+ All Categories
Home > Documents > LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates...

LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates...

Date post: 15-Mar-2018
Category:
Upload: hakiet
View: 212 times
Download: 0 times
Share this document with a friend
24
Ready to Go On? Skills Intervention Ratios and Rates 7-1 LESSON A ratio is a comparison of two quantities that uses division. Writing Ratios Use the table to write each ratio. A. Jazz CDs to Blues CDs 2 or to 2 or : What are these ratios comparing? B. Rock CDs to total CD collection 12 or to or : 12 What are these ratios comparing? Equivalent ratios are ratios that name the same comparison. Writing Equivalent Ratios Write three equivalent ratios to compare the number of stars with the number of moons in the pattern. Compare the number of stars to the number of moons. 4 8 4 8 4 There is star for every moons. 4 8 4 8 2 2 If you double the pattern, there will be stars and moons. So, , , and are equivalent ratios. number of stars number of moons Vocabulary ratio equivalent ratios Barbara’s CD Collection Jazz 3 Blues 2 Rock 7 Copyright © by Holt, Rinehart and Winston. 132 Holt Mathematics All rights reserved. Name Date Class
Transcript
Page 1: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Ready to Go On? Skills InterventionRatios and Rates7-1

LESSON

A ratio is a comparison of two quantities that uses division.

Writing RatiosUse the table to write each ratio.

A. Jazz CDs to Blues CDs

�2

� or to 2 or :

What are these ratios comparing?

B. Rock CDs to total CD collection

�12

� or to or : 12

What are these ratios comparing?

Equivalent ratios are ratios that name the same comparison.

Writing Equivalent RatiosWrite three equivalent ratios to compare the number of stars withthe number of moons in the pattern.

� �� Compare the number of stars to the number of moons.

�48

� � �48

��

4� � �� There is star for every moons.

�48

� � �48

••

22

� � �� If you double the pattern, there will be stars and

moons.

So, ��, ��, and �� are equivalent ratios.

number of stars���number of moons

Vocabulary

ratioequivalent ratios

Barbara’s CDCollection

Jazz 3

Blues 2

Rock 7

Copyright © by Holt, Rinehart and Winston. 132 Holt MathematicsAll rights reserved.

Name Date Class

Page 2: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 133 Holt MathematicsAll rights reserved.

Name Date Class

A 26-ounce box of Shaky Flake cereal costs $5.79. A 14-ounce boxcosts $2.69. Which box costs less per ounce? Explain.

Understand the Problem

1. Are you asked to find the exact cost per ounce of either box?What are you asked to find?

Make a Plan

2. What two ratios can you compare to solve the problem?

3. Why would it make sense to try estimation and number sensebefore calculating?

Solve

4. Do you get more than or less than twice as much cereal in thebigger box? Explain.

5. Now see if you pay less than twice as much. Write �, �, or � tocomplete these statements.

$2.69 $2.70 2 • $2.70 $5.40 2 • $2.69 $5.40

So, 2 • $2.69 $5.79

6. Which box costs less per ounce? Explain.

Check

7. Solve another way to check your answer. Write � , �, or �.

$2.80/14 oz $0.20/oz and $2.69 $2.80, so $2.69/14 oz $0.20/oz

$5.20/26 oz $0.20/oz and $5.20 $5.79, so $5.79/26 oz $0.20/oz

Ready to Go On? Problem Solving InterventionRatios and Rates7-1

LESSON

Page 3: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Ready to Go On? Skills InterventionUsing Tables to Explore Equivalent Ratios and Rates7-2

LESSON

Copyright © by Holt, Rinehart and Winston. 134 Holt MathematicsAll rights reserved.

Name Date Class

Ratios are commonly written as fractions. You can put thenumerator of the fraction in the top row of the table and thedenominator in the bottom row. To find equivalent ratios, you canmultiply each number in the ratio by the same number and place theproduct in the space to the right of the first number.

You can do the same to find equivalent rates. You can also use atable to make predictions.

Making a Table to Find Equivalent Ratios

Write equivalent ratios for �12

�.

In each column, the top and bottom numbers are both multiplied by

the same number. , , , and are all equal to .The ratios are equivalent.

