# Big Ideas Math Answers Grade 6 Chapter 4 Percents

Refer to our Big Ideas Math Book 6th Grade Answer key chapter 4 Percents and solve the problems. You can understand the concepts in-depth with the help of the Big Ideas Math Book Answers 6th Grade solution key. We provide the step by step explanations for all the questions by using the figures. You can easily understand the concepts in-depth with the help of the Big Ideas Math Answers Grade 6 Chapter 4 Percents.

## Big Ideas Math Book 6th Grade Answer Key Chapter 4 Percents

Students who feel difficulty in solving the problems can quickly understand the concepts with the help of our Big Ideas Math Book 6th Grade Answer key for Chapter 4 Percents. In order to excel in the exam, we suggest the students of 6th standard refer to the Big Ideas Math Book 6th Grade Chapter 4 Percents Answer key.

Performance

Lesson 1: Percents and Fractions

Lesson 2: Percents and Decimals

Lesson: 3 Comparing and Ordering Fractions, Decimals, and Percents

Lesson: 4 Solving Percent Problems

Chapter – 4: Concepts

### Percents STEAM Video/Performance

Chargaff’s Rules

DNA is a molecule made up of four nucleotide bases called adenine (A), thymine (T), cytosine (C), and guanine (G). DNA contains the genetic information for a living organism. What can you learn about an organism from its DNA?
Watch the STEAM Video “Chargaff’s Rules.” Then answer the following questions.
1. Veronica says that the DNA of most mammals contains about 60 percent A and T nucleotides and 40 percent C and G nucleotides. What do you think this means?

According to the above stated DNA structure both adenine and thymine contains 60%, cytosine and guanine contain 40%. The difference between them is 20%.

Explanation:
In the above-given DNA structure, they stated that adenine and thymine contain 60%, cytosine and guanine contain 40% and the difference is 20%.
60% – 40% = 20%

2. Use your answer in Question 1 to determine which of the following DNA samples is most likely to belong to a mammal. Explain your reasoning.

Sample 2 satisfies the condition because the 1st question statement is near to the sample2.

Explanation:
Sample 2 is near to the 1st question.

Genetic Ancestry

After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the results of your friend’s ancestry test.

You will be asked to compare the portions of your friend’s ancestry from different regions of the world. How can you order the portions of your friend’s ancestry from least to greatest?

Native American, SouthWest Asian, Mediterranean, Northern European, African.

Explanation:
Native American = (1/50) = 0.02
African = (30/40) = 0.75
Northern European = 0.10
SouthWest Asian = (3/75) = 0.04
Mediterranean = 0.06

### Percents Getting Ready for Chapter 4

Chapter Exploration

Question 1.
THE MEANING OF A WORD
Work with a partner. Match the “cent” word with its deﬁnition.

one hundredth of a dollar

Explanation:
cent meaning

Question 2.
THE MEANING OF A WORD
Work with a partner. Describe a situation where you have seen the word perused and explain its use. In your own words, what do you think the word percent means? Use the word percent in a sentence.
Work with a partner. Represent the shaded portion of the square as
(a) a fraction whose denominator is 100,
(b) a fraction in the simplest form,
(c) a decimal, and
(d) a percent.

A fraction whose denominator is 100.

Explanation:
Per meaning in percentage.
Question 3.

4%

Explanation:
The Total number of boxes is 100. In the above-given boxes, 4 boxes are filled with color.
(4/100) x 100 = 4%.

Question 4.

15%

Explanation:
The number of boxes are 100. In the above-given boxes, 15 are filled with color.
(15/100) x 100 = 15%

Question 5.

30%

Explanation:
The number of boxes are 100. In the above-given boxes, 30 are filled with color.
(30/100) x 100 = 30%

Question 6.

50%

Explanation:
The Total number of boxes are 100. In the above-given boxes, 50 boxes are filled with color.
(50/100) x 100 = 50

Question 7.

