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Unformatted text preview: Fifth Grade
Fifth
Math Course I
Math
Ratio, Proportion, and Percent 1 Ratios
Ratios A ratio is a comparison of numbers
ratio
that can be expressed as a fraction.
that If there were 18 boys and 12 girls in
If
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:
in
18 to 12 18 : 12 18
12 2 Ratios The ratio of 18 to 12 is another
The
18
way to represent the fraction 12
way
All three representations are
All
equal.
equal. 18
18 18
to 12 = 18:12 = 12 The first operation to perform on
The
a ratio is to reduce it to lowest
terms
terms
÷6
18
=
12 18:12 = 3
2 18:12 = ÷6 = 3:2 3
2 3 Ratios A basketball team wins 16 games
basketball
and loses 14 games. Find the
reduced ratio of:
reduced Wins to losses – 16:14 = 16 = 8
Wins
16:14
14
7 14
7
Losses to wins – 14:16 =
=
Losses
14:16
16
8 Wins to total games played –
Wins
16:30 = 16 = 8
16:30
30
15 The order of the numbers is critical
4 Ratios A jjar contains 12 white, 10 red
ar
and 18 blue balls. What is the
reduced ratio of the following?
reduced White balls to blue balls? Red balls to the total number of
Red
balls?
balls? Blue balls to balls that are not blue? 5 Proportions A proportion is a statement that
proportion
one ratio is equal to another
ratio.
ratio. Ex: a ratio of 4:8 = a ratio of 3:6
3
1 4:8 = 4 = 1 and 3:6 =
=2
6
2
8 4:8 = 3:6
4= 3
8 These
These 6 ratios form a proportion
proportion
6
since they are equal to other.
since Proportions In a proportion, you will notice
In
that if you cross multiply the
cross
terms of a proportion, those
crossproducts are equal.
crossproducts 4
8 = 3
6 3
2 = 18
18
7
12 3 x 12 = 2 x 18 (both equal 36)
12 4 x 6 = 8 x 3 (both equal 24) Proportions Determine if ratios form a
Determine
proportion
proportion
12
12
21
21 and 8
14
14 10
10
17
17 and 20
20
27
27 3
8 and 9
24
24
8 Proportions The fundamental principle of
The
proportions enables you to solve
problems in which one number
of the proportion is not known.
of For example, if N represents the
For
number that is unknown in a
proportion, we can find its value.
9 Proportions
N=
12
12 3
4 4 x N = 12 x 3
12 Cross multiply the proportion 4 x N = 36
36
4xN
4 36
=
4 Divide the terms on both sides
Divide
of the equal sign by the number
next to the unknown letter. (4)
next 1xN=9
N=9 That will leave the N on the left
That
side and the answer (9) on the
right side
right
10 Proportions Solve for N
2=N
5
35
35
5 x N = 2 x 35
35 Solve for N
15
15
N =3
4 5 x N = 70
70 6
7 102
= 102
N 5xN
5 4
N =6
27
27 = 70
5 1 x N = 14
N = 14 11 Proportions At 2 p.m. on a sunny day, a 5 ft
At
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.
find
5
2 =H
27
27 height
height
shadow = height
height
shadow 2 x H = 5 x 27 You must be careful to place
You
2 x H = 135 tche same quantities in in the
orresponding positions
proportion
proportion
H = 67.5 ft.
12 Proportions If you drive 165 miles in 3 hours, how many
If
miles can you expect to drive in 5 hours
traveling at the same average speed?
traveling A brass alloy contains only copper and zinc
brass
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?
made, If a man who is 6 feet tall has a shadow
If
that is 5 feet long, how tall is a pine tree
that has a shadow of 35 feet?
that
13 Percents Percent means out of a hundred
An 85% test score means that out of 100
An
points, you got 85 points.
points,
25% means 25 out of 100
25 = 0.25 25% = 25
100 137% means 137 out of 100 137% = 137 = 1.37
137%
1.37
100 6.5% means 6.5 out of 100 6.5% = 6.5
= 0.065
100 14 Converting Percents to
Converting
Fractions
Fractions To convert a percent to a fraction,
To
drop the % sign, put the number
over 100 and reduce if possible
over Express 30% as a fraction 30% =
30% 30
30
100 = 3
10
10 (a reduced fraction)
(a Express 125% as a fraction 125% = 125 =
100 5
4 =11
4 (a reduced mixed number)
15 Converting Percents to
Converting
Decimals
Decimals To convert a percent to a
To
decimal, drop the % sign and
move the decimal point two
places to the left
places
Express the percents as a
Express
decimal
decimal 30% 125 = .30 % = 1.25
16 Converting Decimals to
Converting
Fractions and Percents
Fractions Convert each percent to a
Convert
reduced fraction or mixed
number and a decimal
number 17% 5% 23% 236% 8%
17 Converting Decimals to
Converting
Percents
Percents To convert a decimal to a
To
percent, move the decimal point
percent move
two places to the right and
attach a % sign.
attach Ex: 0.34 = 34% Ex: 0.01 = 1%
18 Converting Fractions to
Percents
Percents To convert a fraction to a percent,
To
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
percent move
two places to the right)
two
3
4 = .75
4 3.00 = 75% 19 Converting Decimals and
Converting
Fractions to Percents
Fractions Convert the Decimal to a percent .08 =? 3.26 = ? .75 = ? Convert the Fraction to a percent
1
5
7
10
10 20 Percent of a Number Percents are often used to find a part
Percents
of a number or quantity
of
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
Change
or a decimal before you use it in
21
multiplication
multiplication Percent of a Number Find 25% of 76 (as a decimal)
(as
25% = .25 25% of 76 = .25 x 76 = 1
OR
OR Find 25% of 76 (as a fraction)
(as 25% = 1
25%
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
On
possible points. What percent did
you get correct?
you 63
75
75 Since “percent” means “out of a
Since
hundred”, 63 out of 75 is what number
out of 100
out
= P (P is used to represent the percent or part
100 out of 100)
100 75 x P = 6300
75
75
75
75
P = 84
84 Percent Proportion
A
B = P
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? What is 9.5%
What
of 75,000? Percent Proportion
A
B = P
100 A is the amount
B is the base (follows the word “of”)
P is the percent (written with the
word “percent” or 24 % sign)
the ...
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 Winter '08
 JARVIS
 Ratios

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