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MPM 1D
Fractions, Decimals, Percents and Ratios
Part A: A Quick Review of Fractions, Decimals and Percent
1.
To change a decimal to a percent, multiply the decimal by 100.
Write each of the following decimals as a percent.
a) 0.45 = _____%
b) 0.5
e) 1
2.
Name: ___________________
Date: ___________________
c) 0.004
d) 0.596
f) 2.63
To change a fraction to a percent, use one of these methods:
(i) write the fraction as a decimal and multiply by 100.
(ii) find an equivalent fraction with a denominator of 100 and then express the new fraction as a percent.
Write each of the following as a percent.
7
4
a)
b)
10
e)
5
345
f)
100
c)
37
d)
50
28
56
3
2
Part B: Ratios, Equivalent Ratios and Proportions
1.
A ratio compares two numbers with the same units. It is usually written in lowest terms (simplest form).
The numbers in each of the questions a, b, c, d, e, f below are presented in different ways. Each different way
represents a different method of showing a ratio. NOTE that one of the ways of writing a ratio is as a
fraction! This means that ratios can also be written as decimals and as percent values, too!
Refer to the table below to explain what each of the ratios in a, b, c, d, e, f means. The first one is done for
you as an example.
Job
Number of Students
Lifeguard
1
Delivering flyers
3
Fast-food restaurant worker
4
Babysitter
6
a) one to six This is the ratio of lifeguards to babysitters.
b) 3:4
c)
3
14
d) 6:4
e)
4
1
f) 25%
2.
This is the ratio of _________________________ to ______________________.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
Write each ratio in simplest form.
9
a)
b) 8:10
d) three to three
e)
12
6
4
c) five to fifteen
f) 18:8
3.
When it is written in simplest form, a ratio between two numbers has the same units. So, often the units in the
simplest form ratio are not shown.
Write each of the following ratios in simplest form. The first one is done for you as an example.
a)
50 cm to 1 m
d)
2 h to 30 min
50 cm to 100 cm
1 cm to 2 cm
Ratio in simplest form is
1:2
4.
b)
75¢ to $1.25
e)
c)
5 weeks to 5 days
25 mL to 1 L
(1000 mL = 1L)
Ratios that make the same comparison are equivalent ratios or equal ratios.
For each ratio, write TWO equivalent ratios. The first one is done for you as an example.
4
a) 1:4
FIVE equivalent ratios to this ratio could be 2:8 or 3:12 or 0.25 to 1.00 or
or 25%:100%
16
5.
b) 6 to 3
d)
c) 3:7
e)
10
4
0.2
0.5
This time, write each ratio as a percent. The first one is done for you as an example.
𝟕𝟑
a) 73:100 This ratio can be written as
𝒐𝒓 73%.
d) 9:10
𝟏𝟎𝟎
6.
b) 7:100
e)
3:1
c) 3:5
f)
5:4
Complete the table.
Ratio
a)
13:20
Fraction
Decimal
3
4
b)
c)
0.02
9
25
d)
90%
e)
6.
Percent
125%
A statement that ratios are equal is called a proportion. A proportion can be used to solve for a missing value
in one of the equivalent ratios.
Solve each of the following proportions to determine the value 𝑥.
a)
𝑥
16
=
1
4
𝑥 = ______
b)
3
4
=
75
𝑥
𝑥 = ______
c) 4: 𝑥 = 2: 5
𝑥 = _______
Part C: Using Ratios and Proportions to Solve Problems
1. Solve each of the following word problems using your knowledge of ratios and proportions. The first one is
done for you as an example.
a) Six bags of cement are mixed with four bags of sand to make concrete. How many bags of cement are
needed to mix with 12 bags of sand?
Solution:
(i) Write the ratio of cement to sand
6 bags of cement : 4 bags of sand
(ii) Use the ratio from (i) above to write a proportion involving 12 bags of sand.
𝟔
𝒙
=
𝟒
𝟏𝟐
(iii) Solve the proportion for the number of bags of cement needed to mix with 12 bags of sand.