100%

Explanation:
The Total number of boxes are 100. In the above given 100 boxes are filled with color.

(100/100) x 100 = 100

Question 8.

0%

Explanation:
The number of boxes are 100. In the above given no boxes are filled with color.
(0/100) x 100 = 0

Vocabulary

The following terms are used in this chapter. Think about what each term might mean and record your thoughts.

### Lesson 4.1 Percents and Fractions

Cent means one hundred, so percent means per one hundred. The symbol for percent is %.

EXPLORATION 1

Interpreting Models
Work with a partner. Write a percent, a fraction, and a ratio shown by each model. How are percents, fractions, and ratios related?
a.

Percentage = 60%
Fraction = 6/10
Ratio = 3:5

Explanation:
In the above-given boxes, 60 boxes are filled with color.
Percentage = (60/100) x 100 = 60
Fraction = (60/100) = 6/10
Ratio = 6:10 = 3:5
The Relationship between Fractions, Percentages, Ratios is since a percent can be written as a fraction as well as a ratio. The ratio and fraction are same.

b.

Percentage = 8%
Fraction = 8/100
Ratio = 2:25

Explanation:
In the above given boxes, 8 boxes are filled with color.
percentage = (8/100) x 100 = 8
Fraction = 2 : 25
Ratio = 2:5
The Relationship between percents, ratios, fractions are percents can be written as ratios. The ratios and fractions are the same.
c.

Percentage = 51%
Fraction = 51/100
Ratio = 51:100

Explanation:
percentage = (51/100) x 100 = 51%
Fraction = 51 : 100
In the above given boxes 51 boxes are filled with color.

d.

Percentage = 25%
Fraction = 1/4
Ratio = 1:4

Explanation:
percentage = (25/100)
Fraction = 0.25
In the above given boxes 51 boxes are filled with color.

4.1 Lesson

Try It
Write the percent as a fraction or mixed number in simplest form.

Question 1.
5%
1: 20

Explanation:
(5/100) = 1: 20

Question 2.
168%
42/25

Explanation:
(168/100 )= 42: 25

Question 3.
36%
3/25

Explanation:
(36/100) = 3: 25

Question 4.
83%

83/100

Explanation:
(83/100) = 83: 100

Key Idea
Writing Fractions as Percents
Words Write an equivalent fraction with a denominator of 100. Then write the numerator with the percent symbol.

Try It
Write the fraction or mixed number as a percent.

Question 5.
$$\frac{31}{50}$$

62%

Explanation:
(31/50)  = (31 x 2)/(50 x 2) = 62/100 = 62%
Question 6.
$$\frac{19}{20}$$

19/20

Explanation:
(19/20) = (19 x 5)/(20 x 5) = 95/100 = 95%

Question 7.
$$\frac{1}{200}$$

1/200

Explanation:
(1/200) = (1 x 1)/(2 x 1) = 0.5%

Question 8.
1$$\frac{1}{2}$$

3/2

Explanation:
(3/2) = (3 x 50)/(2 x 50) = 150%

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 9.
WRITING A FRACTION
Write 40% as a fraction in simplest form. Draw a model that represents this fraction.

2/5

Question 10.
WRITING A PERCENT
Write $$\frac{9}{20}$$ as a percent.

45

Explanation:
9/20 x 100 = 45

Question 11.
WHICH ONE DOESN’T BELONG?
Which number does not belong with the other three? Explain your reasoning.

0.01

Explanation:
They are in the fraction and 0.01 is in the decimal

Question 12.
OPEN-ENDED
Write three different fractions that are less than 40%.

1/10, 1/5, 3/10

Explanation:
10%,20%,30%

Question 13.
NUMBER SENSE
Can 1$$\frac{1}{4}$$ be written as a percent? Explain.

25%

Explanation:
(1/4) x 100 = (50/2) = 25

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 14.
You and a friend ﬁll balloons with water. Two out of every 25 balloons pop while they are being ﬁlled. What percent of the balloons do not pop while they are being ﬁlled?

