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Chapter 6 Glencoe Math Connects, Course 2

Solve.

1. Estimate. 3 4 _

5 + 2

1 _

3

2. Subtract. 7 2 _

6 - 4

1 _

8

3. Solve. Check your solution. n _

3 = 7

4. Divide. 2 4 _

5 ÷

7 _

20

5. How many 3 _

4 -inch lengths can be cut from a

12-inch length of ribbon?

6. Test Practice Guy purchased a one-gallon

container of ether for a science experiment.

When he was finished, 1 _

16 of the container was

full. How many fluid ounces of ether did Guy use?

A 8 B 12 C 64 D 120

ANSWERS

1. 6

2. 3 5 _

24

3. 21

4. 8

5. 16

6. D

Use with Lesson

6-1(over Chapter 5)

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P rinter P DF

5-Minute Check

Math Connects, Course 2 123

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A is a comparison of two quantities by division.

Ratios that express the relationship between two

quantities are equivalent ratios.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLE Write Ratios in Simplest Form

APPLES Mr. Gale bought a basket Mr. Gale’s Apples

12 Fuji

9 Granny Smith

30 Red Delicious

of apples. Using the table, write a ratio comparing the Red Delicious apples to the Granny Smith apples as a fraction in simplest form.

Red Delicious 30_9

= 30

10

_ 9 3 or

Granny Smith

The ratio of Red Delicious apples to Granny Smith apples

is .

EXAMPLE Identify Equivalent Ratios

Determine whether the ratios 12 onions to 15 potatoes and 32 onions to 40 potatoes are equivalent.

12 onions : 15 potatoes = 12 ÷ 3__15 ÷ 3

or

32 onions : 40 potatoes = 32 ÷ 8__40 ÷ 8

or

The ratios simplify to the same fraction. They are

.

ORGANIZE ITRecord a term or concept from Lesson 6–1 under the Ratios tab and write a defi nition along with an example to the right of the defi nition.

®

Ratios

MAIN IDEA

• Write ratios as fractions in simplest form and determine whether two ratios are equivalent.

6–1

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6–1

124 Math Connects, Course 2

Copyright ©

Glencoe/M

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-Hill, a division of T

he McG

raw-H

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panies, Inc.Check Your Progress

a. FLOWERS A garden has 18 roses and 24 tulips. Write a ratio comparing roses to tulips as a fraction in simplest form.

b. Determine whether the ratios 3 cups vinegar to 8 cups water and 5 cups vinegar to 12 cups water are equivalent.

EXAMPLE

POOLS It is recommended that no more than one person be allowed into the shallow end of an outdoor public pool for every 15 square feet of surface area. If a local pool’s shallow end has a surface area of 1,800 square feet, are the lifeguards correct to allow 120 people into that part of the pool?

Recommended Ratio

1:15 = persons per square feet

Actual Ratio

120:1,800 = 120 _ 1,800

or persons per square feet

Since the ratios simplify to the same fraction, they are

. The lifeguards are correct.

Check Your Progress SCHOOL A district claims that they have 1 teacher for every 15 students. If they actually have 2,700 students and 135 teachers, is their claim correct?

HOMEWORKASSIGNMENTPage(s):

Exercises:

REMEMBER IT Ratios such as 120 :1,800 can also be written in simplest form as 1:15.

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Chapter 6 Glencoe Math Connects, Course 2

Write each ratio as a fraction in simplest form.

1. 36 to 21

2. 16 to 64

3. 22 meters to 180 meters

Determine whether the ratios are equivalent.

Explain.

4. 4:6 and 52:78

5. 8:17 and 32:64

6. Test Practice Among the staff at Roosevelt

Elementary, 68 teachers prefer coffee and 20

prefer tea. Which ratio shows the relationship of

coffee drinkers to tea drinkers in simplest form?

A 10:34 B 17:5 C 5:17 D 34:10

ANSWERS

1. 12

_ 7 2.

1 _

4 3.

11 _

90

4. Yes; 4:6 = 2 _

3 and 52:78 =

2 _

3

5. No; 8:17 = 8 _

17 , 32:64 =

1 _

2 , and

8 _

17 ≠

1 _

2

6. B

Use with Lesson

6-2(over Lesson 6-1)

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P rinter P DF

5-Minute Check

Math Connects, Course 2 125

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A ratio that two quantities with different

kinds of units is called a rate.

When a rate is simplifi ed so that it has a

of 1 unit, it is called a unit rate.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLES Find Unit Rates

READING Julia read 52 pages in 2 hours. What is the average number of pages she read per hour?

