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A ratio is the comparison of
two whole numbers written in
the same unit.
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Example:
Your school’s basketball team has won 7 games and
lost 3 games. What is the ratio of wins to losses?
Because we are comparing wins to losses the first
number in our ratio should be the number of wins
and the second number is the number of losses.
7
games won = _______
7 games = __
The ratio is ___________
3 games 3
games lost
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A comparison of two whole numbers in the same units.
4 carnations to 9 roses
4 Possible Ways to Write a Ratio
4
4 : 9 4 to 9
9
sometimes . . . 4 out of 9
as in 4 carnations out of 9 roses
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The Giant One is used to reduce ratios.
4
÷
10
2
2
=
2
5
A ratio is in simplest form, or is reduced if
the numerator and denominator have no
common factors other than one.
3 1
3
÷ =
4 1
4
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Ratios can be simplified (reduced), this
is called simplest form. To find the
simplest form divide the numerator and
denominator by the greatest common
factor.
12 6
2
÷ =
18 6
3
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Put each ratio in simplest form.
1)
40
8
1
=
= 1
35
7
7
2)
16
4
=
3
12
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Put each ratio in simplest form.
3) 36 out of 42
4) 24 to 6
36
6
=
42
7
24
4
=
6
1
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Write the ratio 3 yards to 12 feet in simplest form.
First convert yards to feet.
3 yards = 3 ● 3 feet There are 3 feet in a yard.
= 9 feet
Multiply.
Now write the ratio.
3 yards = 9 feet = 9 ÷ 3 = 3
12 ÷ 3 4
12 feet
12 feet
The ratio is 3 , 3:4, or 3 to 4.
4
Simplify.
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Write the ratio 36 inches to 4 feet in simplest form.
First convert feet to inches.
4 feet = 4 ● 12 inches
There are 12 inches in a foot.
= 48 inches Multiply.
Now write the ratio.
36 inches = 36 inches = 36 ÷ 12= 3
4 feet
48 inches 48 ÷ 12 4
The ratio is 3 , 3:4, or 3 to 4.
4
Simplify.
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You must
always use
the same
unit of
measure!
Put each ratio in simplest form.
1)
3 weeks 21 days
=
5 days
5 days
21
=
5
2) 32 inches = 32 inches
1 foot
12 inches
32
8
=
12
3
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Write the ratio 15 bikes to 9 skateboards in
simplest form.
Write the ratio as a
bikes = 15
fraction.
9
skateboards
=
15 ÷ 3
9÷3
=
5
3
Simplify.
The ratio of bikes to skateboards is 5:3,5 to 3, or 5
3
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Write the ratio 24 shirts to 9 jeans in simplest
form.
Write the ratio as a
shirts = 24
fraction.
9
jeans
=
24 ÷ 3
9÷3
=
8
3
Simplify.
The ratio of shirts to jeans is 8:3, 8 to 3, or 8
3
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The GIANT ONE is used to simplify ratios.
4
÷
10
2
2
=
2
5
16
÷
20
4
4
=
4
5
To determine if two ratios are equivalent
simplify each ratio by dividing.
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Simplify to tell whether the ratios are
equivalent.
3 and 2
27
18
3 = 3 ÷ 3 =1
27 27 ÷ 3 9
2 = 2 ÷ 2 =1
18 18 ÷ 2 9
1 1
Since 9= 9 ,
the ratios are
equivalent.
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Simplify to tell whether the ratios are
equivalent.
12 and 27 12 = 12 ÷ 3 4
=
15
36 15 15 ÷ 3 5
27 = 27 ÷ 9 3
=
36 36 ÷ 9 4
4 3
Since 5 ≠4 ,
the ratios are
not equivalent.
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A ratio that compares two
quantities with different units of
measure is called a rate.
Examples: $23 per foot
55 mph
$5/ per person
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20 in. 20 in.
5
=
=
3 ft.
36 in.
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A comparison of two
whole numbers in the
same units.
Always written as
two numbers.
3
4 : 9 15 to 1
2
Never write the units.
Reduce to simplify.
300 mi.
= 60 mi. / hr.
5 hr.
A comparison of a number
to one in different units.
Always written as a single
number on a per unit basis.
30.7 words / min .
3 children / family
Always write the units.
Divide to simplify.
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Rates are simplified by writing them as a unit rate.
A unit rate has a second term that is a single unit.
Example: 10 people can read a total of 50 pages.
50 pages for 10 people
5 pages for 1 person.
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A unit rate when you have a denominator of 1
Your family drove 200 miles in 5 hours. The total
amount of fuel used was 10 gallons of gas.
What was the average rate of fuel consumption?
miles
gallons
200 miles
10 gallons
=
20 miles
1 gallon
2) What was the average rate of speed?
miles
hour
200 miles
5 hours
=
40 miles
1 hour
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Find the unit rate:
Amount per one
1) 84 students in 4 classrooms
84 students
= 21 students / classroom
4 classrooms
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Find the unit rate:
Amount per one
2) $30 for 6 lunches
$30
= $5.00 / lunch
6 lunches
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Find the unit rate:
Amount per one
3) 10,000 cars sold by 2000 dealers
10, 000 cars
= 5 cars /1 dealer
2000 dealers
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Take Out Your Study Guide!!!
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Ratios
#1
A ratio is a comparison of two whole
numbers in the same unit.
4 Possible Ways to Write a Ratio
5
7
5: 7
5 to 7
5 girls to 7 boys
You solve a ratio by simplifying the fraction.
4
÷
10
2
2
=
2
5
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#2 EQUIVALENT RATIOS
To determine if two ratios are equivalent
simplify each ratio by dividing.
3 and 9
15
45
3
15
9
45
÷3 =
÷3
1
5
÷9 =
÷9
1
5
1 1
Since = ,
5 5
the ratios are
equivalent.
The GIANT ONE is used to simplify ratios.
16
÷
20
4
4
=
4
5
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#3
Ratios in Simplest Form
To find the simplest form divide the numerator
and denominator by the GCF.
Write the ratio 15 bikes to 9 skateboards in
simplest form.
bikes
skateboards
15 Write the ratio as a fraction.
9
15 ÷ 3 = 5 Simplify.
=
3
9÷3
=
The ratio of bikes to skateboards is 5:3, 5 to 3, or 5
3
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