92%

Explanation:
Given that or every 25 ballons 2 ballons are popped, It means 23 ballons are not popped . For 100 ballons 92 ballons are not popped.

Question 15.
During the month of April, it rains 2 days for every 3 days that it does not rain. What percent of the days in April does it rain?

20 Days

Explanation:
In April month there are 30 days, so for every 3 days it rains 2 days.
3 x10 = 30 days
2 x10 = 20 days

Question 16.
DIG DEEPER!
There are 100 students in a band. Forty percent are 12 years old, $$\frac{1}{2}$$ are 13 years old, and the rest are 14 years old. Write the portion of the band for each age as a fraction and a percent.

12 years old = 40%, 2:5.
13 years old = 50%, 1:2.
14 yars old = 10%,1:10.

Explanation:
In the given quesion 40% are 12 years old ,50% are 13 years old and the rest are 14 years old.
percent = 40% , fraction = 2: 5
percent = 50% , fraction = 1:2
percent = 10% , fraction = 1: 10

### Percents and Fractions Practice 4.1

Review & Refresh

Copy and complete the statement. Round to the nearest hundredth if necessary.

Question 1.

3000m

Explanation:
1 km = 1000 m so 3 x 1000 =3000m

Question 2.

112 c

Explanation:
1 gal = 6 c so 7 gal = 112 c

Question 3.

1.5 yd

Explanation:
1 Inch = 0.0277778 yds so 54 inches = 1.5 yds

Question 4.

6 kilometers

Explanation:
1 mile = 1.6093kms. So 4 miles = 6.4 km ~6 kms

Question 5.

1
Explanation:
1 liter = 0.2647 gal
6.5 liters = 1

Question 6.

20 kgs

Explanation:
1 lb = 0.4535 kgs so 45lb = 20 kgs

Divide

Question 7.
120 ÷ 12

10

Explanation:
12 x 10 = 120

Question 8.
208 ÷ 4

52

Explanation:
4×52 = 208

Question 9.
195 ÷ 15

13

Explanation:
15×13 = 195

Question 10.
1428 ÷ 34

42

Explanation:
34×42 = 1428

Question 11.
8528 ÷ 164

52

Explanation:
164×52 = 8528

Question 12.
295 ÷ 8

36.875

Explanation:
36.875 x 8 = 295

Use the table to write the ratio.

USING TOOLS
Use a 10-by-10 grid to model the percent. (See Exploration 1, p. 163)

Question 17.
10%

1/10

Explanation:
10 x (1/100) = 1/10

Question 18.
55%

11/20

Explanation:
55 x (1/100) = 11/20

Question 19.
45%

9/20

Explanation:
45 x (1/100) = 9/20

WRITING PERCENTS AS FRACTIONS
Write the percent as a fraction or mixed number in simplest form.

Question 20.
45%

9:20

Explanation:
45 x (1/100) = 9:20

Question 21.
90%

9:10

Explanation:
90 x (1/100) = 9:10

Question 22.
15%

3:20

Explanation:
(15/100) = 3:20

Question 23.
7%

7:100

Explanation:
(7/100) = 7:100

Question 24.
34%

17:50

Explanation:
(34/100) = (17/50) = 17:50

Question 25.
79%

79:100

Explanation:
(79/100) = 79:100

Question 26.
77.5%

151:200

Explanation:
(775/1000) = 151/200 = 151:200

Question 27.
188%

47:25

Explanation:

(188/100) = 94/50 =47/25

Question 28.
8%

2:25

Explanation:
(8/100) = (4/500) = 2/25

Question 29.
224%

56:25

Explanation:
(224/100) = 112/50 = 56/25

Question 30.
0.25%

1:400

Explanation:
(25/10000) = (5/2000) = 1/400

Question 31.
0.4%

1:250

Explanation:
(4/1000) = (2/500) = 1/250

Question 32.
YOU BE THE TEACHER
Your friend writes 225% as a fraction. Is your friend correct? Explain your reasoning.

correct

Explanation:
(225/100) = (45/20) = 9/4

WRITING FRACTIONS AS PERCENTS
Write the fraction or mixed number as a percent.

