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VCE 11 General 2023

4.03 Ratios, proportion and rates

Worksheet
Ratios
1

Write the ratio 2:3 in words.

2

Write the ratio for the number of shaded squares to unshaded squares:

a
b
3

A bridge is made up of 3 lengths, PQ, QR and RS as shown below:

a

What is the total length of the bridge?

b

In what ratio are PQ and RS ?

c

In what ratio are PQ and PS ?

d

In what ratio are PQ, QR, and RS ?

4

Simplify the following ratios:

a

48:135

b

\dfrac{2}{7}:\dfrac{5}{7}

c

\dfrac{4000}{10\,000}:\dfrac{3000}{10\,000}

d

\dfrac{6}{5}:\dfrac{7}{10}

e

\dfrac{4}{7}:\dfrac{8}{5}

f

\dfrac{1}{5}:\dfrac{9}{7}

g

\dfrac{20}{3}:4

h

7\dfrac{2}{9}:6

i

5.4:0.75

5

Write 50 cents to \$2.10 as a fully simplified ratio by first converting to the same units, and then simplifying.

6

Simplify the following ratios:

a

3400 metres to 2 kilometres

b

40 minutes to 4 hours

c

3 years to 15 years

d

\dfrac{18}{25} \text{ kg} to 230 \text{ g}

e

\dfrac{6}{7} of an hour to 2\dfrac{1}{2} hours

f

\$0.60 to \$2.20

g

3.8 \text{ kg} to 180 \text{ g}

h

48 meters to 64 meters

7

A journalist spent a total of 24 hours researching, writing and editing a news report. She also spent 14 hours researching and 6 hours writing.

a

How many hours did she spend editing the report?

b

Find, in simplest form, the ratio in which her time was divided between researching, writing and editing.

Rates
8

Convert the following rates:

a

300 \text{ mL/h} to \text{ mL/min}

b

54 \text{ km/h} to \text{ m/sec}

c

18\,000 \text{ m/h} to \text{ cm/sec}

d

4000 \text{ g/min} to \text{ kg/h}

9

A tap fills up a 98 Litre tub in 2 hours. What is the rate of water flow of the tap?

10

If 9600 litres of water flow through a tap in 8 hours, what is the tap's flow rate per minute?

11

Luke earned \$1134 in 6 hours. What his hourly rate of pay?

Proportions
12

The following pairs of quantities are in proportion. Find the missing value for each pair.

a

\dfrac{⬚}{10}:\dfrac{35}{50}

b

\dfrac{16}{⬚}:\dfrac{8}{10}

c

\dfrac{2}{⬚}:\dfrac{10}{15}

d

\dfrac{⬚}{32}:9

13

To make 3 cups of rice, Ben needs 5 cups of water. To make 15 cups of rice, he needs 25 cups of water. Write this as a proportion by filling in the blanks below.

\dfrac{3 \text{ cups rice}}{⬚ \text{ cups water}}= \dfrac{⬚ \text{ cups rice}}{⬚ \text{ cups water}}
Quantities in ratio
14

How many parts are there in the ratio 20:3?

15

Find the total number of parts in the following ratios.

a

2:3

b

7:17

c

73:53

d

5:7:9

16

25.9 is divided into two parts in the ratio 5:2.

a

What is the value of the larger part?

b

What is the value of the smaller part?

17

20 is divided into three parts: A, B, and C, in the ratio 2:5:3. Find the value of:

a

A

b

B

c

C

18

The ratio of males to females on a train is 7:4. If the train is carrying 429 passengers:

a

Find the number of males on the train.

b

Find the number of females on the train.

19

James and John share \$77 in the ratio 5:2.

a

What fraction of the total amount to be shared does John receive?

b

Therefore, how much money must John receive?

20

Divide 28 kilograms into the ratio 8:4:2.

a

What is the largest value?

b

What is the smallest value?

21

A piece of rope is cut into three lengths in the ratio 6:7:10. If the shortest length is 24 \text{ m}:

a

Find the middle length of the rope.

b

Find the longest length of the rope.

c

Calculate the total length of the rope.

22

The length of a garden bed is split into three sections for carrots, potatoes and pumpkin respectively in the ratio 4:2:1.

If the total length of the garden bed is 14 metres:

a

What is the length of the side for carrots?

b

What is the length of the side for potatoes?

c

What is the length of the side for pumpkin?

23

The perimeter of a rectangle is 110 \text{ cm} and the ratio of its length to its width is 6:5.

a

How many parts are in the ratio?

b

What is the sum of the length and width of the rectangle?

c

What is the length of the rectangle?

d

What is the width of the rectangle?

e

What is the area of the rectangle?

f

What is the ratio of the area to the perimeter?

24

Dave and Luke bought a scratch ticket that cost \$10. Dave contributed \$8 and Luke's contribution was \$2. They won \$30\,000.

They decide to share their winnings in the same ratio as they contributed:

a

How much should Dave receive of the prize?

b

How much should Luke receive of the prize?

25

Concrete is mixed in the ratio of 1 cement, 2 sand and 3 gravel.

How much gravel is needed for 4.2 cubic metres of concrete?

The unitary method
26

Dave can wash 2 cars in 4 minutes.

a

How long would it take for him to wash 1 car?

b

How long would it take him to wash 20 cars?

27

Eileen can wash 7 plates in 28 minutes and lace 11 boots in 55 minutes.

a

How long does it take to wash 1 plate?

b

How long does it take to lace 1 boot?

c

How long would it take for Eileen to wash 13 plates and lace 19 boots?

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Outcomes

U1.AoS2.6

concepts of ratio, proportion, percentage, percentage change and rate, and unitary method

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