Write the rate as a fraction. Then fi nd an equivalent rate with a denominator of 1.

52 pages in 2 hours = 52 pages__2 hours

Write the rate as a fraction.

= 52 pages ÷ ___ 2 hours ÷

Divide the numerator and denominator by .

= pages__ hours

Simplify.

SODA Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest hundredth if necessary.

$3 for 6 cans = $3__6 cans

Write the rate as a fraction.

=$3 ÷ 6__

6 cans ÷ 6Divide the numerator and the denominator by 6.

= ___ Simplify.

6–2 Rates

MAIN IDEA

• Determine unit rates.

ORGANIZE ITUnder the rate tab, take notes on rate and unit rate. Be sure to include examples.

®

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6–2

126 Math Connects, Course 2

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.Check Your Progress Find each unit rate.

a. 16 laps in 4 minutes b. $3 for one dozen cookies

EXAMPLE Compare Using Unit Rates

TEST EXAMPLE The costs of 4 different sizes of orange juice are shown in the table. Which container costs the least per ounce?

Amount Total Cost

16 oz $1.28

32 oz $1.92

64 oz $2.56

96 oz $3.36

A 96-oz container C 32-oz container

B 64-oz container D 16-oz container

Read the Item

Find the unit price, or the cost per ounce of each size of orange juice. Divide the price by the number of ounces.

Solve the Item

$1.28 ÷ ounces = per ounce.

$1.92 ÷ ounces = per ounce.

$2.56 ÷ ounces = per ounce.

$3.36 ÷ ounces = per ounce.

The -ounce container of orange juice costs the least per

ounce. The answer is .

REMEMBER IT The word rate is often understood to mean unit rate.

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6–2

Math Connects, Course 2 127

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.Check Your Progress

MULTIPLE CHOICE The costs Amount Total Cost

16 oz $3.12

32 oz $5.04

64 oz $7.04

96 oz $11.52

of different sizes of bottles of laundry detergent are shown below. Which bottle costs the least per ounce?

F 96-oz container

G 64-oz container

H 32-oz container

J 16-oz container

EXAMPLE Use a Unit Rate

POTATOES An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes?

Find the unit rate.

18 potatoes in 6 minutes = 18 ÷ 6 __ 6 ÷ 6

= 3 _ 1

The unit rate is potatoes per minute.

3 potatoes __

1 min · 50 min = potatoes

He can peel potatoes in 50 minutes.

Check Your Progress Sarah can paint 21 beads in 7 minutes. At this rate, how many beads can she paint in one hour?

HOMEWORKASSIGNMENTPage(s):

Exercises:

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Chapter 6 Glencoe Math Connects, Course 2

Find each unit rate. Round to the nearest

hundredth if necessary.

1. $3.99 for 16 ounces 2. 730 miles in 14 hours

3. $28 for 15 cassettes

4. Which is the better unit price: $1.99 for a 3-ounce

bottle or $2.49 for a 4-ounce bottle?

Determine whether the following statement is

sometimes, always, or never true. Explain by

giving an example or a counterexample.

5. The denominator of a unit rate can be a decimal.

6. Test Practice Cassandra leaves college to go

home for the summer. She lives 424 miles away

and arrives in 8 hours. Which ratio shows her

rate of travel in simplest form?

A 53:1 B 53 C 1:53 D 212:4

ANSWERS

1. $0.25 per ounce 2. 52.14 miles per hour

3. $1.87 per cassette 4. $2.49 for a 4-ounce bottle

5. Never; A unit rate is a rate that is simplified so that it has a denominator of 1 unit. For example, the

unit rate 50 words

_ 1 minute

is read 50 words per minute.

6. A

(over Lesson 6-2)

Use with Lesson

6-3

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P rinter P DF

5-Minute Check

128 Math Connects, Course 2

Copyright ©

Glencoe/M

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-Hill, a division of T

he McG

raw-H

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panies, Inc.A Plan for Problem Solving6–3

WRITE ITExplain how rate of change is similar to unit rates.

MAIN IDEA

• Identify rate of change and slope using tables and graphs.

A rate of change is a rate that describes how one quantity changes in relation to another and is usually expressed as a

.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLE Find Rate of Change from a Table

The table shows the number of miles a car drove on a trip. Use the information to fi nd the approximate rate of change.