Question 33.
$$\frac{1}{10}$$

0.1%

Explanation:
(1/10 x 100) = (10/100) = (1/10) = 0.1%

Question 34.
$$\frac{1}{5}$$

0.2%

Explanation:
(1/5) x 100 = (20/100) = (10/100) = (1/5) = 0.2%

Question 35.
$$\frac{11}{20}$$

0.55%

Explanation:
(11/20) x 100 = (55/100) = 0.55%

Question 36.
$$\frac{1}{400}$$

0.0025%

Explanation:
(1/400) x 100 = (1/400) = 0.0025%

Question 37.
$$\frac{2}{25}$$

0.08%

Explanation:
(2/25) x 100 = (8/100) = 0.08%

Question 38.
$$\frac{27}{50}$$

0.27

Explanation:
(27/50) x 100 = (54/200) = 0.27%

Question 39.
$$\frac{3}{250}$$

0.3%

Explanation:
(3/250) x 100 = (12/40)  = 0.3%

Question 40.
$$\frac{18}{25}$$

0.72%

Explanation:
(18/25) x 100 = (72/100) = 0.72%

Question 41.
1$$\frac{17}{20}$$

0.85%

Explanation:
(17/20) x 100 = (85/100) = 0.85%

Question 42.
2$$\frac{41}{50}$$

282%

Explanation:
2 x (41/50) =(141/50)  = 2.82 x 100 = 282%

Question 43.
3$$\frac{1}{200}$$

300.5%

Explanation:
3 x (1/200) = (601/200) = 3.005 x 100 = 300.5

Question 44.
4$$\frac{7}{500}$$

200700%

Explanation:
4 x (7/500) = (2007/500) = 2007 x 100 = 200700

Question 45.
YOU BE THE TEACHER
Your friend writes $$\frac{14}{25}$$ as a percent. Is your friend correct? Explain your reasoning.

correct

Explanation:
(14/25) = (56/100) = 0.56%

Question 46.
MODELING REAL LIFE
During a 10-year period, 6 out of 30 Major League Baseball teams won the World Series. What percent of Major League Baseball teams won the World Series during the 10-year period?

5%

Explanation:
Out of 30 games, 6 matches are won for 100 games 15 matches are won
(6/30) = (X/100)
X = 5

Question 47.
MODELING REAL LIFE
A doctor conducts an experiment to test new treatments for a medical condition. Of the 16 volunteers in the experiment, 4 do not receive any treatment. What percent of the volunteers do not receive any treatment?

25%

Explanation:
In the above-given statement out of 16 volunteers in the experiment, 4 do not receive any treatment. So (4/4) = 16. If it is 100% (100/4) = 25

Question 48.
LOGIC
Of the students in your class, 12% are left-handed and the rest are right-handed. What fraction of the students are left-handed? Are there more right-handed or left-handed students? Explain.

12% of students are left handed = 3: 25

Explanation:
Given that 12% are left handed and remaining are right handed = 100% – 12% = 88%.
There are more right-handed students.

Question 49.
NUMBER SENSE
You have 125% of the tickets required for a prize. What fraction of the required tickets do you have? Do you need more tickets for the prize? Explain.

5:4

Explanation:
We have 125% of the tickets required for a prize. No we do not need more tickets for the prize. We have more enough 125 percent of the tickets required for a prize.

FINDING PERCENTS
Find the percent.

Question 50.
3 is what percent of 8?

37.5

Explanation:
(3/8)  x 100 = 37.5

Question 51.
13 is what percent of 16?

81.25

Explanation:
(13/16) x 100 = 81.25

Question 52.
9 is what percent of 16?

56.25

Explanation:
(9/16) x 100 = 56.25

Question 53.
33 is what percent of 40?