×3
𝟔
𝟒
=
𝒙
𝟏𝟐
𝒙 = 𝟏𝟖
×3
(iv) Write a sentence to present your final solution.
Twelve bags of sand will have to be mixed with 18 bags of cement.
b)
Scientists estimate that 8 out of every 9 people are right-handed. In a school of 360 students, how many
students would you expect to be right handed?
c)
Alice plays on the basketball team. On average, she makes 1 basket for every 3 shots she takes.
Assuming her average shot ratio holds, determine the number of baskets she will likely make out of 138
shots.
d)
Here is some information about televisions.



Traditional televisions have a ratio of width to height of 4:3.
Television sizes are given as the length of the diagonal of the screen. So, a 27-inch
television is 27 inches from one corner to the diagonally opposite corner.
There is an optimal distance for a person to sit from a television for ideal viewing. The
ratio of the size of a television screen (the length of the diagonal) to the distance a
person should sit from the screen is 1:6.
Darren wants to buy a new television. He finds a traditional television for a good price. He measures its
width as 24 inches and determines that its diagonal is 30 inches.
(i) Determine the height of the television in inches.
(ii) Determine the optimal distance for Darren to sit from his television for ideal viewing. Give
your final answer in units of feet. Note that 12 inches = 1 foot.
Part D: Using Ratios and Proportions In Solving Percent Problems
You may need to use a calculator for some of these problems.
1. Solve. The first one is done for you as an example.
a) Find 60% of 120.
Solution:
(i) Write a proportion.
60
𝑥
=
100 120
(ii) Method 1: Using your knowledge of equivalent fractions/ratios, solve for x.
× 1.2
𝑥 = 60 × 1.2
= 72
60
𝑥
=
100 120
× 1.2
Method 2: Make 60% into a decimal, then multiply the decimal by 120 to find 60% of 120.
60% =
60
100
𝑜𝑟 0.60
And 60% of 120 = 0.60 x 120
= 72
(iii) Write a summary sentence to present the final solution.
60% of 120 is 72.
b) Find 48% of 600.
c) Find 9% of $3.00.
d) Find 325% of 88.
2.
Solve.
a) What percent of 300 is 75?
b) What percent of 70 is 35?
÷3
𝑥
=
100
75
300
𝑥 is 25. So, 75 is 25% of 300.
÷3
c) What percent of 144 is 18?
3.
d) What percent of 660 is 66?
Solve.
a) 25% of a number is 150. What is the number?
×6
25
150
=
100
𝑥
b) 5% of a number is 20. What is the number?
X = 600
So the number is 600.
×6
c) 20% of a number is 5. Find the number.
4.
Fill in the table.
Original Price
$4.50
Discount as
a % of original price
10%
$54.20
20%
$2.79
17%
d) 125% of what number is 45?
Sale Price
Sale price = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 − $ 𝑜𝑓 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
Sale price = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 − (% 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 × 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒)
= $4.50 − (10% × $4.50)
= $4.50 − (0.10 × $4.50)
= $4.05 So, the sale price is $4.05.
5.
Fill in the table.
Original Price
$4.50
Markup as
a % of original price
10%
$54.20
20%
$2.79
17%
New Selling Price
new price = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 + $ 𝑚𝑎𝑟𝑘𝑢𝑝
new price = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 + (% 𝑚𝑎𝑟𝑘𝑢𝑝 × 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒)
= $4.50 + (10% × $4.50)
= $4.50 + (0.10 × $4.50)
= $4.95 So, the new price is $4.95.
6.
William scored 48% of the 50 points his team scored in a basketball game. How many points did he score?
7.
Gillian’s got 14 marks of a possible 20 marks correct on her test. Determine the test mark as a percentage.
8.
An electronic toy sells usually for $55 but right now there is a $5.00 rebate from the manufacturer. Determine the
percent of the discount from the manufacturer to the nearest tenth of a percent.