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7-1 Ratios and Proportions
Pre-Algebra Homework
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Pre-Algebra
7-1
7-1 Ratios
Ratiosand
andProportions
Proportions
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
7-1 Ratios and Proportions
Warm Up
Write each fraction in lowest terms.
1. 14
16
7
8
2. 24
64
3
8
3. 9
72
1
8
4. 45
120
3
8
Pre-Algebra
7-1 Ratios and Proportions
Problem of the Day
A magazine has page numbers from 1
to 80. What fraction of those page
numbers include the digit 5?
17
80
Pre-Algebra
7-1 Ratios and Proportions
Today’s Learning Goal Assignment
Learn to find
equivalent ratios
to create
proportions.
Pre-Algebra
7-1 Ratios and Proportions
BrainPOP Videos
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Pre-Algebra
7-1 Ratios and Proportions
Vocabulary
ratio
equivalent ratio
proportion
Pre-Algebra
7-1 Ratios and Proportions
Relative density is the ratio of the density of a
substance to the density of water at 4°C. The
relative density of silver is 10.5. This means that
silver is 10.5 times as heavy as an equal volume
of water.
The comparisons of water to silver in the table
are ratios that are all equivalent.
Comparisons of Mass of Equal Volumes
of Water and Silver
Water
1g
2g
3g
4g
Silver
10.5 g
21 g
31.5 g
42 g
Pre-Algebra
7-1 Ratios and Proportions
Reading Math
Ratios can be written in several ways. A colon is
often used. 90:3 and 90 name the same ratio.
3
Pre-Algebra
7-1 Ratios and Proportions
A ratio is a comparison of two quantities by
division. In one rectangle, the ratio of shaded
squares to unshaded squares is 7:5. In the other
rectangle, the ratio is 28:20. Both rectangles
have equivalent shaded areas. Ratios that make
the same comparison are equivalent ratios.
Pre-Algebra
7-1 Ratios and Proportions
Additional Example 1: Finding Equivalent Ratios
Find two ratios that are equivalent to each
given ratio.
Multiply or divide the
numerator by the same
A. 9 = 9 • 2 = 18
27 27 • 2 54
nonzero number.
9
9 ÷ 9 =1
Two ratios equivalent
=
27 27 ÷ 9 3
to 9 are 18 and 1 .
27
54
3
64 = 64 • 2 = 128
B. 24
24 • 2
48
64 = 64 ÷ 8 = 8
24 ÷ 8
24
3
Pre-Algebra
Two ratios equivalent
to 64 are 128 and 8 .
24
48
3
7-1 Ratios and Proportions
Try This: Example 1
Find two ratios that are equivalent to each
given ratio.
Multiply or divide the
numerator by the same
A. 8 = 8 • 2 = 16
16 16 • 2 32
nonzero number.
8
8 ÷ 4 =2
Two ratios equivalent
=
16 16 ÷ 4 4
to 8 are 16 and 2 .
16
32
4
32 =
B. 16
32 =
16
Pre-Algebra
32 • 2
= 64
16 • 2
32
32 ÷ 8
=4
16 ÷ 8
2
Two ratios equivalent
to 32 are 64 and 4 .
16
32
2
7-1 Ratios and Proportions
Ratios that are equivalent are said to be
proportional, or in proportion. Equivalent
ratios are identical when they are written in
simplest form.
Pre-Algebra
7-1 Ratios and Proportions
Additional Example 2: Determining Whether Two
Ratios are in Proportion
Simplify to tell whether the ratios form a
proportion.
A. 3 and 2
27
18
3
3 ÷ 3 =1
=
27 27 ÷ 3 9
2
2 ÷ 2 =1
=
18 18 ÷ 2 9
B. 12 and 27 12 = 12 ÷ 3 = 4
15
36 15 15 ÷ 3 5
27 = 27 ÷ 9 3
36 36 ÷ 9 = 4
Pre-Algebra
1= 1
Since
,
9 9
the ratios are in
proportion.
Since 4  3 ,
5 4
the ratios are not
in proportion.
7-1 Ratios and Proportions
Try This: Example 2
Simplify to tell whether the ratios form a
proportion.
A. 3 and 9
15
45
3
3÷3= 1
=
15 15 ÷ 3
5
9
9÷9= 1
=
45 45 ÷ 9 5
B. 14 and 16
49
36
14 = 14 ÷ 7 2
49 49 ÷ 7 = 7
16 = 16 ÷ 4 4
36 36 ÷ 4 = 9
Pre-Algebra
1= 1
Since
,
5 5
the ratios are in
proportion.
Since 2  4 ,
7 9
the ratios are not
in proportion.
7-1 Ratios and Proportions
Additional Example 3: Earth Science Application
At 4°C, four cubic feet of silver has the same
mass as 42 cubic feet of water. At 4°C,
would 210 cubic feet of water have the same
mass as 20 cubic feet of silver?
? 20
4 =
42
210
? 20 ÷ 10
4÷2 =
42 ÷ 2
210 ÷ 10
2 = 2
21
21
Pre-Algebra
Since 2 = 2 ,
21
21
210 cubic feet of water
would have the same mass
at 4°C as 20 cubic feet of
silver.
7-1 Ratios and Proportions
Try This: Example 3
At 4°C, two cubic feet of silver has the same
mass as 21 cubic feet of water. At 4°C,
would 105 cubic feet of water have the same
mass as 10 cubic feet of silver?
? 10
2 =
21
105
? 10 ÷ 5
2 =
105 ÷ 5
21
2 = 2
21
21
Pre-Algebra
Since 2 = 2 ,
21
21
105 cubic feet of water
would have the same mass
at 4°C as 10 cubic feet of
silver.
7-1 Ratios and Proportions
Lesson Quiz: Part 1
Find two ratios that are equivalent to each
given ratio.
1. 4
15
Possible answer: 8 , 12
30 45
2. 8
Possible answer: 16 , 24
42 63
21
Simplify to tell whether the ratios form a
proportion.
3. 16 and 32 8 = 8; yes
20 5 5
10
4. 36 and 28
18
24
Pre-Algebra
3 14 ; no
2 9
7-1 Ratios and Proportions
Lesson Quiz: Part 2
5. Kate poured 8 oz of juice from a 64 oz bottle.
Brian poured 16 oz of juice from a 128 oz bottle.
What ratio of juice is missing from each bottle?
Are the ratios proportional?
8 and 16 ; yes, both equal 1
8
64
128
Pre-Algebra