82.5

Explanation:
(33/40) x 100 = 82.5

Question 54.
Modeling Real Life
A survey asked students to choose their favorite social media website.
a. What fraction of the students chose Website A?
b. What percent of the students chose Website C?

a = 5:20, b = 0.22

Explanation:
The fraction of students who choose website A is 35. 35 :100 = 5:20
The percent of students who choose website c is 22.(  25/100) = 0.22

Question 55.
DIG DEEPER!
The percent of the total area of the United States that is in each of four states is shown.

a. Write the percents as fractions in simplest form.b. Compared to the map of Florida, is the map of Alaska the correct size? Explain your reasoning.
c. RESEARCH
Which of the 50 states are larger than Illinois?

Question 56.
CRITICAL THINKING
A school fundraiser raised 120% of last year’s goal and 25% of this year’s goal. Did the fundraiser raise more money this year? Explain your reasoning.

Question 57.

No

Explanation:
The fundraiser did not raise more money this year. Last year fundraiser raised 120% and this year fundraiser raised 25%,
CRITICAL THINKING
How can you use a 10-by-10 grid to model $$\frac{1}{2}$$?

Question 58.

REASONING
Write $$\frac{1}{12}$$ as a percent. Explain how you found your answer.

8.33

Explanation:
(1/12) x 100 = 8.33

### Lesson 4.2 Percents and Decimals

EXPLORATION 1
Interpreting Models
Work with a partner. Write a percent and a decimal shown by each model. How are percents and decimals related?

a :  Fraction = 100% , Decimal = 1.0
b : Fraction = 33%, Decimal = 0.33
c : Fraction = 37%, Decimal = 0.37
d : Fraction = 64%, Decimal = 0.64
e : Fraction = 50%, Decimal = 0.5
f : Fraction = 60%, Decimal = 0.6
g : Fraction = 130%, Decimal = 0.65

Explanation:
a : 100% =  (100/100) = 1 and Decimal = 1.0. The total boxes are filled.
b : 33% = (33/100) = 0.33.  So 33% boxes are filled.
c : 37% = (37/100) = 0.37. So 37 boxes are filled.
d : 64% = (64/100) = 0.64. So 64 boxes are filled.
e : 50% = (50/100) = 0.5. So 50 boxes are filled.
f : 60% = (60/100) = 0.6. So 60 boxes are filled.
g : 130% = (130/200) = 0.65. So 130 boxes are filled.

4.2 Lesson

Try It

Write the percent as a decimal. Use a model to represent the decimal.

Question 1.
24%

(24/100) = (6/25) = 0.24

Explanation:

Question 2.
3%

(3/100) = 0.03

Explanation:

Question 3.
107%

1.07 = (107/100)

Explanation:

Question 4.
92.5%

92.5% = (925/1000) = 0.925

Explanation:

Key Idea
Writing Decimals as Percents
Words Multiply by 100, which moves the decimal point two places to the right. Then add a percent symbol.

Try It
Write the decimal as a percent.

Question 5.
0.94

94%

Explanation:
94% = (94/100) = 0.94

Question 6.
1.2

120%

Explanation:
120% = (120/100) = 1.2

Question 7.
0.316

31.6%

Explanation:
31.6% = (31.6/100) = 0.316

Question 8.
0.005

5%

Explanation:
5% = (5/1000) = 0.005

Try It

Question 9.
WHAT IF? You earn 90 out of a possible 100 points on the test. Write “90 out of 100” as a fraction, a decimal, and a percent.

Fraction = 90: 100
Decimal = 0.9
percent = 90%

Explanation:
They had given that 90 out of possible 100 points on the test. So 90% = (90/100), fraction = 90 :  100, decimal = 0.9.

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

WRITING PERCENTS AS DECIMALS
Write the percent as a decimal. Use a model to represent the decimal.

