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Primary Maths · Year 6Chapter 4 · Fractions
Year 6 · Fractions · Lesson 4.4

Year 6: Adding and subtracting fractions and mixed numbers

Part of the Year 6 fractions chapter. Chapter overview · whole chapter on one page

4.4

Adding and subtracting fractions and mixed numbers

Year 6
Add and subtract fractions with different denominators and mixed numbers, Use equivalent fractions with a common denominator

To add or subtract fractions with different bottom numbers, first make the bottoms the same. Then add or subtract the top numbers. Look at the bars: 13 is the same as 412, and 14 is the same as 312. So 13 + 14 = 412 + 312 = 712.

A mixed number has a whole part and a fraction part. You can add or subtract the whole parts and the fraction parts separately, or change each mixed number to an improper fraction first. This chapter uses the improper fraction method, because it always works. When you subtract, it also avoids having to borrow a whole number.

1/31/4total
Four twelfths plus three twelfths makes seven twelfths.

Key ideas

  • To add or subtract, make the bottom numbers the same first (use the lowest common denominator).
  • Only the top numbers are added or subtracted. The bottom number stays the same.
  • For mixed numbers, change each one to an improper fraction: 2 1/3 = 7/3 (2 × 3 + 1 = 7).
  • Give the answer in its simplest form, and change an improper answer back to a mixed number.
Worked example 4.4.1
Work out 13 + 14.

Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.

Method. Write both fractions with the LCM of their bottoms, then add the top numbers.

  1. Find the lowest common denominator. Use the LCM of the two bottom numbers.
    LCM of 3 and 4 = 12
  2. Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.
    13 = 412
    14 = 312
  3. Add the top numbers. The bottom number stays the same, because the pieces are the same size.
    412 + 312 = 712

Check. 712 − 14 = 13. ✓

Watch out. Only the top numbers are added or subtracted. Do not add the bottom numbers.

Worked example 4.4.2
Work out 56 − 38.

Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.

Method. Write both fractions with the LCM of their bottoms, then subtract the top numbers.

  1. Find the lowest common denominator. Use the LCM of the two bottom numbers.
    LCM of 6 and 8 = 24
  2. Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.
    56 = 2024
    38 = 924
  3. Subtract the top numbers. The bottom number stays the same, because the pieces are the same size.
    2024 − 924 = 1124

Check. 1124 + 38 = 56. ✓

Watch out. Only the top numbers are added or subtracted. Do not add the bottom numbers.

Worked example 4.4.3
Work out 2 13 + 1 34. Give your answer as a mixed number.

Key words. A mixed number has a whole part and a fraction part, such as 2 1/3. An improper fraction has a top number that is bigger than its bottom number, such as 7/3. The two forms are the same amount.

Method. Write both fractions with the LCM of their bottoms, then add the top numbers.

  1. Write each mixed number as an improper fraction. Multiply the whole number by the bottom, then add the top. The bottom stays the same.
    213: 2 × 3 + 1 = 7, so 73
    134: 1 × 4 + 3 = 7, so 74
  2. Find the lowest common denominator. Use the LCM of the two bottom numbers.
    LCM of 3 and 4 = 12
  3. Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.
    73 = 2812
    74 = 2112
  4. Add the top numbers. The bottom number stays the same, because the pieces are the same size.
    2812 + 2112 = 4912
  5. Write the answer as a mixed number. The top is bigger than the bottom, so take out the whole parts.
    4912 = 4112

Check. 4112 − 134 = 213. ✓

Watch out. Only the top numbers are added or subtracted. Do not add the bottom numbers.

Worked example 4.4.4
Work out 3 14 − 1 56. The top fraction is smaller, so you need to change the whole number first.

Key words. A mixed number has a whole part and a fraction part, such as 2 1/3. An improper fraction has a top number that is bigger than its bottom number, such as 7/3. The two forms are the same amount.

Method. Write both fractions with the LCM of their bottoms, then subtract the top numbers.

  1. Write each mixed number as an improper fraction. Multiply the whole number by the bottom, then add the top. The bottom stays the same.
    314: 3 × 4 + 1 = 13, so 134
    156: 1 × 6 + 5 = 11, so 116
  2. Find the lowest common denominator. Use the LCM of the two bottom numbers.
    LCM of 4 and 6 = 12
  3. Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.
    134 = 3912
    116 = 2212
  4. Subtract the top numbers. The bottom number stays the same, because the pieces are the same size.
    3912 − 2212 = 1712
  5. Write the answer as a mixed number. The top is bigger than the bottom, so take out the whole parts.
    1712 = 1512

Check. 1512 + 156 = 314. ✓

Watch out. Only the top numbers are added or subtracted. Do not add the bottom numbers.

Watch out

Do not add the bottom numbers. 13 + 14 is not 27. Also, when you subtract a mixed number, check whether the top fraction is smaller. If it is, use improper fractions or borrow one whole.

Exercise 4D  Adding and subtracting fractions

Non-calculator
1
FWork out each addition. Give each answer in its simplest form.
(a)12 + 13
(b)25 + 110
(c)34 + 16
(d)58 + 14
2
FWork out each subtraction. Give each answer in its simplest form.
(a)34 − 13
(b)56 − 12
(c)710 − 14
(d)45 − 38
3
FWork out each addition. Give your answers as mixed numbers.
(a)213 + 134
(b)125 + 212
(c)316 + 114
4
FWork out each subtraction. Give your answers as mixed numbers.
(a)314 − 156
(b)413 − 234
(c)518 − 212
5
PSAva has 34 of a litre of juice. She drinks 13 of a litre. How much juice is left? Give your answer in its simplest form.
1/3 drunkleft3/4 litre
6
PSSam walks 2 12 km to the park and then 1 34 km to the shop. How far does Sam walk altogether? Give your answer as a mixed number.
7
PSA jug holds 2 13 litres. Ella pours out 34 of a litre. How much is left in the jug?
8
RLily says that 12 + 13 = 25. What has Lily done wrong? Write the correct answer.
9
RFind the missing fraction: 14 + ? = 56. Explain how you found it.
10
RChallenge: find two different unit fractions (with a top number of 1) that add up to 12. Both bottom numbers must be less than 20.

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