Using a Table to Make Predictions aboutEquivalent Ratios and Rates

Find an equivalent ratio whose numerator is 10.

The numerator 10 is between and in the table so the

denominator will be between and .

5 � � 10

Multiply the denominator of �155� by . 15 � � .

The equivalent ratio is .10

2

6

3

9

5

15

20

60

OriginalNumerator

OriginalDenominator

1

2

1 � 2

2 � 2

1 � 3

2 � 3

1 � 4

2 � 4

1 � 5

2 � 5

2

4

3

6

4

8

5

10

Page 4: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 135 Holt MathematicsAll rights reserved.

Name Date Class

A table is a good tool that can help you find equivalent ratios andrates. By organizing the information visually, it is easier to see thesolution to a problem.

The table below shows how many seashells Katie finds for thenumber of minutes she spends looking. Predict how long it will takeher to find 12 shells.

Understand the Problem

1. How many shells does Katie collect in the first five minutes?

2. What is the ratio of shells to minutes in the first interval?

Make a Plan

3. The 12 seashells are between which two numbers in the table?

4. The corresponding amount of time is between which two numbers?

5. What is the simplest ratio that the ratio for 12 shells will equal?

6. Write the equivalent ratios.

7. How can you find the missing amount of time?

Solve

8. How long did it take Katie to find 12 seashells?

Check

9. Why does it make sense that it takes Katie 30 minutes to find 12 shells?

2

5

Number of Seashells

Time Spent (min)

4

10

6

15

10

25

24

60

Ready to Go On? Problem Solving InterventionUsing Tables to Explore Equivalent Ratios and Rates7-2

LESSON

MSM07C1_RTGO_ch07_132-155_B 6/18/06 11:59 AM Page 135 (Black plate)

Page 5: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 136 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Skills InterventionProportions7-3

LESSON

A proportion is an equation that shows two equivalent ratios.

Modeling ProportionsWrite a proportion for the model.

� �� What is the ratio of ovals to squares?

Next separate the squares and ovals into equal groups.

� �� Complete the ratio.

A proportion shown by the model is �� � ��.

Using Cross Products to Complete ProportionsFind the missing value in the proportion.

�29

� � �2m7�

�29

� � �2m7� Find the cross products.

9 • � 2 • Are cross products equal?

9 � Multiply.

�9

� � �� Divide both sides by to undo themultiplication.

m � Solve for m.

number of ovals in each group����number of squares in each group

number of ovals���number of squares

Vocabulary

proportion

Page 6: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 137 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Skills InterventionSimilar Figures7-4

LESSON

Two or more figures are similar if they have exactly the sameshape. Similar figures have corresponding sides andcorresponding angles. Corresponding sides have lengths thatare proportional. Corresponding angles are congruent.

Finding Missing Measures in Similar FiguresThe two triangles are similar. Find the missing length y and themeasure of �E.

�39

� � �� Write aproportion usingcorrespondingside lengths.

3 • � 9 • Are the crossproducts equal?

� Multiply.

�� � �45

� Divide to undo the multiplication.

y � cm

Angle E is congruent to Angle and m� � .

So the measure of �E is also .

Problem Solving ApplicationKyle’s garden is similar to Erin’s garden. Kyle’s garden is 8 ft wideand 10 ft long. The width of Erin’s garden is 14 ft. To the nearestfoot, what is the length of Erin’s garden?

�180

ftft

� � �� Write a proportion using corresponding side lengths.

8 • � 10 • Are the cross products equal?

� Multiply.

�� � �1480

� Divide to undo the multiplication.

� � Round to the nearest foot.

The length of Erin’s garden is about .

Vocabulary

similarcorresponding

anglescorresponding

sides

E

3 cm

9 cmy cm

5 cm

4 cm 12 cm

55°

F

Page 7: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 138 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Skills InterventionIndirect Measurement7-5

LESSON

One way to find measurements that you cannot measure directlyis to use similar figures and proportions. This method is calledindirect measurement.

Using Indirect MeasurementUse the similar triangles below to find the missing heights.

