Transcript 5-1 Ratios and Proportions

5-1
5-1 Ratios
Ratiosand
andProportions
Proportions
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
5-1 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
Course 3
5-1 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
Course 3
5-1 Ratios and Proportions
Learn to find equivalent ratios to create
proportions.
Course 3
5-1 Ratios and Proportions
Vocabulary
ratio
equivalent ratio
proportion
Course 3
5-1 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.
7:5
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28:20
5-1 Ratios and Proportions
Reading Math
Ratios can be written in several ways. 7 to 5,
7:5, and 7 name the same ratio.
5
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5-1 Ratios and Proportions
Additional Example 1: Finding Equivalent Ratios
Find two ratios that are equivalent to each
given ratio.
Multiply or divide the
numerator and
9
9
•
2
18
A.
=
=
denominator by the
27 27 • 2 54
same 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
Course 3
Two ratios equivalent
to 64 are 128 and 8 .
24
48
3
5-1 Ratios and Proportions
Check It Out: Example 1
Find two ratios that are equivalent to each
given ratio.
Multiply or divide the
numerator and
A. 8 = 8 • 2 = 16
denominator by the
16 16 • 2 32
same nonzero number.
8
8 ÷ 4 =2
Two ratios equivalent
=
16 16 ÷ 4 4
to 8 are 16 and 2 .
16
32
4
32 = 32 • 2 =
B. 16
16 • 2
32 = 32 ÷ 8 =
16 ÷ 8
16
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64
32
4
2
Two ratios equivalent
to 32 are 64 and 4 .
16
32
2
5-1 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.
Course 3
5-1 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
Course 3
1= 1
Since
,
9 9
the ratios are in
proportion.
Since 4  3 ,
5 4
the ratios are not
in proportion.
5-1 Ratios and Proportions
Check It Out: 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
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1= 1
Since
,
5 5
the ratios are in
proportion.
Since 2  4 ,
7 9
the ratios are not
in proportion.
5-1 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
4÷2
42 ÷ 2
2
21
Course 3
Since 2 = 2 ,
21
21
210 cubic feet of water
? 20 ÷ 10
=
Divide. would have the same mass
210 ÷ 10
at 4°C as 20 cubic feet of
silver.
= 2
21
5-1 Ratios and Proportions
Check It Out: 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
Since 2 = 2 ,
21
21
105 cubic feet of water
? 10 ÷ 5
2 =
Divide. would have the same mass
105 ÷ 5
21
at 4°C as 10 cubic feet of
silver.
2 = 2
21
21
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5-1 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
Possible answer: 16 , 24
2. 8
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
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3 14 ; no
2 9
5-1 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
Course 3