Fractions of amounts, simplifying, comparing and adding.
CoreIn almost every paper that tests this subjectAbout 60 seconds a question in the test
The big idea
A fraction shows parts of a whole: the denominator (bottom) is how many equal parts, the numerator (top) is how many you have.
To find a fraction of an amount, divide by the denominator and multiply by the numerator. To simplify, divide top and bottom by their highest common factor.
Tips that save marks
To compare fractions, convert to a common denominator or to decimals.
You can only add numerators when the denominators match.
Always check if your final answer can be simplified.
A worked example
What is 3/8 of 64?
64 ÷ 8 = 8 (one eighth).
8 × 3 = 24.
Answer: 24.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
Work out:
58 − 24
Show the worked answer
Answer: B, 18
How to work it out
Make the bottom numbers the same.
4 × 2 = 8, so 24 = 48.
Then 58 − 48 = 18.
Why the other options are wrong
A (98): This adds the fractions instead of subtracting.
C (332): This multiplies the bottom numbers without changing the tops to match.
D (34): This subtracts the bottom numbers too. Only the top numbers are subtracted, once the bottoms match.
E (38): This takes away 2 twelfths-style parts without changing 24 to match the bottom number 8.
Question 2Aim for about 60 seconds
Work out the subtraction:
4 − 13
Show the worked answer
Answer: A, 323
How to work it out
Take 13 from one of the wholes: 1 − 13 = 23.
That leaves 3 wholes and 23: 323.
Why the other options are wrong
B (413): This adds the fraction on instead of taking it away.
C (313): This takes 1 whole away but keeps 13. What is left of that whole is 23.
D (17): This adds the whole number to the bottom; the bottom number names the size of the parts and does not change.
E (33): This takes the top number from the whole number, mixing wholes and parts.
Question 3Aim for about 60 seconds
What is 8/9 of 135?
Show the worked answer
Answer: B, 120
How to work it out
Divide by the bottom number, then multiply by the top: 135 ÷ 9 = 15, and × 8 = 120.
Question 4Aim for about 60 seconds
Write 6/10 in its simplest form.
Show the worked answer
Answer: C, 3/5
How to work it out
Find the highest number that divides into both: 2.
Divide top and bottom by it: 6 ÷ 2 = 3 and 10 ÷ 2 = 5.
So the answer is 3/5.
Question 5Aim for about 60 seconds
Write 7/49 in its simplest form.
Show the worked answer
Answer: D, 1/7
How to work it out
Find the highest number that divides into both: 7.
Divide top and bottom by it: 7 ÷ 7 = 1 and 49 ÷ 7 = 7.
Want a plan built around the topics your child finds hardest?
Prism starts with a free assessment across maths, English, verbal and non-verbal reasoning, then builds a weekly plan for your target schools. Parents follow progress free.