Question 10.
32%

32% = (32/100) = 0.32

Explanation:

Question 11.
54.5%

54.5% = (54.5/100 = 0.545

Explanation:

Question 12.
108%

108% = (108/100) = 1.08

Explanation:

WRITING DECIMALS AS PERCENTS
Write the decimal as a percent.

Question 13.
0.71

71%

Explanation:
(71/100) = 71%

Question 14.
0.052

52%

Explanation:
(52/1000) = 52%

Question 15.
9.66

966%

Explanation:
966% = (966/100) = 9.66

Question 16.
WRITING
Explain why the decimal point moves left when dividing a number by 100.

It moves 2 digits left because it has 2 zeros.

Explanation:
It is dividing by 100 so the decimal point moves left when dividing a number by 100.

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 17.
Write the amount of occupied space on the computer as a percent.

0.18%

Explanation:
In the above given condition the total capacity is 150GB and the free space is 132GB. The remaining space is 18.

Question 18.
Salinity is a measure of the salt content of a body of water. One researcher measures the salinity of the Indian Ocean as 3.2%. Another researcher measures the salinity of the Dead Sea as 34%. A bucket of water from the Indian Ocean contains 56 grams of salt.

How much salt is contained in the same amount of water from the Dead Sea? Justify your answer.

34%

Explanation:
They have said that 34% of salt is ontained in the dead water.

### Percents and Decimals Practice 4.2

Review & Refresh

Write the fraction or mixed number as a percent.

Question 1.
$$\frac{7}{50}$$

0.14%

Explanation:
(7/50) x 100 = (7 x 2)/(50 x 2) = (14/100) = 0.14

Question 2.
$$\frac{2}{5}$$

0.4%

Explanation:
(2/5) x 100 = (2 x 20)/(5 x 100) = (40/100) = 0.4

Question 3.
$$\frac{1}{250}$$

0.004%

Explanation:
(1/250) x 100 = (1 x 4)/(250 x 4) = (4/1000) = 0.004

Question 4.
$$\frac{1}{500}$$

0.002%

Explanation:
(1/500) x 100 = (1 x 1)/(500 x 1) = 0.002

Represent the ratio relationship using a graph.

Question 5.

Question 6.

Multiply. Write the answer in simplest form.

Question 7.

(6/63)

Explanation:
(3 x 2) = 6 ,(7 x 9) = 63

Question 8.

(5/60)

Explanation:
(5 x 1) = 5,(12 x 5) = 60

Question 9.

(126/30)

Explanation:
(14 x 9) = 126,(3 x 10) = 30

Question 10.

(91/12)

Explanation:
(13 x 7) = 91, (6 x 2) = 12

Concepts, Skills, & Problem Solving

INTERPRETING MODELS
Write the percent and the decimal shown by the model. (See Exploration 1, p. 169.)

Question 11.

51%, 0.51

Explanation:
In the above given box 51 boxes are filled with color. So 51% = (51/100) = 0.51

Question 12.

144%, 0.72

Explanation:
In the above given box 144 boxes are filled with color. So 144% = (144/200) = 0.72

WRITING PERCENTS AS DECIMALS
Write the percent as a decimal.

Question 13.
78%

0.78

Explanation:
(78/100) = 0.78

Question 14.
55%

0.55

Explanation:
(55/100) = 0.55

Question 15.
18.5%

0.185

Explanation:
(18.5/100) = 0.185

Question 16.
57.4%

0.574

Explanation:

(57.4 /100) = 0.574

Question 17.
33%

0.33

Explanation:
(33/100) = 0.33

Question 18.
9%

0.09

Explanation:
(9/100) = 0.09

Question 19.
47.63%

0.4763

Explanation:
(47.63/100) = 0.4763

Question 20.
91.25%

0.9125

Explanation:
(91.25/100) = 0.9125

Question 21.
166%

1.66

Explanation:
(166/100) = 1.66

Question 22.
217%

2.17

Explanation:
(217/100) = 2.17

Question 23.
0.06%

6%

Explanation:
(6/100) = 0.06

Question 24.
0.034%

WRITING DECIMALS AS PERCENTS
Write the decimal as a percent.

