Maths: Fractions

Fraction questions come in two kinds. One kind asks what fraction something is, like how much of a triangle is shaded.

The other kind asks for a fraction of an amount, like 3/5 of 45 cakes. Here, you work out how many are left.

Both come down to one idea: a whole, cut into equal parts. You pick from five answers, and fraction answers come in their simplest form. GL's papers never draw the bar for you: it's a picture you hold in your head. The video above and the worked examples below work through the same questions, with the options in the same order.

The method

Four steps: find the whole, cut it into equal parts, take the parts you need, check what's asked.

The same four steps work for both kinds of question: a fraction of an amount, and what fraction something is.

Worked example

There are 45 cakes on a stall at the school fair. People buy 3/5 of them. How many cakes are left?

A. 9 B. 27 C. 36 D. 15 E. 18

1. Find the whole. Work out what the fraction is a fraction of. Here, people buy 3/5 of the cakes, so the whole is all 45 cakes. Picture them as one bar.
2. Cut it into equal parts. The bottom number says how many parts. Here it's 5, so picture the bar cut into five equal parts. 45 shared into five is 9, so each part is 9 cakes. 15 is option D. That shares 45 into three, the top number. But the bottom number says five parts, so D is out.
3. Take the parts you need. The top number says how many parts to take. People buy 3/5, so take three parts. Start with one part, then build up: 9, 18, 27. So 27 cakes are bought. 9 is option A, but that's only one part, so A is out. 36 is option C. That's what's left if only one part is bought, but three parts were bought, so C is out too.
4. Check what's asked. Taken or left? The question asks how many cakes are left. 27 is option B, but those are the cakes bought, so B is out. Two parts are left, and two 9s make 18. Check: 18 and 27 make 45, the whole. So the answer is E.

Answer: E — 18 (45 ÷ 5 = 9; 3 parts bought = 27; 2 parts left = 18)

A second worked example

The same four steps work when a question asks what fraction something is.

What fraction of the triangle is shaded?

A big triangle is cut into 9 small triangles, in 3 rows: 1 at the top, then 3, then 5. In each row they point up, down, up, and so on. 3 of them are shaded: the one at the top, the one pointing down in the middle row, and the one in the bottom right-hand corner.

A. 1/9 B. 1/3 C. 1/2 D. 3/5 E. 2/3

1. Find the whole. It's the whole triangle. 3/5 uses only the five triangles in the bottom row as the whole, so D is out.
2. Cut it into equal parts. It's already cut into nine small triangles, all the same size, whichever way they point. 1/2 counts only the six pointing up, so C is out.
3. Take the parts you need. Three of the nine are shaded. That's 3/9.
4. Check what's asked. What fraction is shaded? 3/9 isn't one of the answers, because fraction answers come in their simplest form. Group the nine parts in threes. That makes three groups, and the shaded parts fill one of them. So 3/9 is 1/3. 2/3 is the part that isn't shaded, so E is out. 1/9 divides only the top number, so A is out too. So the answer is B.

Answer: B — 1/3 (3 of 9 equal parts are shaded, and 3/9 = 1/3)

Things to watch out for

1. Equal parts first. Only count pieces when they're all the same size. Here, a triangle is cut into 16 small triangles in 4 rows, and 2 of them are shaded. Its lines also split it into 4 big triangles. One half counts the 2 shaded pieces out of the 4 big parts, but each shaded piece is only a quarter of a big part. Picture every big part cut into four: 2 of 16 equal parts, which is 1/8.
2. One part is a step, not the answer. What is 5/6 of 42? One part is 7, and 7 is option A, but the question asks for five parts. Build up: 7, 14, 21, 28, 35.
3. Taken or left — and of what? 24 children are in a hall, and 1/3 go outside. Then 1/4 of the rest go to the library. The rest is a new whole: the 16 children still inside. A quarter of 16 is 4. 6 is a quarter of all 24, so it uses the wrong whole.
4. Same-size parts before you compare. To put 3/5, 9/10, 7/10 and 4/5 in order, smallest first, picture the fifths cut into tenths. 3/5 is 6/10, and 4/5 is 8/10. Now they line up: six, seven, eight, nine tenths. Going by the top numbers alone puts 4/5 before 7/10. And 6/10 is 0.6.

Related

• The complete 11+ question-type guide
• Maths: Ratio and Proportion — find what one part is worth, then scale
• Maths: Percentages — split the percentage into easy blocks
• Maths: Word Problems — plan, then finish every step

All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.