A. A telephone pole casts a shadow that is 80 feet long. At thesame time, a person who is 5 feet tall casts a shadow that is8 feet long. How tall is the telephone pole?

�5h

� � �� Write a proportion.

• h � 5 • The crossproducts areequal.

� Multiply.

�� � �� Divide to undo themultiplication.

h � Solve for h.

The telephone pole is tall.

B. A giraffe casts a shadow that is 24 meters long. At the sametime, a meter stick casts a shadow that is 4 meters long. How tallis the giraffe?

�1h

� � �� Write a proportion.

• h � 1 • The cross productsare equal.

� Multiply.

�� � �� Divide to undo themultiplication.

h � Solve for h.

The giraffe is tall.

h

24 m4 m

1 m

h

80 ft8 ft

5 ft

Vocabulary

indirectmeasurement

Page 8: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 139 Holt MathematicsAll rights reserved.

Name Date Class

You can use similar triangles to measure astronomical distances.

(Diagram not to scale)To measure the diameter of the Moon, you can hold a penny so thatit just covers the Moon. The lines of sight form two similar triangles, �ABC and �ADE, as shown. The distance from the penny to your eye is 2.1 m. The diameter of the penny is 1.9 cm. The distance from theEarth to the Moon is 385,000 km. Calculate the diameter of the Moon.

Understand the Problem1. What are you trying to find?

Make a Plan

2. Complete the proportion. How can you use the proportion to findthe diameter of the Moon?

3. The diameter of the penny and the distance from the penny toyour eye are in different units. What will you do?

Solve

4. What is the distance in cm from your eye to the penny?

5. Substitute the numbers you know into the proportion in Exercise 2and then solve it. Use x for the diameter of the Moon.

Check6. The penny’s diameter is about of its distance.

The Moon’s diameter is about of its distance.

diameter of moon���distance to moon

diameter of penny���distance of penny

eye pennyMoon

A C

BD

E

Ready to Go On? Problem Solving InterventionIndirect Measurement7-5

LESSON

Page 9: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 140 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Skills InterventionScale Drawings and Maps7-6

LESSON

A scale drawing is a drawing of a real object that is proportionallysmaller or larger than the real object. A scale is a ratio betweentwo sets of measurements.

Finding Actual Distances

A. On the map the distance between Lafayette andIndianapolis is 2 in. What is the actual distance?

�310

inm.i

� � �min.

i� Write a proportion.

Let x represent theactual number ofmiles betweenLafayette andIndianapolis.

30 • � 1 • The cross productsare equal.

� Multiply.

The actual distance between Lafayette and

Indianapolis is .

B. Rochester, Indiana, is 90 mi from Indianapolis.On the map, how far should Rochester be fromIndianapolis?

�310

inm.i

� � �imn.

i� Write a proportion.

Let x represent how far Rochester should be away from Indianapolis on the map.

30 • � 1 • Are the cross products equal?

� Multiply.

�30

� � �9300� Divide to undo the multiplication.

x � Solve for x.

Rochester should be away from Indianapolis on the map.

Vocabulary

scale drawingscale

Rochester

Lafayette

Indianapolis

Scale: 1 in. � 30 miles

Page 10: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 141 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Problem Solving InterventionScale Drawings and Maps7-6

LESSON

Because most maps are scale drawings, you can use them to figure out actual distances.

If you are going from Allsworth to Cowley, how many miles longer is it to go through Bayville?

Understand the Problem

1. What two routes will you compare?

Make a Plan

2. If you know the map distances of the two routes, how could you find theactual distances?

3. What instrument could you use to find the distances on the map?

Solve

4. Fill in each map distance.

Indirect Route: Allsworth to Bayville is cm

Bayville to Cowley is cm

Total for indirect route cm

Direct Route: Allsworth to Cowley is cm

5. What is the actual distance of each route?

Check

6. Make sure you answer the question that the problem asks.

Allsworth

Cowley

Bayville

50 mi0Scale: 1 cm = 10 miles

Page 11: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 142 Holt MathematicsAll rights reserved.

Name Date Class

7-1 Ratios and RatesUse the table to write the following ratios.