+ 65 + 65 +

Distance (miles) 65 130 195 260Time (hours) 1 2 3 4

+ 1 + 1 + 1

change in distance

____ change in time

=

_

The distance increased

miles for every hour.

So, the rate was 65 miles per hour.

Check Your Progress The table shows the number of miles a car drove on a trip. Use the information to fi nd the rate of change.

Distance (miles) 44 88 132 176Fuel (gallons) 2 4 6 8

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6–3

Math Connects, Course 2 129

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The constant rate of change in y with respect to the

constant change in is called the slope of a line.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLE Find Rate of Change from a Graph

GRAPH THE DATA Find the slope of the line. Explain what the slope represents.

Graph the points and connect them with a line.

Hours Amount Earned

3 $456 $909 $135

Pick two points on the line, such as (3, 45) and (6, 90), to fi nd the slope.

slope = change in y

__ change in x

= 90 -

___ 6 -

= 45 _ 3 or

The slope is and represents the amount earned per hour.

Check Your Progress The table shows the cost of renting a bicycle. Graph the data. Find the slope of the line. Explain what the slope represents.

y

x

Amou

nt E

arne

d (d

olla

rs)

3 6 9Hours

1501401301201101009080706050403020100

Earnings

Hours Cost

2 $84 $166 $24

Cost

($)

8

16

24

Hours2 4 6 8

32

40

1 3 5 7 90

ORGANIZE ITUnder the rate of change and slope tab, take notes on how to fi nd the slope of a line.

®

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Chapter 6 Glencoe Math Connects, Course 2

1. The table shows the number of miles Greg walked

during a walk-a-thon. Use the information to find

the approximate rate of change in miles per hour.

Time (hr) 1 2 3

Distance (mi) 4 8 12

2. The graph represents the

number of patients that can

be seen in a doctor’s office

based on the number of

nurses on duty. Determine

the slope.

3. Test Practice Use the information in the table to

find the rate of change.

Number of Students Number of Slices of Pizza10 30

15 45

20 60

A 20 slices per student C 3 students per slice

B 3 slices per student D 20 students per pizza

ANSWERS

1. 4 miles per hour

2. 5 patients per nurse

3. B

(over Lesson 6-3)

Use with Lesson

6-4

0

5

10

15

20

25

1 32 4 5

y

x

(4, 20)

(3, 15)

(2, 10)

(1, 5)

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P rinter P DF

5-Minute Check

130 Math Connects, Course 2

Copyright ©

Glencoe/M

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-Hill, a division of T

he McG

raw-H

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panies, Inc.

A unit ratio is a ratio in which the denominator is unit.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLES Convert Larger Units to Smaller Units

Convert 2 miles into feet.

Since 1 mile = 5,280 feet, the unit ratio is .

2 mi = 2 mi · 5,280 ft

__ 1 mi

Multiply by 5,280 ft

__ 1 mi

.

= 2 mi · 5,280 ft

__ 1 mi

Divide out common units.

= ft or 10,560 ft Multiply.

So, 2 miles = feet.

ELEVATOR The elevator in an offi ce building has a weight limit posted of one and a half tons. How many pounds can the elevator safely hold?

1 1 _ 2 t = 1 1 _

2 t · Multiply by

since there are

pounds in 1 ton.

= 1 1 _ 2 · 2,000 lb or 3,000 lb Multiply.

So, the elevator can safely hold pounds.

Check Your Progress Complete.

a. 8 yd = � ft b. 4 1 _ 2 T = � lb

6–4

REMEMBER IT You multiply to change from larger units of measure because it takes more smaller units than larger units to measure an object.

Measurement: Changing Customary Units

MAIN IDEA

• Change units in the customary system.

Explain how estimating can help you solve a problem. (Lesson 6-1)

REVIEW IT

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6–4

Math Connects, Course 2 131

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.EXAMPLES Convert Smaller Units to Larger Units

Convert 11 cups into pints.

Since 1 pint = 2 cups, the unit ratio is 2 c _ 1 pt

, and its

reciprocal is .

11 c = 11 c · 1 pt

_ 2 c

Multiply by .

= 11 c · 1 pt

_ 2 c

Divide out common units.

= 11 ·

= 11 _ 2 pt

Multiplying 11 by 1

_ 2 is the same

as dividing 11 by 2.

= pt

So, 11 cups = pints.

SOCCER Tracy kicked a soccer ball 1,000 inches. How many feet did she kick the ball?

Since 1 foot = 12 inches, multiply by . Then divide out common units.

1,000 in. = 1,000 in. · 1 ft _ 12 in.

