Transcript Slide 1

5-3 Identifying and Writing Proportions
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
5-3 Identifying and Writing Proportions
Warm Up
Find the unit rate.
1. 18 miles in 3 hours
6 mi/h
2. 6 apples for $3.30
$0.55 per apple
3. 3 cans for $0.87
$0.29 per can
4. 5 CDs for $43
$8.60 per CD
Holt CA Course 1
Evaluate.
3(15 – 6) + (18 – 12)2
A. 36
B. 45
C. 63
D. 75
5-3 Identifying and Writing Proportions
California
Standards
Number Sense (NS1.2) - Interpret and
use ratios in different contexts (e.g.,
batting averages, miles per hour) to show
the relative sizes of two quantities,
using appropriate notations
( a , a to b, a:b ).
b
Holt CA Course 1
5-3 Identifying and Writing Proportions
Objective: You will learn how to
find equivalent ratios and identify
proportions.
Holt CA Course 1
5-3 Identifying and Writing Proportions
Vocabulary
equivalent ratios
proportion
Holt CA Course 1
5-3 Identifying and Writing Proportions
Students are measuring the
width w and the length l of their
heads. The ratio of l to w is 10
inches to 6 inches for Jean and
25 centimeters to 15
centimeters for Pat.
Holt CA Course 1
5-3 Identifying and Writing Proportions
These ratios can be written as the
10
25
and
. Since both ratios
6
15
to 5, they are equivalent.
3
Fractions
simplify
Equivalent ratios are ratios that name the
same comparison.
Holt CA Course 1
5-3 Identifying and Writing Proportions
An equation stating that two ratios are
equivalent is called a proportion. The equation,
or proportion, below states that the ratios 10
6
and 25 are equivalent.
15
10 = 25
15
6
Reading Math
If two ratios are equivalent, they are said to be
proportional to each other, or in proportion.
Holt CA Course 1
5-3 Identifying and Writing Proportions
Example 1: Comparing Ratios in Simplest Forms
Determine whether the ratios are proportional.
24 , 72
51 128
8
24 ÷ 3
=
17
51 ÷ 3
Simplify
24
51
72 ÷ 8
9
=
16
128 ÷ 8
Simplify
72
128
Since
8 ≠ 9 , the ratios are not proportional.
16
17
Holt CA Course 1
5-3 Identifying and Writing Proportions
Example 2: Comparing Ratios in Simplest Forms
Determine whether the ratios are proportional.
150 ,
105
90
63
10
150 ÷ 15
=
7
105 ÷ 15
90 ÷ 9
10
=
7
63 ÷ 9
Since
Holt CA Course 1
Simplify
150
105
Simplify
90
63
10 10
=
, the ratios are proportional.
7
7
5-3 Identifying and Writing Proportions
Check It Out! Example 3
Determine whether the ratios are proportional.
54 , 72
63 144
6
54 ÷ 9
=
7
63 ÷ 9
Simplify
54
63
72 ÷ 72 1
=
144 ÷ 72 2
Simplify
72
144
Since
Holt CA Course 1
1
6
≠
, the ratios are not proportional.
2
7
5-3 Identifying and Writing Proportions
Check It Out! Example 4
Determine whether the ratios are proportional.
135 , 9
75
4
135 ÷ 15
9
=
75 ÷ 15
5
9
4
Since
Holt CA Course 1
Simplify
135
75
9 is already in simplest form.
4
9
9
≠
, the ratios are not proportional.
4
5
5-3 Identifying and Writing Proportions
Example 5: Comparing Ratios Using a Common Denominator
Directions for making 12 servings of rice
Servings Cups of Cups of
call for 3 cups of rice and 6 cups of
of Rice
Rice
Water
water. For 40 servings, the directions
call for 10 cups of rice and 19 cups of
12
3
6
water. Determine whether the ratios of
40
10
19
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
Write the ratio as a fraction.
Ratio of rice to water, 12 servings:
6
10
Write the ratio as a fraction.
Ratio of rice to water, 40 servings:
19
3 = 3 · 19
6
6 · 19
Since
= 57
114
10 = 10 · 6 = 60
19
114
19 · 6
Write the ratios with a
common denominator,
such as 114.
57
60
≠
, the two ratios are not proportional.
114
114
Holt CA Course 1
5-3 Identifying and Writing Proportions
Check It Out! Example 6
Use the data in the table to determine whether the ratios of beans
to water are proportional for both servings of beans.
Servings of Beans
Cups of Beans
Cups of Water
8
4
3
35
13
9
Write the ratios of beans to water for 8 servings and for 35 servings.
Ratio of beans to water, 8 servings:
Ratio of beans to water, 35 servings:
4 = 4·3
3
3·3
= 12
9
4
3
13
9
13
9
Write the ratio as a fraction.
Write the ratio as a fraction.
Write the ratios with a
common denominator,
such as 9.
Since 12 ≠ 13 , the two ratios are not proportional.
9
Holt CA Course 1
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5-3 Identifying and Writing Proportions
You can find an equivalent ratio by
multiplying or dividing the numerator
and the denominator of a ratio by the
same number.
Holt CA Course 1
5-3 Identifying and Writing Proportions
Example 7: Finding Equivalent Ratios and Writing Proportions
Find a ratio equivalent to each ratio. Then use the ratios
to find a proportion.
A. 3
Multiply both the
5
numerator and
3
3
·
2
6
=
=
denominator by any
5
5 · 2 10 number, such as 2.
3 = 6
10 Write a proportion.
5
B. 28
Divide both the
16
28 = 28 ÷ 4 = 7 numerator and
denominator by any
16 16 ÷ 4
4
number, such as 4.
28 = 7
4 Write a proportion.
16
Holt CA Course 1
5-3 Identifying and Writing Proportions
Check It Out! Example 8
Find a ratio equivalent to each ratio. Then use the ratios
to find a proportion. Possible Answers:
A. 2
Multiply both the
3
numerator and
2
2
·
3
6
=
=
denominator by any
3
3·3
9 number, such as 3.
2 = 6
9 Write a proportion.
3
B. 16
Divide both the
12
16 = 16 ÷ 4 = 4 numerator and
3 denominator by any
12 12 ÷ 4
number, such as 4.
16 = 4
12
3 Write a proportion.
Holt CA Course 1
5-3 Identifying and Writing Proportions
On-Line
Tutoring
Holt CA Course 1
5-3 Identifying and Writing Proportions
Lesson Quiz: Part I
Determine whether the ratios are proportional.
9
12
1. 30 , 40
3 , 3 ; proportional
10 10
12 10
2. 21 , 15
4 , 2 ; not proportional
7 3
Find a ratio equivalent to each ratio. Then use
the ratios to write a proportion.
3.
3
8
15 ; 3 = 15
40
8
40
Holt CA Course 1
4. 3
7
9 ; 3 = 9
21
21 7
5-3 Identifying and Writing Proportions
Lesson Quiz: Part II
5. In one pre-school, there are 5 children for every
teacher. In another pre-school, there are 20
children for every 4 teachers. Determine whether
the ratios of children to teachers are proportional
in both pre-schools.
5 = 20
4
1
Holt CA Course 1