1. red to blue shirts

2. blue to striped shirts

3. white to black shirts

4. One grocery store sells a carton of a dozen eggs for $1.99.Another grocery store sells a carton of 18 eggs for $2.29. Whichis the better deal?

7-2 Using Tables to Explore Equivalent Ratios and RatesUse a table to find three equivalent ratios.

5. 6.

7. The table below shows how much money Jordan collected for a charity drive from the number of houses he visited. How many houses did he visit to collect $77?

7-3 ProportionsFind the missing value in each proportion.

8. �57

� � �3n5� 9. �

6x

� � �1326� 10. �

43

� � �2z4�

Money Collected

Houses Visited

$14

6

$21

9

$42

18

$63

27

$98

42

60

100

___

___

___

___

___

___

30

50

6

10

3

5

8

4

___

___

___

___

___

___

16

8

24

12

32

16

Ready to Go On? Quiz7A

SECTION

Shirts in Derek’s Closet

Blue 4

Red 2

Striped 4

White 9

Black 3

Page 12: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 143 Holt MathematicsAll rights reserved.

Name Date Class

7-4 Similar FiguresUse the similar figures below to find the following measurements.

11. �Y

12. r

7-5 Indirect MeasurementUse the drawing below to answer the questions.

13. How tall is the person?

14. How long is the flagpole’s shadow?

7-6 Scale Drawings and MapsUse the map below and a centimeter ruler.

15. How far is it from the bank to the pet store?

16. How far is it from the park to school?

17. Lisa and her mother start at school and want to meet at the library. Lisa stops bythe park and then goes through the center of town to the library. Lisa’s motherstops at home on her way to the library. Whose trip is longer?

Grocery

Park

Bank

HomeFireStation

School

Pet Store Library

Scale 1 cm = 0.75 km

r

2 m

Y10 m Z

X

8 m

84°

42°

54°

43 ft

8.6 ft

7 ft

Ready to Go On? Quiz continued

7ASECTION

MSM07C1_RTGO_ch07_132-155_B 6/18/06 11:59 AM Page 143 (Black plate)

Page 13: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 144 Holt MathematicsAll rights reserved.

Name Date Class

Sometimes routes shown on maps are not the most direct pathfrom point A to point B. Often, they show the shortest distancebetween two points by roads. The actual shortest distance isoften referred to as the distance “the crow flies” because whenbirds fly, they can fly directly from one place to another withoutfollowing roads.

From Point A to Point B to Point C shows the path a car mighttake by roads. The route between Point A and Point C showsthe distance as the crow flies. Note that the first route goesalong the legs of a right triangle and the second route goes along the hypotenuse. Ifyou know the distance of the legs, you can use the Pythagorean Theorem to find thedistance as the crow flies.

32 � 42 � x2 9 � 16 � x2 25 � x2 5 � x

Use the drawing and a centimeter ruler to answer the questions below.

1. What is the distance “the crow flies”?

2. Which distance is shorter, by road or as “the crow flies”?

Find the missing distance.

3. x 4. r 5. k 6. f

Use a centimeter ruler.

7. The map shows Eric’s and Anna’s routes.Eric can walk 2 kilometers per hour. Annawalks at 3 kilometers per hour. You can findthe time each trip takes by dividing thedistance by their rate of speed. Who getsfrom Eric’s house to school first?

x r

k

f4 in. 2 ft

5 in.

10.7 cm

5.83 m5 m

8.16cm

7.3 ft

Eric’s Path

Anna’s Path1 cm � 0.4 km

1 cm � 3.5 m

Ready to Go On? EnrichmentAs the Crow Flies7A

SECTION

A

C

B3 cm

4 cm

MSM07C1_RTGO_ch07_132-155_B 6/18/06 11:59 AM Page 144 (Black plate)

Page 14: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 145 Holt MathematicsAll rights reserved.

Name Date Class

A percent is a ratio of a number to 100.

Modeling PercentsUse a 10-by-10 square grid to model 16%.

A 10-by-10 grid has squares.

16% means out of 100, or �100�.

How many squares will you shade?

Shade the squares to model 16%.

Writing Percents as Fractions78% of the planets in our solar system have moons. Write 78% as afraction in simplest form.