= 1,000 in. · ft

= 1000 _ 12

ft or ft

So, Tracy kicked the soccer ball .

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6–4

132 Math Connects, Course 2

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

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panies, Inc.Check Your Progress Complete.

a. 21 qt = � gal b. 78 oz = � lb

EXAMPLE

LEMONADE Paul made 6 pints of lemonade and poured it into 10 glasses equally. How many cups of lemonade did each glass contain?

Begin by converting 6 pints to cups.

6 pt = 6 pt ·

_ 1 pt

= 6 · 2 cups or cups

Find the unit rate which gives the number of cups per glass.

12 cups

__ 10 glasses

= 6 _ 5 or

cups per glass

Check Your Progress CANDY Tom has 3 pounds of candy he plans to divide evenly among himself and his 3 best friends. How many ounces of candy will each of them get?

HOMEWORKASSIGNMENTPage(s):

Exercises:

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Chapter 6 Glencoe Math Connects, Course 2

ANSWERS

1. 7

2. 10

3. 6,600

4. 16

5. 10,560 feet

6. D

Complete.

1. 21 ft = yd

2. 160 oz = lb

3. 1 1 _

4 mi = ft

4. 2 c = fluid oz

5. Stella lives 2 miles from school. How many feet

from the school does Stella live?

6. Test Practice If 1,760 yards = 1 mile, then

4 miles = ___?__ yards.

A 1 _

4 B 4 C 440 D 7,040

Use with Lesson

6-5(over Lesson 6-4)

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P rinter P DF

5-Minute Check

Math Connects, Course 2 133

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.6–5 Measurement: Changing Metric Units

The metric system is a system of measures.

The meter is the base unit of .

The liter is the base unit of .

The gram measures .

The base unit of mass in the metric system is the

.

EXAMPLES Convert Units in the Metric System

Complete 7.2 m = � mm.

To convert from meters to millimeters,

by .

7.2 × =

So, 7.2 m = mm.

Complete 40 cm = � m.

To convert from centimeters to meters, by .

40 ÷ =

So, 40 cm = m.

ORGANIZE ITUnder the metric units tab, take notes on how to change metric units, include examples involving length, capacity, and mass.

®

MAIN IDEA

• Change metric units of length, capacity, and mass.

BUILD YOUR VOCABULARY (pages 121–122)

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6–5

134 Math Connects, Course 2

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.Check Your Progress Complete.

a. 7.5 m = � cm b. 3,400 mm = � m

EXAMPLE

FARMS A bucket holds 12.8 liters of water. Find the capacity of the bucket in milliliters.

You are converting from to milliliters. Since the

bucket holds 12.8 liters, use the relationship 1 L = mL.

1 L = 1,000 mL Write the relationship.

× 1 L = 12.8 × 1,000 mL Multiply each side by 12.8 since you have 12.8 liters.

12.8 L = mL To multiply 12.8 by 1,000,

move the decimal point

places to the right.

So, the capacity of the bucket in milliliters is mL.

Check Your Progress BOOKS A box of textbooks has a mass of 32,850 grams. What is the mass of the box in kilograms?

HOMEWORKASSIGNMENTPage(s):

Exercises:

WRITE ITExplain how you can multiply a number by a power of ten.

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Chapter 6 Glencoe Math Connects, Course 2

Complete.

1. 640 cm = � m

2. 0.05 m = � mm

3. 894 mg = � g

4. 124.5 kL = � L

5. 65,000 mL = � L

6. Test Practice The longest suspension bridge in

the United States is the Verrazano-Narrows in

the Lower New York Bay. It spans 1,298 meters.

How many kilometers long is this bridge?

A 1,298,000 km C 12.98 km

B 129.8 km D 1.298 km

ANSWERS

1. 6.4

2. 50

3. 0.894

4. 124,500

5. 65

6. D

(over Lesson 6-5)

Use with Lesson

6-6

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P rinter P DF

5-Minute Check

136 Math Connects, Course 2

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.6–16–6

Two quantities are proportional if they have a

rate or ratio.

A proportion is an equation stating that two ratios or rates

are .

In a proportion, a cross product is the of

the numerator of one ratio and the denominator of the

other ratio.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLE Identify Proportional Relationships

MATH Before dinner, Mohammed solved 8 math problems in 12 minutes. After dinner, he solved 2 problems in 3 minutes. Is the number of problems he solved proportional to the time?

