Decimals And Ratio Worksheet (Page 5 of 13) in pdf

Check

Strengthen

Extend

Test

MASTER

P149

P151

P155

P159

11 Work out

6.4

Q11a hint

a 2.724 × 3.25

b 4.59 × 2.764

Ratio and proportion with decimals

Set out in columns,e.g.

c 8.91 × 5.126

d 7.261 × 9.28

2724

e 6.903 × 0.425

f 23.241 × 7.26

× 325

You will learn to:

•

Use ratios involving decimals

12 a Work out the volume of this cuboid.

•

Solve proportion problems.

3.6 cm

9.6 cm

Fluency

4.2 cm

3 : 5

6 : 9

5 : 16

14 : 21

b Another cuboid has a volume of 35.52 m

Q12b Strategy hint

12 : 19 30 : 45

4 : 9

BUILDER

Its length is 4 m and its width is 2.4 m.

Make a sketch.

Which of these ratios are

What is its height?

Explore

equivalent to 2 : 3?

Why learn this?

Why do some old TV programmes

Increasing or decreasing quantities in proportion

13 Work out

have space at the sides of the

does not always give us whole numbers.

screen?

a 15 ÷ 0.1

b 2.6 ÷ 0.1

c 85.3 ÷ 0.01

d 572 ÷ 0.01

e 7.6 ÷ 0.01

f 0.3 ÷ 0.1

Exercise 6.4

Investigation

Reasoning

1 Write each ratio in its simplest form.

1 Choose a number.

a 8 : 4

b 12 : 3

c 15 : 25

Carry out these operations on your number.

d 4 : 18

e 7 : 49

f 40 : 60

×100

×10

×0.1

×0.01

÷100

÷10

÷0.1

÷0.01

2 a Share £20 in the ratio 2 : 3.

2 Repeat part 1 with another number.

b Share £36 in the ratio 4 : 5.

3 Are any of these operations equivalent?

c A piece of rope 24 m long is cut in the ratio 5 : 3.

Use your answers to parts 1 and 2 to complete these rules.

How long is each piece of rope?

×100 is equivalent to

is equivalent to ÷0.1

Worked example

is equivalent to ÷10

×0.01 is equivalent to

Share £114 between Alice, Bert and Chen in the ratio 5 : 2 : 1.

4 What do you think the rules are for

5 + 2 + 1 = 8 parts

First ﬁ nd out how many

a ×0.001

b ÷0.001?

£114 ÷ 8 = £14.25 per part

parts there are in total.

Test your rules.

Alice: 5 × £14.25 = £71.25

Find out how much

Bert: 2 × £14.25 = £28.50

Explore

Why does a sharp axe cut better than a blunt one?

one part is worth.

Chen: 1 × £14.25 = £14.25

Look back at the maths you have learned in this lesson.

How can you use it to answer this question?

Check: £71.25 + £28.50 + £14.25 = £114

Multiply the amount that one part is

worth by each value in the ratio.

15 Reﬂ ect

Q15 hint

a What happens when you divide a positive number by a number

3 Share each quantity in the ratio given.

a Look back at some of the

between 0 and 1?

a £108 in the ratio 2 : 3 : 4

b £486 in the ratio 1 : 3 : 5

calculations you did in Q5.

Q4a hint

c £510 in the ratio 1 : 2 : 3

d £242 in the ratio 1 : 2 : 3 : 5

b What happens when you multiply a positive number by a number

b Look back at some of the

between 0 and 1?

e 429 m in the ratio 2 : 3 : 6

468 kg in the ratio 3 : 6 : 7

Simplify using powers of 10.

calculations you did in lesson 6.2.

28.5 has one decimal place, so

c Write your own ‘What happens when …?’ question and answer it.

g 591 km in the ratio 1 : 2 : 4 : 5

h £1032 in the ratio 3 : 5 : 9

multiply both sides of the ratio by 10,

Discussion

How should you round when working with ratios in money?

then simplify.

What about kg? Why?

40 : 28.5

×10

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

400 : 285

a 40 : 28.5

b 70 : 51.2

c 25.5 : 17

d 28.6 : 5.15

80 :

Topic links : Multiplying and dividing by 10 and 100,

Metric measures, Imperial measures

143

Unit 6

Decimals and ratio

144

Theta 2, Section 6.3

Decimals And Ratio Worksheet Page 5

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