Question 25.
0.74

74%

Explanation:
(74/100) = 0.74

Question 26.
0.52

52%

Explanation:
(52/100) = 0.52

Question 27.
0.89

89%

Explanation:
(89/100) = 0.89

Question 28.
0.768

768%

Explanation:
(768/1000) = 0.768

Question 29.
0.99

99%

Explanation:
(99/100) = 0.99

Question 30.
0.49

49%

Explanation:
(49/100) = 0.49

Question 31.
0.487

48.7%

Explanation:
48.7% = (48.7/100) = 0.487

Question 32.
0.128

12.8%

Explanation:
12.8% = (12.8/100) = 0.128

Question 33.
3.68

368%

Explanation:
368% = (368/100) = 3.68

Question 34.
5.12

512%

Explanation:
512% = (512/100) = 5.12

Question 35.
0.0371

3.71%

Explanation:
3.71% = (3.71/100) = 0.0371

Question 36.
0.0046

46%

Explanation:
46% = (46/1000) = 0.0046

Question 37.
YOU BE THE TEACHER
Your friend writes 0.86 as a percent. Is your friend correct? Explain your reasoning.

No my friend is not correct.

Explanation:
0.86 = 0.086 = 0.0086.

MATCHING
Match the decimal with its equivalent percent.

Question 38.
0.42

0.42 = 0.042 = 0.0042

Explanation:
(42/100) = 0.42

Question 39.
4.02

4.02 = 4.002 = 4.0002

Explanation:

Question 40.
0.042

0.042 = 0.0042 = 0.00042

Explanation:
(42/100000) = 0.00042

Question 41.
0.0402
A. 4.02%
B. 42%
C. 4.2%
D. 402%

A

Explanation:
4.02% = (4.02/100) = 0.0402

Question 42.
MODELING REAL LIFE
About 80% of the precipitation that enters Crater Lake falls directly on the surface of the lake. Write this percent as a decimal.

0.8

Explanation:
(80/100) = 0.8 . In the above-given statement, they are given in percentage and said that write it in the decimal points.

Question 43.
MODELING REAL LIFE
About 0.34 of the length of a cat is its tail. Write this decimal as a percent.

34%

Explanation:
(34/100) = 0.34. In the given question, they are given in decimal and they said that convert it in percents.

Question 44.
OPEN-ENDED
Write three different decimals that are between 10% and 20%.

0.13,0.16,0.19

Explanation:
In the above-given question, they said to write the decimals between 10% and 20%. So 13%,16%,19% is between the 10% and 20%.

WRITING PERCENTS AS FRACTIONS AND DECIMALS
Write the percent as a fraction in simplest form and as a decimal.

Question 45.
36%

Decimal = 0.36, Fraction = 18 : 25

Explanation:
36% = (36/100) = 0.36 , fraction = 18: 25
Question 46.
23.5%

Decimal = 0.235, Fraction = 47: 200

Explanation:
23.5% = (23.5/100) = 0.235 , fraction = 47 : 200

Question 47.
16.24%

Decimal = 0.1624, Fraction =

Question 48.
DIG DEEPER!
The percents of students who travel to school by car, bus, and bicycle are shown for a school of 825 students.

a. Write the percents as decimals.

car:0.2 , school bus:0.48 , bicycle:0.08

Explanation:
In the above-given figures, they have given in percents and said to write in decimals.
b. Write the percents as fractions.

c. What percent of students use another method to travel to school?

24%

Explanation:
They go by walk or either they go by bike.

d. RESEARCH
Make a bar graph that represents how the students in your class travel to school.

Question 49.
LOGIC
A running back was the MVP (most valuable player) in 0.14 of the ﬁrst 50 Super Bowls.
a. What percent of the MVPs were running backs?
b. What fraction of the MVPs were not running backs?