To identify proportional relationships, you can compare unit rates or compare ratios by comparing cross products. Let’s

compare ratios by comparing .

problems minutes

8 _ 12

� 2 _ 3 problems

minutes

8 · 3 = · 2

24 = 24

Since the cross products are , the number of

problems solved is proportional to the time.

Algebra: Solving Proportions

MAIN IDEA

• Solve proportions.

KEY CONCEPT

Proportion A proportion is an equation stating that two ratios are equivalent.

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6–6

Math Connects, Course 2 137

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.Check Your Progress Determine if the quantities $30

for 12 gallons of gasoline and $10 for 4 gallons of gasoline are proportional.

EXAMPLES Solve a Proportion

Solve 5 _ 8 = 18 _ x .

5 _ 8 = 18 _ x Write the proportion.

5 · x = 8 · 18 Find the cross products.

5x = Multiply.

5x _ = 144 _

Divide each side by .

x = Simplify.

Solve 3.5 _

14 = 6 _ n .

3.5 _ 14

= 6 _ n Write the proportion.

3.5 · n = 14 · 6 Find the cross products.

3.5n = Multiply.

3.5n __ = 84 __

Divide each side by .

n = Simplify.

Check Your Progress Solve each proportion.

a. 9 _ 15

= k _ 18

b. 4.6 _ w = 4 _ 5

HOMEWORKASSIGNMENTPage(s):

Exercises:

ORGANIZE ITUnder the proportions tab, take notes on how to solve a proportion. Include examples.

®

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Chapter 6 Glencoe Math Connects, Course 2

Determine whether each pair of ratios forms

a proportion.

1. 2 _ 12

and 8 _

48

2. 1 _ 9 and

3 _

36

3. 3 _ 4 and

4 _

5

Solve each proportion.

4. 3 _ 7 =

x _

21

5. 6 _ 15

= 18

_ x

6. Test Practice The ratio of native Spanish

speakers to native English speakers in a local

high school is 3 to 8. If there are 254 students at

the school that are native English speakers, how

many students are native Spanish speakers?

A 32 B 36 C 96 D 682

ANSWERS

1. yes 4. 9

2. no 5. 45

3. no 6. C

Use with Lesson

6-7(over Lesson 6-6)

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P rinter P DF

5-Minute Check

Math Connects, Course 2 139

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.6–8

Scale drawings and scale models are used to represent

objects that are too or too to be

drawn at actual size.

The scale gives the ratio that compares the

of the drawing to the real object.

BUILD YOUR VOCABULARY (pages 121–122)

EXAMPLE Use a Map Scale

MAPS What is the actual distance between Portland and Olympia?

Step 1 Use a ruler to fi nd the map distance between the two cities. The map distance is about

.

Step 2 Write and solve a proportion using the scale. Let d represent the actual distance between the cities.

map

actual

3 _ 8 inch

__ 23 mi

= 1.69 inches __ d mi

map

actual

3 _ 8 × d = 23 × 1.69 Cross products.

0.375d = 3.887 Multiply. Write 3 _ 8

as a decimal.

d = Divide both sides by 0.375.

The distance between the cities is about kilometers.

Scale Drawings

ORGANIZE ITUnder the scale tab, explain how to solve a problem involving scale drawings. Be sure to include an example.

®

MAIN IDEA

• Solve problems involving scale drawings.

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6–8

140 Math Connects, Course 2

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.Check Your Progress MAPS On a map of California,

the distance between San Diego and Bakersfi eld is about

11 2 _ 5 centimeters. What is the actual distance if the scale is

1 centimeter = 30 kilometers?

EXAMPLE Use a Blueprint Scale

ARCHITECTURE On the blueprint of a new house, each square has

a side length of 1 _ 4 inch. If the length

of a bedroom on the blueprint is

1 1 _ 2 inches, what is the actual length

of the room?

Write and solve a proportion.

Scale Length of Room

blueprint

actual

1 _ 4 inch

___ =

___ t feet

blueprint

actual

1 _ 4 · t = Cross products

1 _ 4 t = 15 _

4 Multiply.

t = Simplify.

The length of the room is .

WRITE ITExplain why these two scales are equivalent scales:

1 _ 2 inch = 4 miles

1 inch = 8 miles

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6–8

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.Check Your Progress On a blueprint of a new house,

each square has a side length of 1 _ 4 inch. If the width of the

kitchen on the blueprint is 2 inches, what is the actual width of the room?

EXAMPLE Find a Scale Factor

Find the scale factor of a blueprint if the scale is

1 _ 2 inch = 3 feet.

