Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Find the unit rate. 1. 18 miles in 3
hours 2. 6 apples for 3.30 3. 3 cans for
0.87 4. 5 CDs for 43
6 mi/h
0.55 per apple
0.29 per can
8.60 per CD
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Problem of the Day Bob made a square table top
with 100 white square tiles. He painted the tiles
along the edge of the table red. How many tiles
are red?
36
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Learn to find equivalent ratios and to identify
proportions.
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Vocabulary
equivalent ratios proportion
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Students in Mr. Howells math class are measuring
the width w and the length l of their faces. The
ratio of l to w is 6 inches to 4 inches for Jean
and 21 centimeters to 14 centimeters for Pat.
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These ratios can be written as the
fractions and . Since both simplify
to , they are equivalent. Equivalent
ratios are ratios that name the same
comparison.
6 4
21 14
3 2
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An equation stating that two ratios are
equivalent is called a proportion. The equation,
or proportion, below states that the ratios
and are equivalent.
6 4
21 14
21 14
6 4

Reading Math
Read the proportion by saying six is
to four as twenty-one is to fourteen.
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If two ratios are equivalent, they are said to be
proportional to each other, or in proportion.
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Additional Example 1A Comparing Ratios in
Simplest Forms
Determine whether the ratios are proportional.
24 51
72 128
,
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Additional Example 1B Comparing Ratios in
Simplest Forms
Determine whether the ratios are proportional.
150 105
90 63
,
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Check It Out Example 1A
Determine whether the ratios are proportional.
54 63
72 144
,
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Check It Out Example 1B
Determine whether the ratios are proportional.
135 75
9 4
,
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Additional Example 2 Comparing Ratios Using a
Common Denominator
Directions for making 12 servings of rice call
for 3 cups of rice and 6 cups of water. For 40
servings, the directions call for 10 cups of rice
and 19 cups of water. Determine whether the
ratios of rice to water are proportional for both
servings of rice.
Write the ratios of rice to water for 12 servings
and for 40 servings.
3 6
Ratio of rice to water, 12 servings
Write the ratio as a fraction.
10 19
Ratio of rice to water, 40 servings
Write the ratio as a fraction
Write the ratios with a common denominator,
such as 114.
3 6
10 19
60 114
3 19 6 19
57 114
10 6 19 6




57 114
60 114
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Check It Out Example 2
Use the data in the table to determine whether
the ratios of beans to water are proportional for
both servings of beans.
Write the ratios of beans to water for 8 servings
and for 35 servings.
4 3
Ratio of beans to water, 8 servings
Write the ratio as a fraction.
13 9
Ratio of beans to water, 35 servings
Write the ratio as a fraction
Write the ratios with a common denominator,
such as 27.
4 3
4 9 3 9
36 27
13 9
39 27
13 3 9 3




36 27
39 27
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You can find an equivalent ratio by multiplying
or dividing both terms of a ratio by the same
number.
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Additional Example 3 Finding Equivalent Ratios
and Writing Proportions
Find a ratio equivalent to each ratio. Then use
the ratios to find a proportion. Possible
Answers
3 5
A.
3 5
3 2 5 2
6 10

Multiply both the numerator and denominator by
any number such as 2.

6 10
3 5

Write a proportion.
28 16
B.
Divide both the numerator and denominator by any
number such as 4.
28 16
28 4 16 4
7 4


28 16
7 4

Write a proportion.
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Check It Out Example 3
Find a ratio equivalent to each ratio. Then use
the ratios to find a proportion. Possible
Answers
2 3
A.
2 3
2 3 3 3
6 9
Multiply both the numerator and denominator by
any number such as 3.


6 9
2 3

Write a proportion.
16 12
B.
Divide both the numerator and denominator by any
number such as 4.
16 4 12 4
4 3
16 12


16 12
4 3

Write a proportion.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz Part I
Determine whether the ratios are proportional.
9 30
12 40
12 21
10 15
1.
2.
,
,
Find a ratio equivalent to each ratio. Then use
the ratios to write a proportion.
3 8
3 7
4.
3.
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Lesson Quiz Part II
5. In preschool, there are 5 children for
every one teacher. In another preschool there are
20 children for every 4 teachers. Determine
whether the ratios of children to teachers are
proportional in both preschools.
20 4
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Lesson Quiz for Student Response Systems
1. Determine whether the ratios are
proportional. , A. proportional B. not
proportional
12 20
18 30
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Lesson Quiz for Student Response Systems
2. Determine whether the ratios are
proportional. , A. proportional B. not
proportional
21 56
14 49
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Lesson Quiz for Student Response Systems
2 9
3. Identify a ratio equivalent to . Then use
the ratios to write a proportion. A.
C. B. D.
10 35
5 35
2 9
10 35
2 9
5 35
10 45
5 45
10 45
5 45
2 9
2 9
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Lesson Quiz for Student Response Systems
4 5
4. Identify a ratio equivalent to . Then use
the ratios to write a proportion. A.
C. B. D.
12 15
12 20
4 5
12 15
4 5
12 20
12 18
15 20
12 18
15 20
4 5
4 5
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Lesson Quiz for Student Response Systems
5. In one school, there are 12 students for every
classroom. In another school, there are 36
students for every 4 classrooms. Determine
whether the ratios of students to classrooms are
proportional in both schools. A. C.
? proportional not
proportional B. D. ?
proportional not proportional
12 36
1 3
12 1
36 4
36 3
36 1
12 1
12 4