42 (or 127⁄42)

All arithmetic skills

Skill 1ASkill 1BSkill 2ASkill 2BSkill 3ASkill 4ASkill 4BSkill 5ASkill 5BSkill 6ASkill 6BSkill 6CSkill 6DSkill 7ASkill 8ASkill 9ASkill 10ASkill 10CSkill 11ASkill 11BSkill 11CSkill 12ASkill 13ASkill 14A

Arithmetic skills overview · Year 6 overview