For a rectangle, length : width = 7 : 4. The perimeter of the rectangle is 88 cm. Work out the length and the width, in cm.

length (cm) = 28, width (cm) = 16

Is ratio on the Foundation paper as well as Higher?

Yes. Spec references R4 to R8 are common content on Edexcel 1MA1, so ratio appears on both tiers. Foundation questions usually stop at simplifying and sharing an amount; Higher adds combining two ratios through a shared quantity, working from a difference, and ratios that change after items are moved between shares.

How many marks is ratio worth on Edexcel GCSE Higher?

A straightforward share-out is 2-3 marks and a problem-solving ratio question is usually 4-5. Each paper is 80 marks, so ratio is rarely more than a handful of marks in its own right, but it also turns up inside percentage, similar shape, probability and compound measure questions.

Is ratio on the non-calculator paper?

Yes, Paper 1 is non-calculator and ratio appears there regularly. Edexcel picks totals that divide exactly by the number of parts on that paper, so if a division is not coming out neatly, check that you divided by the sum of the parts rather than by one of them.

How do you turn a ratio into a fraction?

Add the parts to get the denominator. In 3 : 5 there are 8 parts, so the first quantity is (3)/(8) of the total and the second is (5)/(8). Writing (3)/(5) is the single most common error on this topic, and it wipes out the rest of the question.

Ratio - Edexcel GCSE Higher Maths

Typically 3-6 marks per paper, plus ratio buried inside other questions · Spec 1MA1

Ratio covers spec references R4 to R8 on Edexcel's 1MA1 specification, with N11 for the fractions that appear inside ratio problems. It is common content, so Foundation students meet it as well, but the Higher versions carry the harder work: linking two separate ratios through a shared quantity, working from a difference rather than a total, and dealing with a ratio that changes when items move from one share to the other.

Edexcel can set ratio on any of the three papers. Paper 1 is non-calculator, so the numbers there are chosen to stay manageable by hand, with totals that divide exactly by the number of parts. On Papers 2 and 3 the arithmetic gets less tidy and the context does more of the work, often wrapping ratio around a percentage, an area or a price per kilogram. A short share-out is 2-3 marks; a problem-solving ratio question is usually 4-5 marks and sits in the back half of the paper.

Nearly every mark turns on one move: find what one part is worth, then scale. What loses marks is not the arithmetic but the layout: calculations scattered around the page, with no line an examiner can point at and credit. Write a labelled ratio line, write down what one part equals, and then check what the question actually asked for. The last mark often goes because the paper wanted the difference, or the total, or one person's new share, and the script stops at the value of one part.

Worked example

In a car park, the number of red cars to the number of blue cars is in the ratio

4 : 3

. The number of blue cars to the number of silver cars is in the ratio

6 : 5

. There are 45 silver cars in the car park. Work out the total number of red, blue and silver cars in the car park.

[4 marks]

Blue appears in both ratios, so make the blue figure match. Multiplying red : blue $= 4 : 3$ by 2 gives $8 : 6$ , which agrees with the 6 in blue : silver $= 6 : 5$ .
M1: scaling one ratio so the shared quantity takes the same value in both
Join them into one three-part ratio: red : blue : silver $= 8 : 6 : 5$ .
M1: a correct combined ratio (both original ratios must still be visible in it)
Silver is 5 parts and there are 45 silver cars, so one part is $45 \div 5 = 9$ cars.
M1: using the given quantity to find the value of one part
There are $8 + 6 + 5 = 19$ parts altogether, so the total is $19 \times 9 = 171$ cars.
A1: 171 cars, with the ratio working shown

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The numbers are chosen so that every question works without a calculator, which is how Paper 1 sets ratio; the harder ones mirror the combining, difference and transfer problems that appear later in a Higher paper. You can type a fraction such as 3/8 into a numeric answer box, and where two values are asked for, both have to be right to score.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

Write the ratio $18 : 24 : 30$ in its simplest form.

Answer options for question 1
$3 : 4 : 5$ $9 : 12 : 15$ $6 : 8 : 10$ $3 : 4 : 6$
Question 2 Exam pace [3 marks]

A biscuit recipe uses flour, butter and sugar in the ratio $6 : 4 : 3$ by mass. Kim uses 240 g of butter. Work out the mass of flour she needs, in grams.

