Decimals And Ratio Worksheet (Page 6 of 13) in pdf

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Real / Problem-solving

2p coins used to be made from a mix of

6.5

copper, tin and zinc in the ratio 95 : 3.5 : 1.5.

STEM: Using ratios

a A 2p coin had a mass of 7 g. What were the masses of copper, tin

and zinc in the coin?

You will learn to:

b Sally had £1 in 2p pieces. What was the total mass of the coins?

•

Solve engineering problems using ratio and proportion

Real

Turquoise paint is made by mixing blue, green and yellow in the

Q6 hint

•

Use unit ratios.

ratio 2.5 : 1.4 : 0.1.

Simplify the ratio into whole numbers.

Copy and complete the table to show how much of each colour is

Then share the amount of paint in the

needed to make the quantities shown.

new ratio.

Fluency

Size

Blue

Green

Yellow

Simplify each ratio.

1 litre

4 : 7

4 : 8

6 : 16

1.5 litres

5 : 20

3 : 5

24 : 28

Explore

2.5 litres

Can all the ratios be simpliﬁ ed?

Why learn this?

How do mountain bikes get up

Real / Reasoning

A photo-printing service offers the following picture

Most machines have gears, and gears depend

steep hills?

sizes:

on ratios.

6 × 4 inches, 7 × 5 inches, 8 × 6 inches, 10 × 8 inches, 12 × 8 inches.

A digital camera takes photographs in the ratio 3 : 2.

Exercise 6.5: Engineering ratios

Which sizes of photo can be printed from this camera?

STEM

The aspect ratio describes the ratio ‘width : height’ of an image.

1 Divide each quantity in the ratio given.

Q8 hint

Most modern televisions have an aspect ratio of 16 : 9.

a 567 kg in the ratio 5 : 1

How high would screens be with these widths?

A screen 16 cm wide would be

b 486 metres in the ratio 3 : 2

9 cm tall.

a 32 cm

b 30.5 cm

c 41.7 cm

d 44.3 cm

c £7816 in the ratio 2 : 3 : 5

How wide would screens be with these heights?

e 27 cm

f 17.5 cm

g 26.4 cm

h 35.2 cm

2 Simplify each ratio into a whole number ratio in its simplest form.

a 5.2 : 4.5

b 8.2 : 6.3

Reasoning

The triathlon is a race where competitors swim, cycle and

run. Four recognised lengths of race are shown in the table below.

c 8.5 : 2.25

d 2.56 : 1.37

Race

Swim

Cycle

Run

3 Wood’s metal is an alloy made from bismuth, lead, tin and cadmium.

Sprint

0.75 km

20 km

5 km

Mixing these amounts will make 1 kg of Wood’s metal.

Olympic

1.5 km

40 km

10 km

bismuth

500 g

Half Ironman

1.9 km

90 km

21.1 km

Q9a hint

lead

250 g

Ironman

3.8 km

180.2 km

42.2 km

First ﬁ nd the total distance of the race.

tin

125 g

a What proportion of the Sprint triathlon is running?

Then write the proportion for ‘run’ as

cadmium

125 g

b Cycling is Tom’s strongest sport. Which race or races would give

a fraction, and simplify.

him the best chance of winning?

How much of each metal is needed to make 2.5 kg?

Explore

Why do some old TV programmes have space at the sides

of the screen?

Worked example

Key point

What have you learned in this lesson to help you answer this

A new TV has aspect ratio of 16 : 9. Express this as a unit ratio .

You can compare ratios by writing

question? What other information do you need?

them as unit ratios . In a unit ratio,

Give your answer to two decimal places.

11 Reﬂ ect

one of the two numbers is 1.

16 : 9

a Look back at Q5a. Write all the steps you took to work out the

Divide both sides of the ratio

÷ 9

answer.

by the smallest number, 9

1.78 : 1

b Look back at Q9. Write the steps you took to work out the answer.

c Lou says, ‘Question 5 was about ratio. A ratio compares one part

Q11c hint

to another part. Question 9 was about proportion. A proportion

Use your steps for Q5a and Q9

4 Write each ratio as a unit ratio .

compares one part to the whole thing.’

to help you.

Give each answer to a maximum of two decimal places.

Is Lou correct?

a 9 : 5

b 11 : 4

c 17 : 33

d 11 : 23

145

Theta 1, Section 6.4

Unit 6 Decimals and ratio

146

Decimals And Ratio Worksheet Page 6

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