78% � �100

� Write the percent as a fraction with a denominator of 100.

�100

��� � �� To simplify the fraction, divide by the GCD.

Written as a fraction, 78% is ��.

Writing Percents as Decimals44% of the planets in our solar system have rings. Write 44% asa decimal.

44% � �100

� Write the percent as a fraction with a denominator of 100.

Written as a decimal, 44% is .

Write the fraction as a decimal.100�4�4�.0�0�

���

���

Ready to Go On? Skills InterventionPercents7-7

LESSON

Vocabulary

percent

Page 15: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 146 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Problem Solving InterventionPercents7-7

LESSON

You can use what you know about fractions to help estimatepercents.

What percent of each figure is shaded? Match each figure with oneof the percents listed.

Understand the Problem

1. What does it mean if 25% of a figure is shaded?

Make a Plan

2. How can you use fractions to help solve this problem?

Solve

3. What is an equivalent fraction for each of the percents listed?

4. How can you tell that less than �14

� of figure A is shaded?

5. Without counting squares, how can you tell that �12

� of figure D is shaded?

6. Match each figure to the percent that tells how much is shaded.

Check

7. Estimate to check.

A B C D

50%

25%

20%

75%

Page 16: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 147 Holt MathematicsAll rights reserved.

Name Date Class

Ready to Go On? Skills InterventionPercents, Decimals, and Fractions7-8

LESSON

Writing decimals and fractions as percents sometimes makes thenumbers easier to understand.

Writing Decimals as PercentsMethod 1: Use place value.

0.85

0.85 � �100

� Use what you know about place value to express the decimal

as a fraction. How many hundredths is 0.85?

�100

� � % What number will you write with the percent symbol?

Method 2: Multiply by 100.

0.7453

0.7453 • How will you move the decimal point right two places?

Multiply. Add the percent symbol.

Writing Fractions as PercentsMethod 1: Write an equivalent fraction with a denominator of 100.

In Mr. Tait’s class, �2570� of the students tutor younger students.

What percent of Mr. Tait’s students help tutor younger students?

�2570�

�2570

••� � �

100� Multiply by to change the denominator to 100.

�100

� � % Write the numerator with the percent symbol.

% of Mr. Tait’s students help tutor younger students.

Method 2: Use division to write the fraction as a decimal.

�34

Divide the numerator by the denominator.

0.75 � % Multiply by . Write with the percent symbol.

4�3�.0�0�

Page 17: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 148 Holt MathematicsAll rights reserved.

Name Date Class

You can change fractions to decimals to solve some problems.

A banner is 10 feet long and 4 feet high. Part of it is a red rectanglethat is 6 feet by 3 feet. What percent of the banner is red?

Understand the Problem

1. For what two things do you know the dimensions?

Make a Plan

2. If you knew what fraction of the banner is red, how could youfind what percent is red?

3. Complete the equation to show how you can find the fraction ofthe banner that is red.

fraction of banner that is red �

Solve

4. What is the area of the red rectangle? Of the whole banner?

5. What fraction of the banner is red? What percent is that? Explain.

Check

6. Check your conversion from a fraction to a percent. Completethe proportion and see if the two ratios really are equal.

area of red rectangle �� � �

100�

percent that is redarea of banner

Solve

7. What percent of the banner would a blue rectangle 8 feet long and 2 feet wide be?

area of���

area of

Ready to Go On? Problem Solving InterventionPercents, Decimals, and Fractions7-8

LESSON

Page 18: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 149 Holt MathematicsAll rights reserved.

Name Date Class

You can use percents to help you solve word problems.

Consumer Math ApplicationSean has baked 60% of his cookies. If he has been baking for24 minutes, how long will it take him to bake the rest of thecookies?

�1%00� � �

oisf

� 60% of the cookies are baked, so 24 minutes is60% of the total baking time. Set up a proportion.

�100

� � �� What have you been asked to find?

• � 100 • The cross products are equal.

� Multiply.

�6600m� � �� Divide to undo the multiplication.

m � What is the total baking time?

� 24 � Subtract to find the time remaining.