Your answer (fractions like 1/2 are fine)
Question 3 Exam pace [3 marks]

For a rectangle, length : width $= 7 : 4$ . The perimeter of the rectangle is 88 cm. Work out the length and the width, in cm.

length (cm) = width (cm) =
Question 4 Stretch [3 marks]

A bag contains only red counters and blue counters. The ratio of the number of red counters to the number of blue counters is $3 : 5$ . There are $n$ blue counters in the bag. Write an expression, in terms of $n$ , for the total number of counters in the bag.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 5 Stretch [4 marks]

In a school the ratio of the number of students who walk to school to the number who do not walk to school is $4 : 5$ . $\frac{2}{5}$ of the students who walk to school are in Year 11. 72 students walk to school and are in Year 11. Work out the total number of students in the school.

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [4 marks]

A drink is made by mixing juice and water in the ratio $1 : 4$ by volume. Ravina has 1.2 litres of juice and 4 litres of water, and no more of either. Work out the greatest volume of the drink she can make, in litres.

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Reading $3 : 5$ as thirds and fifths and writing that the first share is $\frac{3}{5}$ of the total. Every figure calculated from that fraction is then wrong, and a 4-mark question scores nothing.

Add the parts before you write any fraction: $3 + 5 = 8$ , so the shares are $\frac{3}{8}$ and $\frac{5}{8}$ . Add the two fractions as a check, because they have to make 1.
Dividing the amount by one number in the ratio rather than by the total number of parts, so £180 shared in $4 : 5$ becomes $180 \div 4 = 45$ and $180 \div 5 = 36$ , two shares that add to £81.

Divide by the sum of the parts, so one part is $180 \div 9 = 20$ , then multiply up. Add your shares at the end: if they do not come back to £180, stop and find the slip before you move on.
Joining two ratios without matching the shared quantity, so $a : b = 3 : 4$ with $b : c = 6 : 7$ gets written as $3 : 4 : 7$ .

Make the shared letter the same number in both ratios first. Scale $3 : 4$ up to $9 : 12$ and $6 : 7$ up to $12 : 14$ , then join them as $9 : 12 : 14$ .
Treating a difference as a total. Told that one person receives £45 more than the other in the ratio $8 : 3$ , the candidate divides £45 by 11 instead of by 5.

Subtract the two ratio numbers to see how many parts the difference is worth: $8 - 3 = 5$ , so one part is $45 \div 5 = 9$ . Only then use 11 parts if the question wants the total.
Simplifying a ratio while the units still differ, turning 40 cm : 2 m into $20 : 1$ .

Convert to the smaller unit before cancelling: 40 cm : 200 cm gives $1 : 5$ . Keep the unit written beside each number until the final line so a mismatch is visible on the page.

Frequently asked questions

Is ratio on the Foundation paper as well as Higher?: Yes. Spec references R4 to R8 are common content on Edexcel 1MA1, so ratio appears on both tiers. Foundation questions usually stop at simplifying and sharing an amount; Higher adds combining two ratios through a shared quantity, working from a difference, and ratios that change after items are moved between shares.
How many marks is ratio worth on Edexcel GCSE Higher?: A straightforward share-out is 2-3 marks and a problem-solving ratio question is usually 4-5. Each paper is 80 marks, so ratio is rarely more than a handful of marks in its own right, but it also turns up inside percentage, similar shape, probability and compound measure questions.
Is ratio on the non-calculator paper?: Yes, Paper 1 is non-calculator and ratio appears there regularly. Edexcel picks totals that divide exactly by the number of parts on that paper, so if a division is not coming out neatly, check that you divided by the sum of the parts rather than by one of them.
How do you turn a ratio into a fraction?: Add the parts to get the denominator. In $3 : 5$ there are 8 parts, so the first quantity is $\frac{3}{8}$ of the total and the second is $\frac{5}{8}$ . Writing $\frac{3}{5}$ is the single most common error on this topic, and it wipes out the rest of the question.

Ratio - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics