Fifth Grade Math Course I

Fifth Grade
Math Course I
Ratio, Proportion, and Percent
1
Ratios
 A ratio is a comparison of numbers
that can be expressed as a fraction.
 If there were 18 boys and 12 girls in

a class, you could compare the
number of boys to girls by saying
there is a ratio of 18 boys to 12 girls.
You could represent that comparison
in three different ways:
 18 to 12
 18 : 12
 18 2
12
Ratios
 The ratio of 18 to 12 is another

way to represent the fraction 18
12
 All three representations are
equal.
18
 18 to 12 = 18:12 = 12
 The first operation to perform on
a ratio is to reduce it to lowest
terms ÷6
18 3
 18:12 = =
12 2
÷6
 18:12 = 3 = 3:2 3
2
Ratios
 A basketball team wins 16 games

and loses 14 games. Find the
reduced ratio of:
 Wins to losses – 16:14 = 16 = 8
14 7
14 7
 Losses to wins – 14:16 = =
16 8
 Wins to total games played –

16:30 = 16 = 8
30 15
 The order of the numbers is critical 4

Ratios
 A jar contains 12 white, 10 red

and 18 blue balls. What is the
reduced ratio of the following?
 White balls to blue balls?
 Red balls to the total number of
balls?
 Blue balls to balls that are not blue?
5
Proportions
 A proportion is a statement that

one ratio is equal to another
ratio.
 Ex: a ratio of 4:8 = a ratio of 3:6
1 3 1
 4:8 = 4 = and 3:6 = 6 = 2
8 2
 4:8 = 3:6
 4 = 3
8 6
 These ratios form a proportion

since they are equal to other. 6
Proportions
 In a proportion, you will notice

that if you cross multiply the
terms of a proportion, those
cross-products are equal.
4 = 3
8 6 4 x 6 = 8 x 3 (both equal 24)
3 = 18
12 3 x 12 = 2 x 18 (both equal 36)
7
2
Proportions
 Determine if ratios form a

proportion
12 and 8
21 14
10 and 20
17 27
3 and 9
8 24
8
Proportions
 The fundamental principle of

proportions enables you to solve
problems in which one number
of the proportion is not known.
 For example, if N represents the

number that is unknown in a
proportion, we can find its value.
9
Proportions
N = 3
12 4
4 x N = 12 x 3 Cross multiply the proportion
4 x N = 36
Divide the terms on both sides of
4xN 36 the equal sign by the number
=
4 4 next to the unknown letter. (4)
1xN=9
That will leave the N on the left
N=9 side and the answer (9) on the
right side 10
Proportions
 Solve for N  Solve for N

2 = N 15 = 3
5 35 N 4
5 x N = 2 x 35
6 = 102
5 x N = 70 7 N
5xN 4 = 6
= 70
5 5 N 27
1 x N = 14
11
N = 14
Proportions
 At 2 p.m. on a sunny day, a 5 ft

woman had a 2 ft shadow, while
a church steeple had a 27 ft
shadow. Use this information to
find the height of the steeple.
5 = H height height
=
2 27 shadow shadow
 2 x H = 5 x 27 You must be careful to place

 2 x H = 135 the same quantities in
corresponding positions in the
 H = 67.5 ft. proportion
12
Proportions
 If you drive 165 miles in 3 hours, how many
miles can you expect to drive in 5 hours
traveling at the same average speed?
 A brass alloy contains only copper and zinc

in the ratio of 4 parts of copper to 3 parts
zinc. If a total of 140 grams of brass is
made, how much copper is used?
 If a man who is 6 feet tall has a shadow

that is 5 feet long, how tall is a pine tree
that has a shadow of 35 feet?
13
Percents
 Percent means out of a hundred
 An 85% test score means that out of 100
points, you got 85 points.
 25% means 25 out of 100
 25% = 25 = 0.25
100
 137% means 137 out of 100

 137% = 137 = 1.37
100
 6.5% means 6.5 out of 100
 6.5% = 6.5 = 0.065
100 14
Converting Percents to
Fractions
 To convert a percent to a fraction,
drop the % sign, put the number
over 100 and reduce if possible
 Express 30% as a fraction
30 3
 30% = 100 = 10 (a reduced fraction)
 Express 125% as a fraction

 125% = 125 = 5 = 1 1
100 4 4
(a reduced mixed number)
15
Converting Percents to
Decimals
 To convert a percent to a
decimal, drop the % sign and
move the decimal point two
places to the left
 Express the percents as a
decimal
 30% = .30
 125 % = 1.25
16
Converting Decimals to
Fractions and Percents
 Convert each percent to a
reduced fraction or mixed
number and a decimal
 17%
 5%
 23%
 236%
 8%
17
Converting Decimals to
Percents
 To convert a decimal to a
percent, move the decimal point
two places to the right and
attach a % sign.
 Ex: 0.34 = 34%
 Ex: 0.01 = 1%
18
Converting Fractions to
Percents
 To convert a fraction to a percent,
divide the denominator of the fraction
into the numerator to get a decimal
number, then convert that decimal to
a percent (move the decimal point
two places to the right)
3 .75
= 4 3.00 = 75%
4
19
Converting Decimals and
Fractions to Percents
 Convert the Decimal to a percent
 .08 = ?
 3.26 = ?
 .75 = ?
 Convert the Fraction to a percent

1
5
7
10 20
Percent of a Number
 Percents are often used to find a part

of a number or quantity
 Ex: “60% of those surveyed”
 Ex: “35% discount”
 Ex: 8.25% sales tax”
 60% of 5690 means 60% x 5690

 35% of $236 means 35% x $236
 8.25% of $180 means 8.25% x $180
 Change the percent into either a fraction
or a decimal before you use it in 21
multiplication
Percent of a Number
 Find 25% of 76 (as a decimal)
 25% = .25
 25% of 76 = .25 x 76 = 1
OR
 Find 25% of 76 (as a fraction)
 25% = 1
4
1
 25% of 76 = x 76 = 19
4
 Find 60% of 3420
 Find 30% of 50
 Find 5% of 18.7 22
Percentage Problems
 On a test you got 63 out of 75
possible points. What percent did
you get correct?
 Since “percent” means “out of a
hundred”, 63 out of 75 is what number
out of 100
63 =
P (P is used to represent the percent or part
75 100 out of 100)
75 x P = 6300 Percent Proportion

75 75
A P
P = 84 B = 100
A is the amount
B is the base (follows the word “of”)
P is the percent (written with the 23
word “percent” or the % sign)
Percentage Problems
 15 is what percent of 50?
 16 is 22% of what number?
 91 is what percent of 364?

Percent Proportion
 What is 9.5% A P
 of 75,000? B = 100
A is the amount
B is the base (follows the word “of”)
P is the percent (written with the
24
word “percent” or the % sign)

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Fifth Grade

Ratio, Proportion, and Percent

 If there were 18 boys and 12 girls in

 The ratio of 18 to 12 is another

 A basketball team wins 16 games

 Wins to total games played –

 The order of the numbers is critical 4

 A jar contains 12 white, 10 red

 A proportion is a statement that

 These ratios form a proportion

 In a proportion, you will notice

 Determine if ratios form a

 The fundamental principle of

 For example, if N represents the

4 x N = 12 x 3 Cross multiply the proportion

 Solve for N  Solve for N

 At 2 p.m. on a sunny day, a 5 ft

 2 x H = 5 x 27 You must be careful to place

 A brass alloy contains only copper and zinc

 If a man who is 6 feet tall has a shadow

 137% means 137 out of 100

 Express 125% as a fraction

 Ex: 0.34 = 34%

 Convert the Fraction to a percent

 Percents are often used to find a part

 60% of 5690 means 60% x 5690

75 x P = 6300 Percent Proportion

 16 is 22% of what number?

 91 is what percent of 364?

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