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5.03 Find part or whole measures with ratios

Worksheet
Divide quantities in a given ratio
1

James and Emma scored goals in their netball game in the ratio 4:3.

a

Find the fraction of the goals scored by James.

b

If they scored a total of 56 goals, how many goals did James score?

c

How many goals did Emma score?

2

Harris and Bella divided lollies between them in the ratio 5:4.

a

Find the fraction of lollies that Bella gets.

b

If there are 27 lollies, how many does Bella get?

c

How many lollies does Harris get?

3

56 building blocks are shared between Mohamad and Isabelle in the ratio 2:5.

a

Find the fraction of the blocks Mohamad receive.

b

How many blocks does Mohamad receive?

c

How many blocks does Isabelle receive?

4

Ben always buys melons and bananas in the ratio 7:3. If he buys 30 pieces of fruit in total, how many melons did he buy?

5

The ratio of adults to children on a train is 2:7. The train is carrying 360 passengers.

a

How many adults are on the train?

b

How many children are on the train?

6

James and Sophia share \$880 in the ratio 2:9.

a

How much money does James get?

b

How much money does Sophia get?

7

Avril is making a scarf that uses two materials. She wants to use the materials in the ratio of \dfrac {11}{15} metres of red for every \dfrac {3}{5} metres of green.

a

Write the simplified ratio of red material to green material.

b

If she needs 33 metres of red material, how many metres of green material will she need?

8

Neil is mixing paint to get a specific shade of orange. He wants a mix of red and yellow paint in the ratio of 3\dfrac {3}{4}:6\dfrac {2}{3}.

a

Simplify the ratio.

b

How many litres of red paint will Neil need if he wants to make 75 litres of orange paint?

9

Kathleen and Luke invest money in a business in the ratio 3:10.

a

What fraction did Kathleen contribute?

b

If Kathleen has invested \$2100, how much did Luke invest?

10

At a sporting event, the ratio of security personnel to spectators is 1:180. If 34\,200 spectators attend the event, how many security personnel will be required?

11

Two kinds of pine trees, type A and type B, are planted in rows. In each row the ratio of type A to type B is 9:8 Altogether, 180 type A trees are planted.

How many type B trees are planted?

12

Xavier and Ursula split the cost of the groceries in the ratio 0.5:1.5. Altogether the groceries cost \$140.

a

Simplify the ratio.

b

How much did Xavier pay for the groceries?

13

A car and a truck are driving down the highway. Their relative speeds are in the ratio \\ 3.1:2.9. If the car is travelling at 93\text{ km/hr}, how fast is the truck travelling?

14

In a zoo the ratio of elephants to lions is 7:4.

a

Find the ratio of elephants to lions to the total number of elephants and lions.

b

Complete the following table of equivalent ratios:

ElephantstoLionstoTotal
7:4:
14::
::110
c

If there are 66 elephants and lions altogether, how many lions are there?

15

The ratio of red, green and black coloured area on a dart board is 12:7:31. The area of the dart board is 150\text{ cm}^2 .

a

Find the number of ratio parts corresponding to the following:

i

Red area

ii

Green area

iii

Black area

iv

Total area

b

Find the size of a single ratio part.

c

Find the area of the following:

i

Red area

ii

Green area

iii

Black area

16

Vanessa competed in a marathon and found that her times for the swimming, cycling and running parts were in the ratio 3:1:2. If the quickest part took 10 minutes, how many minutes did she take to complete the whole marathon?

17

The ratio of students who play badminton, football and softball is 2:5:9.

a

If there are 72 students who play softball, how many students play badminton?

b

Find the total number of students who play one of these sports.

18

The perimeter of a rectangle is 42\text{ cm} and the ratio of its length to its width is 4:3.

a

How many parts are in the ratio?

b

Find the length of the rectangle.

c

Find the width of the rectangle.

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operates with ratios and rates, and explores their graphical representation

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