Answer on paper first, then reveal the mark scheme one mark at a time.
(a) Write the ratio $24 : 36$ in its simplest form. [1]
(b) Write the ratio 45 cm : 2 m in its simplest form. [2]
Ali and Ben share £72 in the ratio $5 : 3$.
Work out how much each person gets. [2]
In a chess club the ratio of boys to girls is $4 : 7$.
There are 15 more girls than boys.
How many people are in the chess club? [3]
$a : b = 3 : 4$ and $b : c = 6 : 5$
(a) Find $a : b : c$. Give your answer in its simplest form. [2]
(b) Given that $c = 40$, find the value of $a$. [1]
A jar contains only red beads and blue beads.
The ratio of red beads to blue beads is $2 : 3$.
Kai adds 12 more red beads to the jar. The ratio of red beads to blue beads is now $6 : 7$.
How many blue beads are in the jar? [4]
Amir, Bella and Cara share some money.
Amir gets $\frac{2}{5}$ of the money.
Bella and Cara share the rest in the ratio $4 : 5$.
Cara gets £150.
How much money does Amir get? [4]
Paint A is made by mixing blue paint and yellow paint in the ratio $1 : 3$.
Paint B is made by mixing blue paint and yellow paint in the ratio $2 : 1$.
Zara mixes some of paint A with some of paint B to make 10 litres of green paint.
In the green paint the ratio of blue paint to yellow paint is $1 : 1$.
How many litres of paint A and how many litres of paint B does Zara use? [5]
(a) Write the ratio $0.6 : 1.5$ in its simplest form. [1]
(b) Write the ratio $\dfrac{3}{4} : \dfrac{5}{6}$ in its simplest form. [2]
The bar chart shows the number of cats, dogs and rabbits at an animal rescue centre.
There are no other animals at the centre.
(a) Write down the ratio of dogs to cats. Give your answer in its simplest form. [1]
(b) What fraction of the animals at the centre are rabbits? Give your answer in its simplest form. [2]
Mina is mixing mortar for a garden wall.
She uses 7.5 kg of cement and 28.5 kg of sand.
(a) Write the ratio of cement to sand in the form $1 : n$. [2]
For the concrete base of the wall she uses gravel and sand in the ratio $5 : 3$.
She uses 28.5 kg of sand in the concrete.
(b) How much gravel does she use? [2]
In a car park there are only red cars and silver cars.
The number of red cars is $\dfrac{3}{5}$ of the number of silver cars.
(a) Write down the ratio of red cars to silver cars. [1]
(b) What fraction of the cars in the car park are red? [1]
(c) Ravi says,
“$\dfrac{3}{5}$ of the cars in the car park are red.”
Explain why Ravi is wrong. [1]
Brass is made from copper and zinc only.
The graph shows the mass of copper, $c$ grams, and the mass of zinc, $z$ grams, in pieces of brass.
(a) Use the graph to find the ratio of copper to zinc in brass. Give your answer in its simplest form. [2]
(b) Write a formula for $c$ in terms of $z$. [1]
(c) A brass door handle has a mass of 1.2 kg.
Work out the mass of copper in the door handle. [2]
Rod A has length $(2x + 3)$ cm.
Rod B has length $(x + 9)$ cm.
The ratio of the length of rod A to the length of rod B is $5 : 4$.
Work out the total length of the two rods. [4]
There are 180 students in Year 10 and 200 students in Year 11.
In Year 10, the ratio of students who walk to school to students who do not walk is $5 : 7$.
In Year 11, the ratio of students who walk to school to students who do not walk is $3 : 5$.
Work out the ratio of students who walk to school to students who do not walk for Year 10 and Year 11 together.
Give your answer in its simplest form. [4]
Ali and Beth have some money.
The ratio of Ali’s money to Beth’s money is $7 : 3$.
Ali gives Beth £24.
The ratio of Ali’s money to Beth’s money is now $3 : 2$.
(a) How much money did Ali have at the start? [3]
Beth then spends $\dfrac{3}{8}$ of the money she now has.
(b) Work out the new ratio of Ali’s money to Beth’s money. Give your answer in its simplest form. [2]
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