Number
Equivalent fractions
Recognise fractions that are worth the same amount.
Half a cake is half a cake however you cut it. Slice it into four and take two, or into six and take three, and you are holding the same amount every time — so 1/2, 2/4 and 3/6 are all worth exactly the same. Fractions that look different but are worth the same amount are called equivalent fractions.
Have a play
Shade some of the bar, then cut it into more pieces. What happens to the shaded part?
Do the same thing to the top and the bottom
Multiplying both numbers by 3 turns 1/2 into 3/6, and dividing both by 4 turns 4/8 back into 1/2. What matters is that the top and the bottom get the same treatment: cutting every piece in half doubles how many pieces there are and doubles how many you have, so nothing has really changed. Doing it to only one of the two numbers changes the fraction completely.
Worked example
Show that 1/2 and 3/6 are worth the same.
Start with 1/2, and multiply the bottom number by 3: 2 × 3 = 6.
Every piece has been cut into three, so there are now six pieces in the whole.
Try it together
Now let us fill in 3/4 = ?/12 together.
The bottom number has changed from 4 to 12, and the top has to follow it.
1.What do you multiply 4 by to get 12?
Have a go
Have a go on your own. Fill in the missing number: 1/3 = ?/12
Hint: Three has been multiplied by four.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.