It will take Sean minutes to bake the rest of the cookies.

Multiplying to Find a Percent of a Number

A. Find 15% of 180.

15% � Write 15% as a decimal.

• 180 � Multiply using the decimal since “of” meansmultiply.

So is 15% of 180.

B. Find 6% of 120.

6% � Write 6% as a decimal.

• 120 � Multiply using the decimal since “of” means multiply.

So is 6% of 120.

Ready to Go On? Skills InterventionPercent Problems7-9

LESSON

Page 19: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 150 Holt MathematicsAll rights reserved.

Name Date Class

You can use percents to find missing information.

A store offers a 15% discount on all items. If you buy the XP-2 DVDplayer, you save $42. How much is the regular price of the player?

Understand the Problem

1. How many dollars is the discount on the DVD player? Whatpercent of the regular price is that?

2. Complete the question to restate the problem.

$ is % of what number?

Make a Plan

3. What decimal is equivalent to 15%?

4. Let p be the regular price of the DVD player. Write an equationyou could solve to find p.

Solve

5. Solve the equation you wrote for Exercise 4 to find the regularprice of the player.

Check

6. Use mental math to see if $42 is 15% of the regular price youfound. Write the regular price in each box.

10% of $ � $

5% is �12

� of 10%, so 5% of $ � �12

� of $ � $

15% is 10% � 5%, so 15% of $ � $ � $ � $42

Find the regular price.

7. A 25% discount on a TV is $125 off the regular price.

Ready to Go On? Problem Solving InterventionPercent Problems7-9

LESSON

Page 20: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 151 Holt MathematicsAll rights reserved.

Name Date Class

A discount is an amount that is subtracted from the regular priceof an item. A tip is an amount added to a bill.

Finding DiscountsA clothing store has a sign that reads “20% off the regular price.” IfShane wants to buy a shirt whose regular price is $17.99, abouthow much will he pay for the shirt after the discount?

Step 1

What will you round $17.99 to?

Step 2

How will you find the discount?

0.20 • � Multiply.

The approximate discount is .

How will you find the approximate cost of the shirt?

$18.00 � � Subtract.

Shane will pay about for the shirt.

Finding TipsMatthew’s haircut cost $15.95. He wants to give the barber a tip thatis 15% of the cost. About how much should his tip be?

Step 1

What will you round $15.95 to?

Step 2

Think: 15% � % � %

10% of $16 � • �

Step 3

5% � 10% �

� $ � � $

Step 4

15% � % � %

� $ � $ � $

Matthew’s tip to the barber should be about .

Ready to Go On? Skills InterventionUsing Percents7-10

LESSON

Vocabulary

discounttip

Page 21: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 152 Holt MathematicsAll rights reserved.

Name Date Class

The basic cost of your meal is $8.00. You use a coupon for 20% off.Next, a sales tax of 5% is added. Then, you leave a 15% tip on thediscounted cost of the meal before tax. How much do you pay in all?

Understand the Problem

1. In what order are the discount, sales tax, and tip applied? Is eachone added to or subtracted from the basic cost of your meal?

2. What amount is the 15% tip based upon?

Make a Plan

3. How can you find x, the amount of the meal after the discount,before tax and tip?

4. How can you find y, the amount of the meal after tax?

5. How can you find z, the final amount you pay including the tip?

Solve

6. Find x, the amount after the discount, before tax and tip, and y,the amount after tax.

7. Find z, the final amount you pay including the tip.

Check

8. Is your answer greater, less than, or equal to the basic cost ofthe meal? Why does that make sense?

Ready to Go On? Problem Solving InterventionUsing Percents7-10

LESSON

Page 22: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 153 Holt MathematicsAll rights reserved.

Name Date Class

7-7 PercentsWrite each percent as a fraction in simplest form.

1. 25% 2. 40% 3. 23%

4. 17% 5. 70% 6. 35%

Write each percent as a decimal.

7. 83% 8. 30% 9. 57%

10. 8% 11. 66.66% 12. 6%

7-8 Percents, Decimals, and FractionsWrite each fraction as a percent.

13. �19040

� 14. �1245� 15. �

13

16. �2101� 17. �

110� 18. �

34

Write each decimal as a percent.

