Maths: Ratio and Proportion

In a ratio question, two amounts change together, like people and flour. Twice as many people need twice as much flour.

You're given one pair: a recipe for four people, and the flour it uses. Then you're asked for the amount that goes with a new number, here six people, and you pick it from five answers.

In GL's papers a ratio question never says "ratio", and never uses a colon. The link comes in words: for every, twice as many, a recipe for four. The video above and the worked example below work through the same question, with the options in the same order.

The method

Four steps: turn it into parts, find one, scale to what's asked, check what's asked.

Every ratio question turns on step 2: what is one part, one lot or one person worth? Find that, and the rest is a multiplication.

Worked example

The table shows a recipe for 4 people. How many grams of flour are needed for 6 people?

Pancakes — Flour 240 g · Milk 220 ml · Sugar 44 g · Butter 32 g

A. 60 g B. 66 g C. 120 g D. 240 g E. 360 g

1. Turn it into parts. Which amounts go together? Here, the parts are people and flour. The recipe for four people uses 240 grams of flour: that's the pair. We want the flour for six people.
2. Find one. What is one part worth? Here, one part is one person, so divide both by four. 240 ÷ 4 = 60: one person needs 60 grams. That's option A, but it's for one person, not six. So A is out.
3. Scale to what's asked. Do the same to both rows. The question asks for six people, so multiply both by six: 6 × 60 = 360 grams. Six people is the recipe for four and half of it again, and the half counts. 240 grams is option D: just one recipe, with the half left off, so D is out. 120 grams is option C: only the half, for the two extra people, so C is out too.
4. Check what's asked. The part they want is flour, in grams. 66 grams is option B, but that's the sugar for six people, not the flour, so B is out. 360 grams is flour for six people, and it's more than the recipe's 240, as it should be. So the answer is E.

Answer: E — 360 g (240 g ÷ 4 = 60 g for one person, and 60 g × 6 = 360 g)

Things to watch out for

1. Ratio comes in words. Look for phrases like for every or twice as many, and turn them into parts first. "For every 2 yellow flowers there are 3 white flowers" is two parts and three parts. "Twice as many story books as poetry books" is two parts and one part.
2. Add the parts before you share. There are 18 books, and twice as many story books as poetry books. Two parts and one part make three shares, not two. 18 shared into three is 6 each. Halving 18 gives 9, but the two groups aren't the same size.
3. One share is a step, not the answer. In the same question, one share is 6. It's even the number of poetry books, so it looks right. But the question asks for story books: that's two shares, so 12.
4. Halves count. Don't round to whole lots. A train travels 80 km in 2 hours. How far does it go in 5 hours? Five hours is two lots of two hours, and half a lot more. Two lots only cover four hours. Add the half lot, 40 km, and it's 200 km.

Related

• The complete 11+ question-type guide
• Maths: Fractions — find the whole, cut it into equal parts
• Maths: Percentages — split the percentage into blocks you can find
• 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.