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

Equivalent fractions

Equivalent fractions practice, from 2/6 = 1/3 to 10/15 = 2/3: first seeing the same amount, then matching the numerator or denominator, then simplifying.

Your child can start here once they can read fractions; the later exercises also need multiplication up to 20 and the times tables. Turning 2/3 into 10/15 means multiplying top and bottom by 5, and simplifying 12/16 means spotting that 4 goes into both, which is the tables at work.

Usually taught in Year 3–4 in England and Wales, around ages 7 to 9. Every child goes at their own pace; this is a guide, not a requirement.

The first of 8 exercises in this topic. See them all

What it looks like for your child

With one exercise from this topic as the example: Make them equal: the numerator.

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

Multiplication to 20 Times tables Reading fractions

Fractions

Equivalent fractions

All the same amount
The same amount, writtenMake them equal: the numerator
Make them equal: the denominatorWith smaller numbers?Make them equal: the numerator, bigger numbers
Bigger piecesMake them equal: the denominator, bigger numbers
Adding fractions Multiplying and dividing fractions

Can come next

first this, then that belongs to

Pick every pie with just as much shaded as the one shown. There are between one and three.

  • 4
    6
    6
    9
  • 6
    12
    2
    4

Pick every fraction worth the same as the pie. There may be one, two or three.

  • 2
    5
    =
    4
    10
  • 1
    2
    =
    6
    12

2/3 = ?/12, or 8/12 = ?/3. The denominator was multiplied or divided to get there; do the same to the numerator.

  • 2
    6
    =
    1
    3
  • 1
    6
    =
    2
    12

2/3 = 8/?, or 8/12 = 2/?. The numerator was multiplied or divided to get there; do the same to the denominator.

  • 1
    3
  • 3
    5

A pie, and fractions to choose from. Can it be written with smaller numbers, or not?

  • 14
    12
    =
    7
    6
  • 16
    10
    =
    8
    5

More than one pie, in small pieces. Which picture shows the same amount, in bigger pieces?

  • 10
    15
    =
    2
    3
  • 14
    16
    =
    7
    8

5/6 = ?/18. The denominator was multiplied to get there; do the same to the numerator.

  • 1
    4
    =
    3
    12
  • 3
    4
    =
    12
    16

5/6 = 15/?. The numerator was multiplied to get there; do the same to the denominator.

Why it matters

That two different fractions can be exactly the same amount surprises many children. Yet it is the basis of almost all the fraction work that follows: adding with different denominators and simplifying an answer both depend on it.

A child who understands why 3/4 and 9/12 are equal doesn't need to cram rules. They are the same slices of cake, only each slice has been cut into three again.

How to approach it

Start with the pictures: which cake has the same amount coloured, even though the slices are different? Then comes the rule that goes with it: whatever you do to the denominator, you do to the numerator too. If the denominator becomes five times as big, so does the numerator: 2/3 = 10/15.

The other way works just the same, but with division. 12/16 can be simplified, because 12 and 16 can both be divided by 4: 3/4. With every fraction, ask your child: can this one be written with smaller numbers?

When is it secure?

All 10 right in one round, and no more than 60 seconds altogether. Around 6 seconds a sum shows your child is no longer counting.