19. 0.12 20. 0.04 21. 0.89

22. 0.6 23. 0.21 24. 1

Ready to Go On? Quiz7B

SECTION

MSM07C1_RTGO_ch07_132-155_B 6/18/06 11:59 AM Page 153 (Black plate)

Page 23: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 154 Holt MathematicsAll rights reserved.

Name Date Class

7-9 Percent ProblemsIn a survey, 400 students were asked to name theirfavorite kind of book. Use the graph of the results toanswer the questions.

25. How many students’ favorite kind of book is Mystery?

26. How many students’ favorite kind of book is Adventure?

27. What percent of students chose Romance?

28. How many students chose Romance?

Find each percentage.

29. 60% of 84 30. 15% of 90 31. 30% of 75

7-10 Using PercentsSolve. Round to the nearest cent.

32. Jordan, Casey, and Michelle are having lunch. Their bill comesto $38.05. Jordan’s meal is 43% of the bill, Casey’s is 27%, andMichelle’s is 30%. How much does each person owe?

33. Mr. and Mrs. Ramirez went out to dinner. Their bill was $48.93. They want to leave a 20% tip. How much do they leave?

34. Carrie earns 12% commission on each pair of shoes she sells. She sold 5 pairs of shoes, at $24.99, $45.99, $63.99, $38.99, and $41.99. How much commission did Carrie earn?

35. Yvette bought a pair of jeans that costs $27.99, a sweater that costs $32.99, and a belt that costs $11.99. The store is having a 15% off sale. How much did Yvette pay?

36. David wants to buy a necklace for his mother. The necklace costs $74.99, but is on sale for 10% off. David has $69. Does he have enough money for the necklace?

37. Texas has a 6.25% sales tax. What is the total cost for a computer purchased in Texas for $599.00?

Ready to Go On? Quiz continued

7BSECTION

AdventureMystery

Humor

Romance14%

Nonfiction 4%Thriller 10%

19%

16% 37%

Page 24: LESSON Ready to Go On? Skills Intervention Ratios and Rates · PDF file7-1 Ratios and Rates LESSON A ratio is a comparison of two ... The lines of sight form two ... Substitute the

Copyright © by Holt, Rinehart and Winston. 155 Holt MathematicsAll rights reserved.

Name Date Class

Some jobs pay “by the hour,” or a flat rate of pay for each hourworked. Other jobs pay “commission,” or a percent of the amountthe employee sells.

Michael works at a clothing store for $7 Sherry earns a 14% commission. If her an hour. How much does he earn in an total sales for the day are $400, how mucheight-hour shift? commission does Sherry earn?

$7 an hour � 8 hours � $56 14% � 400 � $56

Michael earns $56 in an eight-hour shift. Sherry earns $56 in commission.

Solve. Round to the nearest cent.

1. Michael got a raise of $1.25 an hour. How much does he earn in a ten-hour shift?

2. How much does Sherry need to sell in order to earn as much in commission as Michael does in salary?

3. Michael’s employers withhold taxes from his paycheck that are equal to about 17% of his paycheck. How much does he receive from a ten-hour shift, after taxes?

4. Eric gets a job at a record store that pays minimum wage plus a 8% commission. If minimum wage is $5.15 an hour, and Eric sells $230 of merchandise, what does he earn for a 6-hour shift?

5. Robin works as a waitress. She is paid $9 an hour plus tips. If Robin works a five-hour dinner shift and receives $20 in tips, what does she earn?

6. Sherry wants to buy a laptop computer that costs $750. If her average weekly sales are $825, how many weeks will it take her to earn the price of the computer?

7. Eric’s employer decides to give his employees a $5 bonus for every $100 of merchandise sold. During his next 8-hour shift, Eric sells $440 of merchandise. How much does he earn?

8. When Robin works at a wedding reception, she is paid $12/hour and she splits the total amount of tips with the other servers. If the serving staff of 5, including Robin, received $140 in tips during a 6-hour wedding reception, how much does Robin earn?

Ready to Go On? EnrichmentSalary Comparison7B

SECTION


Recommended