1 _ 2 inch

__ 3 feet

= 1 _ 2 inch ___

Convert 3 feet to .

= ·

1

_ 2 inch

__ 36 inches

Multiply by to eliminate

the fraction in the numerator.

= Divide out the common units.

The scale factor is . That is, each measure on the

blueprint is the measure.

Check Your Progress Find the scale factor of a blueprint if the scale is 1 inch = 4 feet.

HOMEWORKASSIGNMENTPage(s):

Exercises:

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Chapter 6 Glencoe Math Connects, Course 2

Suppose you are making a scale drawing. Find

the length of each object on the scale drawing

with the given scale. Then find the scale factor.

1. a subway car 34 feet long; 1 inch = 5 feet

2. a table 1.5 meters long; 3 centimeters = 0.25 meters

3. a football field that is 120 yards; 1 foot = 30 yards

Solve.

4. The distance between New York City and

Washington, D.C., is 3.75 inches on a map of

the United States. If the scale on the map is

1 inch to 90 miles, how far is Washington, D.C.,

from New York City?

5. Test Practice Which ratio accurately shows the

relationship between the actual distance from

Atlanta to New Hope and the scale distance if the

actual distance is 425 miles and the scale

distance is 6 2 _

3 inches?

A 6 2 _

3 :425 B 1:63

3 _

4 C 63

3 _

4 :1 D 70.8:1

ANSWERS

1. 6 4 _

5 in.;

1 _

60 2. 18 cm;

3 _

25 3. 4 ft;

1 _

90

4. 337.5 mi 5. C

Use with Lesson

6-9(over Lesson 6-8)

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P rinter P DF

5-Minute Check

142 Math Connects, Course 2

Copyright ©

Glencoe/M

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-Hill, a division of T

he McG

raw-H

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panies, Inc.

EXAMPLES Percents as Fractions

NUTRITION In a recent consumer poll, 41.8% of the people surveyed said they gained nutrition knowledge from family and friends. What fraction is this? Write in simplest form.

41.8% = 41.8 _ 100

Write a fraction with a denominator of 100.

= 41.8 _ 100

· Multiply to eliminate the decimal in the numerator.

= or Simplify.

Write 12 1 _ 2 % as a fraction in simplest form.

12 1 _ 2 % =

12 1 _ 2 _

100 Write a fraction.

= 12 1 _ 2 ÷ 100 Divide.

= ÷ 100 Write 12 1 _ 2 as an improper fraction.

= × Multiply by the reciprocal of 100.

= or Simplify.

Check Your Progress

a. ELECTION In a recent election, 64.8% of registered voters actually voted. What fraction is this? Write in simplest form.

b. Write 62 1 _ 2 % as a fraction in simplest form.

6–9 Fractions, Decimals, and Percents

MAIN IDEA

• Write percents as fractions and decimals and vice versa.

ORGANIZE ITUnder the Fractions, Decimals, and Percents tab, take notes on writing percents as fractions and fractions as percents. Include examples.

®

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6–9

Math Connects, Course 2 143

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.EXAMPLES Fractions as Percents

PRODUCE In one shipment of fruit to a grocery store, 5 out of 8 bananas were still green. Find this amount as a percent.

5 _ 8 = n _

100 Write a proportion.

500 = 8n Find the cross products.

500 _ = 8n _

Divide each side by .

= n Simplify.

So, 5 _ 8 = 62 1 _

2 % or .

Write 5 _ 12

as a percent. Round to the nearest hundredth if necessary.

5 _ 12

= n _ 100

Write a proportion.

= Find the cross products.

500 12 ENTER 41.66666667 Use a calculator.

So, 5 _ 12

is about .

Write 3 _ 7 as a percent. Round to the nearest hundredth.

3 _ 7 = 0.4285714… Write 3 _

7 as a decimal.

= by 100 and add the .

Check Your Progress Write each fraction as a percent. Round to the nearest hundredth.

a. 13 _ 25

b. 11 _ 15

HOMEWORKASSIGNMENTPage(s):

Exercises:

KEY CONCEPTS

Common Fraction/ Decimal/Percent Equivalents

1_3

= 0. −3 = 33 1_

3 %

2_3

= 0. −6 = 66 2_

3 %

1_8

= 0.125 = 12 1_2

%

3_8

= 0.375 = 37 1_2

%

5_8

= 0.625 = 62 1_2

%

7_8

= 0.875 = 87 1_2

%

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