Maqqii A balanced network of maths skills for primary school children Maths practice

Adding fractions

Adding fractions practice, from 5/11 + 4/11 to 1/3 + 3/4 = 4/12 + 9/12: the same denominator first, then different ones, then finishing off the answer.

Your child can start here once they can read fractions; the later exercises, with different denominators, also need equivalent fractions and the times tables. A sixth and a quarter can only be added once both are in twelfths: finding the 12 is the tables, and rewriting 1/6 as 2/12 is equivalent fractions.

Usually taught in Year 4–5 in England and Wales, around ages 8 to 10. Every child goes at their own pace; this is a guide, not a requirement.

Same denominator
  • 2
    3
    1
    3
    Yes
  • 1
    3
    4
    7
    No

The first of 14 exercises in this topic. See them all

What it looks like for your child

With one exercise from this topic as the example: Add, same denominator.

1 The topic's page has the next exercise ready.
The topic's page has the next exercise ready.
2 Your child plays a round of 10 sums.
Your child plays a round of 10 sums.
3 No mistakes and in time: the exercise is done, and it earns wood for the village.
No mistakes and in time: the exercise is done, and it earns wood for the village.
4 The same page, a round later: the next exercise is ready.
The same page, a round later: the next exercise is ready.

How it fits together

The arrows point to what can be done next. Whatever sits inside a box belongs to it.

Needed first

Times tables Reading fractions Equivalent fractions

Fractions

Adding fractions

Same denominator

Same denominator?
Same denominator
Add, same denominator
Add, same denominator, bigger numbers
Add with whole ones

Different denominators

Over one denominator
Add, different denominatorsOver one denominator, more parts
Add, more parts
Add, different denominators, bigger numbers

Finishing the answer

Add, as small as it goes
Add, then take out the wholesAdd, as small as it goes, bigger numbers
Add, then take out the wholes, bigger numbers
Fractions, everything Multiplying and dividing fractions

Can come next

first this, then that belongs to

Same denominator

  • 2
    3
    1
    3
    Yes
  • 1
    3
    4
    7
    No

Two fractions. Is the number under the line the same? Yes or no.

  • 5
    11
    →
    1
    11
    9
    11
  • 2
    3
    →
    1
    3

Pick every fraction with the same number under the line as the one above. Not the same amount — the same denominator.

  • 10
    12
    +
    11
    12
    =
    21
    12
  • 2
    3
    +
    2
    3
    =
    4
    3

1/5 + 2/5 = ?/5. The denominators are the same, so only the tops add. Together they can come to more than one whole.

  • 5
    11
    +
    4
    11
    =
    9
    11
  • 11
    18
    +
    6
    18
    =
    17
    18

5/11 + 4/11 = ?/11. The denominators are the same, so only the tops add.

  • 1
    10
    20
    +
    2
    5
    20
    =
    3
    15
    20
  • 3
    15
    17
    +
    2
    1
    17
    =
    5
    16
    17

3 5/17 + 2 1/17 = ? ?/17. The whole ones add together, and so do the numerators.

Different denominators

  • 1
    2
    +
    1
    5
    =
    5
    10
    +
    2
    10
  • 1
    3
    +
    1
    4
    =
    4
    12
    +
    3
    12

1/3 + 1/4 = ?/12 + ?/12. Write both with the same denominator, and then they can be added.

  • 1
    6
    +
    1
    2
    =
    8
    12
  • 1
    4
    +
    1
    3
    =
    7
    12

1/3 + 1/4 = ?/12. Both over the same denominator, and then the numerators add.

  • 1
    3
    +
    3
    4
    =
    4
    12
    +
    9
    12
  • 1
    3
    +
    1
    4
    =
    4
    12
    +
    3
    12

2/3 + 1/4 = ?/12 + ?/12. The numerator is not always 1 now: times as many as you have.

  • 1
    4
    +
    2
    3
    =
    11
    12
  • 2
    3
    +
    2
    4
    =
    14
    12

2/3 + 1/4 = ?/12. Together they can now come to more than one whole.

  • 1
    4
    +
    7
    10
    =
    19
    20
  • 2
    9
    +
    2
    6
    =
    10
    18

1/4 + 7/10 = ?/20. Both over the same denominator first, then the numerators add.

Finishing the answer

  • 3
    4
    +
    5
    6
    =
    19
    12
  • 11
    12
    +
    3
    4
    =
    5
    3

1/6 + 1/3 = ?/?. Add them, and write the answer in the smallest numbers.

  • 1
    1
    3
    +
    2
    5
    12
    =
    3
    3
    4
  • 1
    2
    3
    +
    5
    6
    =
    2
    1
    2

1 5/6 + 2/3 = ? ?/?. Add them, write it as small as it goes, and take out the whole pies.

  • 11
    12
    +
    5
    6
    =
    7
    4
  • 5
    16
    +
    3
    4
    =
    17
    16

11/12 + 5/6 = ?/?. Add them, and write the answer in the smallest numbers.

  • 1
    2
    +
    3
    15
    16
    =
    4
    7
    16
  • 2
    7
    12
    +
    3
    2
    3
    =
    6
    1
    4

1/2 + 3 15/16 = ? ?/?. All of it at once: add, make it as small as it goes, take out the whole ones.

Why it matters

Adding fractions shows whether a child understands what a fraction is. A child who works out 1/3 + 1/3 as 2/6 adds the slices together but forgets that they stay the same size. Two thirds of a cake is simply two slices of the same size.

With different denominators, everything practised earlier comes together. You can only add a sixth and a quarter once you write them in the same size of slice, and that is exactly what equivalent fractions teach you.

How to approach it

The exercises build it up in three steps. First the same denominator: only the numerators are added, the denominator stays as it is. Then different denominators: find a denominator that suits both, for 1/6 and 1/4 that could be 12, and write them as 2/12 and 3/12.

Finally, finishing off the answer. 6/8 becomes 3/4, and 7/5 becomes 1 2/5. Don't let your child skip that last step: it is exactly the habit that saves the most work later, with bigger numbers.

When is it secure?

A round of 10 sums in one go without a mistake, within 20 seconds. That is about 2 seconds a sum: no more counting, just knowing.