# Lesson 5 3 Identifying and Writing Proportions Class Notes by S21VtHr

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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.
Evaluate.
1. 18 miles in 3 hours
3(15 – 6) + (18 – 12)2
6 mi/h
2. 6 apples for \$3.30      A. 36
\$0.55 per apple
3. 3 cans for \$0.87        B. 45
\$0.29 per can           C. 63
4. 5 CDs for \$43
\$8.60 per CD            D. 75

Holt CA Course 1
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
Fractions     6
and 25 . Since both ratios
15
simplify   to 5, they are equivalent.
3
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
6   15
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

24 ÷ 3    8      Simplify   24
=                    51
51 ÷ 3   17

72 ÷ 8   9                  72
=        Simplify
128 ÷ 8   16                128

Since     8 ≠ 9 , the ratios are not proportional.
17  16

Holt CA Course 1
5-3 Identifying and Writing Proportions
Example 2: Comparing Ratios in Simplest Forms

Determine whether the ratios are proportional.

150 ,         90
105           63

150 ÷ 15   10        Simplify   150
=                      105
105 ÷ 15    7

90 ÷ 9   10                    90
=            Simplify
63 ÷ 9    7                    63

10 10
Since         =   , the ratios are proportional.
7   7

Holt CA Course 1
5-3 Identifying and Writing Proportions
Check It Out! Example 3

Determine whether the ratios are proportional.
54 , 72
63 144
54 ÷ 9   6         Simplify   54
=                      63
63 ÷ 9   7

72 ÷ 72 1
=           Simplify    72
144 ÷ 72 2                     144

6   1
Since         ≠   , the ratios are not proportional.
7   2

Holt CA Course 1
5-3 Identifying and Writing Proportions
Check It Out! Example 4

Determine whether the ratios are proportional.
135 , 9
75   4

135 ÷ 15   9         Simplify   135
75 ÷ 15 =                       75
5

9     9 is already in simplest form.
4     4

9   9
Since         ≠   , the ratios are not proportional.
5   4

Holt CA Course 1
5-3 Identifying and Writing Proportions
Example 5: Comparing Ratios Using a Common Denominator
Directions for making 12 servings of rice
call for 3 cups of rice and 6 cups of     Servings Cups of Cups of
water. For 40 servings, the directions    of Rice   Rice   Water
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
Ratio of rice to water, 12 servings:       6    Write the ratio as a fraction.
10
Ratio of rice to water, 40 servings:            Write the ratio as a fraction.
19
Write the ratios with a
3 = 3 · 19      = 57       10 = 10 · 6 = 60
common denominator,
6   6 · 19        114      19   19 · 6   114     such as 114.
57     60
Since       ≠     , 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.
4
Ratio of beans to water, 8 servings:             Write the ratio as a fraction.
3
13
Ratio of beans to water, 35 servings:            Write the ratio as a fraction.
9
Write the ratios with a
4 = 4·3     = 12              13       common denominator,
3   3·3       9                9       such as 9.

Since 12 ≠ 13 , the two ratios are not proportional.
9      9

Holt CA Course 1
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
5    10 Write a proportion.
B. 28
16               Divide both the
28 = 28 ÷ 4 = 7 numerator and
denominator by any
16 16 ÷ 4     4
number, such as 4.
28 = 7
16    4 Write a proportion.

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
3    9 Write a proportion.
B. 16
12              Divide both the
16 = 16 ÷ 4 = 4 numerator and
12 12 ÷ 4     3 denominator by any
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                    12 10
1. 30 , 40                   2. 21 , 15
3 , 3 ; proportional        4 , 2 ; not proportional
10 10                       7 3

Find a ratio equivalent to each ratio. Then use
the ratios to write a proportion.

3   15 ; 3 = 15         4. 3    9 ; 3 = 9
3.    8   40   8   40            7   21 7     21

Holt CA Course 1
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
1    4

Holt CA Course 1

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