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4.02 Simplify ratios

Worksheet
Ratios as fractions
1

Write the following ratios as fractions in simplest form:

a
20 \text{ to } 25
b
54 \text{ to } 24
c
75 \text{ to } 90
d

\$179 \text{ to } \$449

e

5.4 \text{ to } 7.2

f

0.6 \text{ to } 2.4

g

45\text{ hours to } 40 \text{ hours}

h

3\text{ hours and } 30 \text{ mins to } 5 \text{ hours}

i

\$1.90 \text{ to } \$8.40

j

6\dfrac{1}{4} \text{ to } 9\dfrac{3}{8}

2

Write the following fractions as ratios of integers:

a
\dfrac{7}{35}
b
\dfrac{11}{8}
c
1\dfrac{2}{5}
d
3\dfrac{2}{5}
3

The ratio \dfrac{2}{3} means the same thing as the ratio \dfrac{3}{2}. Is this statement true or false? Explain your answer.

Equivalent and simplified ratios
4

Simplify the following ratios:

a

48:135

b
7:28
c
7:35
d
42:7
e
46:58
f
10:24
g
18:30
h
400:160
5

Simplify the following ratios:

a
4.2:4.5
b

5.4:0.75

c
0.1:0.05
d
0.9:7.2
6

Simplify the following ratios:

a
\dfrac{3}{7} : \dfrac{8}{7}
b
\dfrac{6}{2} : \dfrac{8}{10}
c
\dfrac{3}{4}:2
d

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

e

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

f

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

g

\dfrac{20}{3}:4

h

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

i

5\dfrac {2}{5}:6

j

1\dfrac {5}{7}: 1\dfrac {9}{11}

7

Simplify the following ratios:

a

13 lemons to 39 lemons

b

6 seconds to 18 seconds

c

15 Newtons to 25 Newtons

d

4 centuries to 350 years

e

32 eggs to 2 dozen eggs

f

3 minutes to 70 seconds

g

28 hours to 5 days

h

5 years to 33 months

8

Simplify the following ratios:

a

40 minutes to 4 hours

b

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

c

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

d

\$0.60 to \$2.20

e

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

9

Consider the ratio \dfrac{2}{5} to \dfrac{16}{25}.

a

What number should be multiplied to both sides of the ratio to cancel out the denominators?

b

Write the ratio \dfrac{2}{5} to \dfrac{16}{25} as a simplified ratio.

c

Hence, write the ratio \dfrac{2}{5} to \dfrac{16}{25} as a fraction in simplified form.

10

Write 13 weeks to 1 year as a fully simplified ratio. Assume 1 year has 52 weeks.

11

For each pair of quantities:

i

Rewrite the two quantities in the same units as whole numbers.

ii

Write the pair of quantities as a simplified ratio.

a

50 cents to \$2.10

b

105 cents to \$1.20

12

For the following, complete the patterns of equivalent ratios by filling in the gaps:

a
\begin{aligned} 2 &: 3 \\ ⬚ &: ⬚ \\ 6 &: 9 \\ 8 &: 12\\ 10 &: ⬚ \end{aligned}
b
\begin{aligned} ⬚ &: 20 \\ 4 &: 16 \\ ⬚ &: 12 \\ ⬚ &: 8\\ 1 &: 4 \end{aligned}
c
\begin{aligned} 18 &: 27 \\ ⬚ &: 21 \\ 10 &: 15 \\ 6 &: ⬚ \\ 2 &: ⬚ \end{aligned}
Applications
13

The table shows the amount of several ingredients in a pack of 150 -gram biscuits:

a

Write the ratio of sugar to fat as a fraction in simplest form.

b

Write the ratio of wheat to milk as a fraction in simplest form.

Number of grams in one pack of biscuits:

fat14 grams
sugar16 grams
milk15 grams
wheat18 grams
14

A bottle contains 27 millilitres of chlorine and 15 millilitres of iodine.

a

Write the ratio of chlorine to iodine as a fraction in simplest form.

b

Write the ratio of iodine to chlorine as a fraction in simplest form.

15

The London Lions had 11 wins and 13 losses in their season.

a

Write the ratio of wins to losses as a fraction in simplest form.

b

Write the ratio of losses to wins as a fraction in simplest form.

16

Xavier and Quiana scored goals in their netball game in the ratio 8:3.

a

Write the total number of parts in the ratio.

b

What fraction of the total number of goals was scored by Xavier?

c

What fraction of the total number of goals was scored by Quiana?

17

A number of building blocks are shared between Elizabeth and Tobias in the ratio 4:3.

a

Write the total number of parts in the ratio.

b

What fraction of the blocks does Elizabeth receive?

c

What fraction of the blocks does Tobias receive?

18

The following table shows the ratio of dogs to cats:

a

Complete the table of equivalent ratios.

b

If there are 270 dogs, how many cats would there be?

c

Simplify the ratio of the number of dogs to cats from part (b).

DogstoCats
9:5
18:10
27:
45:
:50
19

My grandmother's recipe for fruit punch states that 5 cups of apple juice should be mixed with a \dfrac{4}{5} of a cup of lemonade.

Complete the table:

Apple JuiceLemonade
5\dfrac{4}{5}
10\dfrac{8}{5}
15\dfrac{12}{5}
20
25
20

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}}
21

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

a

How many hours did she spend editing the report?

b

Write the ratio of time researching to writing in simplest form.

c

Write the ratio of time writing to editing in simplest form.

d

Write the ratio of time researching to editing in simplest form.

e

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

22

Jimmy is making a patterned lid for a wooden chest. He knows that for every \dfrac{1}{2} metres of mahogony, he needs 40 centimetres of oak.

a

Write the ratio of mahogony to oak in three different ways.

b

How many metres of mahogony would Jimmy need if he wants to use 6 metres of oak?

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Outcomes

1.1.1.2

understand the relationship between fractions and ratio

1.1.1.3

express a ratio in simplest form using whole numbers

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