Boba Maths

Year 6 · Arithmetic skills · Skill 10C

Skill 10C: Adding and subtracting mixed numbers

Add and subtract two mixed numbers with different denominators.

Download the sheets

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.

Download the worksheet Download the answers Generate a new sheet for this skill

Worked examples

With two mixed numbers, you can add the whole numbers and fractions separately. For subtraction, improper fractions avoid awkward exchanges.

Example 1

Adding: wholes first, then fractions

35⁄6 + 23⁄4

  1. Add the whole numbers: 3 + 2 = 5.
  2. Now add the fractions 5⁄6 + 3⁄4.
  3. Find a common denominator. Multiples of 6: 6, 12. Multiples of 4: 4, 8, 12. The first number in both lists is 12.
  4. Change both fractions to have 12 as the denominator. Multiply the top and bottom by the same number.
    5⁄6 = 10⁄123⁄4 = 9⁄12
  5. Add the numerators and keep the denominator: 10 + 9 = 19.
    10⁄12 + 9⁄12 = 19⁄12
  6. 19⁄12 is an improper fraction (the top is bigger than the bottom). As a mixed number it is 17⁄12.
  7. Add the whole number part: 5 + 17⁄12 = 67⁄12.

Answer: 67⁄12

Example 2

Subtracting: change both to improper fractions

51⁄4 − 25⁄6

  1. Change both mixed numbers to improper fractions. 51⁄4 = 21⁄4 and 25⁄6 = 17⁄6.
    5 × 4 + 1 = 212 × 6 + 5 = 17
  2. Common denominator of 4 and 6 is 12: 21⁄4 = 63⁄12 and 17⁄6 = 34⁄12.
    21⁄4 = 63⁄1217⁄6 = 34⁄12
  3. Subtract: 63 − 34 = 29, so the answer is 29⁄12.
  4. 29⁄12 is an improper fraction (the top is bigger than the bottom). As a mixed number it is 25⁄12.
  5. So 51⁄4 − 25⁄6 = 25⁄12.

Answer: 25⁄12

Top tips

  • Adding: wholes together, fractions together, then combine.
  • Subtracting: turn both numbers into improper fractions.
  • Check your answer is sensible by rounding to whole numbers.

Watch out for

  • Forgetting to carry when the fractions add to more than 1.
  • Changing a mixed number into an improper fraction with the wrong top number.

Try some questions

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

  1. 11⁄2 + 11⁄4 =
    Show the answer

    23⁄4 (or 11⁄4)

  2. 27⁄10 + 11⁄5 =
    Show the answer

    39⁄10 (or 39⁄10)

  3. 17⁄9 + 21⁄6 =
    Show the answer

    317⁄18 (or 71⁄18)

  4. 311⁄14 + 25⁄21 =
    Show the answer

    61⁄42 (or 253⁄42)

All arithmetic skills

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

Arithmetic skills overview · Year 6 overview