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Middle Years

3.01 Ratios

Worksheet
Equivalent and simplified ratios
1

Simplify the following ratios:

a

30:70

b

300:350

c

21:12

d
10:24
e
48:135
f

0.3:0.45

g

0.21:0.56

h

0.012:0.028

i
0.1:0.05
j
0.9:7.2
k
1:0.7
l
0.75:2
m

\dfrac{3}{4}:\dfrac{7}{12}

n

\dfrac{1}{5}:\dfrac{8}{9}

o
\dfrac{20}{3}:4
p
7\dfrac{2}{9}:6
q
5.4:0.75
r
4.2:4.5
s
12:45:18
t
3:2.4:0.45
2

Complete the following equivalent ratios:

a

⬚:8 = 1:5

b

⬚:3 = 5:2

c

⬚:2 = 48:16

d

⬚:30 = 4:1

e

⬚:6 = 7:8

f

9:4 = ⬚:5

g

7:4 = ⬚:22

h

7:9 = 88:⬚

i
9:8 = ⬚:32
j
⬚:5 = 132:60
k
0.4:⬚ = 10:28
l
1.8:3 = 27:⬚
3

The ratio of length to width of a company's logo is 4:5. Complete the following table for the given lengths and widths:

Length (m)134
Width (m)0.5517
4

Express the following as a simplified ratio:

a

50 cents to \$2.10

b

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

c

5 years to 33 months

d

624 hours to 71.5 days

Divide quantities in a given ratio
5

Find the total number of parts in the following ratios:

a

2:3

b

7:17

c

20:3

d

73:53

6

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

a

What fraction of the money does John receive?

b

How much money will John receive?

7

20 is divided into two parts, A and B, in the ratio 3:2.

a

Find the value of A.

b

Find the value of B.

8

The ratio of people to chairs is 7:8. If there are 49 people, how many chairs are there?

9

The ratio of cats to dogs is 56:231. If there are 33 dogs, how many cats are there?

10

A salad dressing is supposed to have a 5:16 ratio of vinegar to oil. If there are 13\text{ mL} of vinegar, how many millilitres of oil should be added?

11

The gas in a container consists of 3 parts oxygen and 5 parts helium. How many litres of oxygen are present if there are 200 litres of gas in the container?

12

\$15 is shared between Eileen and Luke in the ratio 7:3. How much money does each get?

13

Tom and Jack divide their earnings of \$714 in the ratio 10:7.

a

Find how much Tom receives.

b

Find how much Jack receives.

14

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 money should Dave receive?

b

How much money should Luke receive?

15

There are two celebration dinners happening at Happy Mo's Restaurant. Each has 6 men at the table. At Beth’s birthday table there is a ratio of men to women of 1:3. At Buzz’s table the ratio is 3:1.

a

Find the number of women at Beth's birthday table.

b

Find the number of women at Buzz's table.

c

Find the ratio of the total number of men to the total number of women at the two tables.

16

Quentin is making a scarf that uses two materials. He will have to use \dfrac{3}{10}\text{ m} of green material for every \dfrac{2}{5}\text{ m} of blue material.

a

Write the simplified ratio of green to blue material.

b

If he needs 15\text{ m} of green material, how many metres of blue material will he need?

17

The movement of Earth and Venus orbiting the Sun is compared. It takes the 8-Earth years and 13-Venus years to go around the sun before they are both at their starting positions.

a

Write the ratio of the number of Earth years to the number of Venus years.

b

One Earth year consists of approximately 365.25 Earth days. How many Earth days make up one Venus year? Round your answer to two decimal places.

18

A piece of rope is cut into three lengths in the ratio 3:4:8. The shortest length of rope is measured to be 18 \, \text{m} long.

a

Find the middle length of the rope.

b

Find the longest length of the rope.

c

Find the total length of the rope.

19

All students in a school play sport on Friday afternoons. The ratio of students who play tennis, soccer and rugby is 3:8:11.

a

If there are 55 students who play rugby, how many students play tennis?

b

How many students play sports on Friday afternoons?

20

Three siblings find 700\, \text{kg} of treasure. They split it up in the ratio 1:4:9. The youngest sibling receives the smallest portion, and the oldest sibling receives the largest.

a

How much treasure will the youngest receive?

b

How much treasure will the eldest sibling receive?

c

After some negotiation, the oldest sibling gives up one share of her treasure to her youngest sibling. Write the new ratio for the division of treasure in simplest form.

21

Roxanne is mixing red, blue and yellow paint in a container. The tub of paint is filled to 300 \, \text{mL}. She remembers that she added 60 \, \text{mL} of red paint and that the ratio of red to blue paint is 4:7.

a

How much blue paint did she use?

b

How much yellow paint did she use?

c

She wants to find the full ratio of red to blue to yellow paint so she can mix it again. Write the new triple ratio.

22

There are three exoplanets orbiting the star Kepler-37. The planets are named Kepler-37b, Kepler-37c, and Kepler-37d. The number of times each exoplanet orbits the star before they are all at their starting positions is shown in the following table:

Planet\text{Kepler-37c}\text{Kepler-37b}\text{Kepler-37d}
Number of orbits8155
a

Write the triple ratio ratio of the number of orbits for Kepler-37b to Kepler-37c to Kepler-37d.

b

The entire cycle takes approximately 199 Earth days for all three exoplanets to return to their starting position. How many Earth days make up one orbit of Kepler-37d?

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