Ratio and fractions. Exemplar, questions and answers

1.

2.

What is the same and what is different about each of
these representations?
1∶2
3∶6
There are twice as many pieces of toast as eggs.

3.

What is the same and what is different about each of
these representations?
They all show a comparison about the quantity of eggs to the
quantity of pieces of toast
1∶2
Ratio of eggs to toast on one plate
3∶6
Ratio of eggs to toast in total
There are twice as many pieces of toast as eggs.
True for each plate and the total

4.

Eva takes 30 minutes and Teddy takes one hour to do the
same homework.
Eva says the ratio of time taken to do homework is 30 ∶ 1
Explain why this is incorrect.

5.

Eva takes 30 minutes and Teddy takes one hour to do the
same homework.
Eva says the ratio of time taken to do homework is 30 ∶ 1
Explain why this is incorrect.
The units of measure need to be the same
e.g. 30 mins ∶ 60 mins or 0.5 hr ∶ 1 hr both of which give 1 : 2

6.

A group of children choose their favourite colour.
30% choose red, 35% choose blue, 25% choose green,
and the rest choose yellow.
Express the ratio of colour choice
red ∶ blue ∶ green ∶ yellow in its simplest form.

7.

A group of children choose their favourite colour.
30% choose red, 35% choose blue, 25% choose green,
and the rest choose yellow.
Express the ratio of colour choice
red ∶ blue ∶ green ∶ yellow in its simplest form.
30 ∶ 35 ∶ 25 ∶ 10 = 6 ∶ 7 ∶ 5 ∶ 2

8.

There are three piles of books.
Pile 1 has twice as many books as pile 2
Pile 3 has half as many books as pile 2
Find the ratio of books in Pile 1 ∶ Pile 2 ∶ Pile 3

9.

Pile 1
Pile 2
Pile 3
There are three piles of books.
Pile 1 has twice as many books as pile 2
Pile 3 has half as many books as pile 2
Find the ratio of books in Pile 1 ∶ Pile 2 ∶ Pile 3
4∶2∶1

10.

Write the ratios in simplest form.
4 kg ∶ 500 g
25 ml ∶ 2 litres
3 hours ∶ 45 mins
35 p ∶ £4.20
600 mm : 20 cm : 3 m

11.

Write the ratios in simplest form.
4 kg ∶ 500 g
8∶1
25 ml ∶ 2 litres
1 ∶ 80
3 hours ∶ 45 mins
4∶1
35 p ∶ £4.20
1 ∶ 12
600 mm : 20 cm : 3 m
3 ∶ 1 ∶ 15

12.

A farmer has 20 goats, 30 sheep and 50 cows.
Decide whether each statement is true or false, and
explain why.
G
G
S
S
S
C
C
C
C
C
50% of the animals are
cows.
30% of the animals are
sheep.
1
of the animals are goats.
5
The ratio of goats to sheep
to cows is 20 ∶ 30 ∶ 50
Other Animals
Cows
What other fractions, percentages and ratios can you write
down?

13.

A farmer has 20 goats, 30 sheep and 50 cows.
Decide whether each statement is true or false, and
explain why.
G
G
S
S
S
C
C
50% of the animals are
cows.
C
C
30% of the animals are
sheep.
True, 50 out of 100
1
of the animals are goats.
5 1
C
True, 30 out of 100
The ratio of goats to sheep
to cows is 20 ∶ 30 ∶ 50
True, = 20%, 20 out of 100 True, but this can be simplified
5
Other Animals
Cows
What other fractions, percentages and ratios can you write
down? Discuss other possible answers as a class.

14.

Match the statements to the corresponding ratios.
You may use bar models to help you.
1
5
1
5