Question 50.
CHOOSING A METHOD
Students in a class were asked to tell their favorite color.

a. Whatpercent said red, blue, or yellow?

Red = 26% , blue = 40% , yellow = 4%

Explanation:
In the above given that the students who like red are 26%, blue is40%, yellow is 4%.
b. How many times more students said red than yellow?

22

Explanation:
The students who like red color more than yellow color is 22%
c. Use two methods to ﬁnd the percent of students who said green. Which method do you prefer? Explain.

The students who said green is 16%.

Explanation:
In the above given the students who like red 26%, blue 40%, yellow 4%, purple 14%. So the total percentage is 100 and the remaining is 16. (100-84) = 16

### Lesson 4.3 Comparing and Ordering Fractions, Decimals, and Percents

EXPLORATION 1
Using a Number Line to Order Numbers

Work with three partners. Create a number line on the ﬂoor. Have your group stand on the number line to represent the four numbers in each list. Use the results to order each list of numbers from least to greatest. How did you know where to stand?

a =
b =
c =
d =
e =
f =

Explanation:
a = 0.25 = 25%
0.5 = (0.5/10) x 100 = 50%
b =  (3/4) = (3/4) x 100 = 75%
(1/20) = (1/20) x 100 = 5%
c = 0.125 = 12.5%
(3/10) = (3/10) x 100 = 30%
d = 1.02 = (1.02/100) x 100 = 102%
(1/100) = (1/100) x 100 = 1%
e = 0.3 = 30%
(1/8) = (1/8) x 100 = 5%
0.75 = (0.75/100) x 100 = 75%
f = (51/50) = (51/50) x 100 = 102%
(9/10) = 90%
1.5 = (1.5/10) x 100 = 150%

4.3 Lesson

When comparing and ordering fractions, decimals, and percents, write the numbers as all fractions, all decimals, or all percents.

Try It
Tell which number is greater.

Question 1.
25%, $$\frac{7}{25}$$

(7/25) is greater

Explanation:
25% = (25/100) = 0.25, (7/25) = 0.28

Question 2.
0.49, 94%

94% is greater

Explanation:
94% = (94/100) = 0.94

Try It
Order the numbers from least to greatest.

Question 3.
$$\frac{3}{10}$$, 15%, 0.2, $$\frac{3}{8}$$, 0.09

0.09, 0.15, 0.2, 0.3, 0.375

Explanation:
(3/10) = 0.3, 15% = 0.15, (3/8) = 0.375. They said to write from least to greast. So 0.09, 0.15, 0.2, 0.3, 0.375.

Question 4.
100%, 0.95, 1.2, $$\frac{5}{4}$$, 110%

0.95, 1, 1.1, 1.2,1.25

Explanation:
100% = 1, (5/4) = 1.25, 110% = 1.1 so 0.95, 1, 1.1, 1.2, 1.25.

Question 5.
WHAT IF?
Your friend makes $$\frac{3}{4}$$ of his shots. Did your friend make more shots than you? your sister?

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

72%
0.85
0.26, 26%
(31/50),62%
(9/20),0.45

Explanation:
Fraction = 18 : 25 ,decimal = 0.72, percent = 72%
Fraction = 17 : 20 , decimal = 0.85, percent = 85%
Fraction = 13 :50 , decimal = 0.26, percent = 26%
Fraction = 31 :50, decimal = 0.62, percent = 62%
Fraction = 9 : 20 , decimal = 0.45, percent = 45%

Question 6.
NUMBER SENSE
Copy and complete the table.

Explanation:

Fraction = 18 : 25 ,decimal = 0.72, percent = 72%
Fraction = 17 : 20 , decimal = 0.85, percent = 85%
Fraction = 13 :50 , decimal = 0.26, percent = 26%
Fraction = 31 :50, decimal = 0.62, percent = 62%
Fraction = 9 : 20 , decimal = 0.45, percent = 45%

Question 7.
NUMBER SENSE
How would you decide whether $$\frac{3}{5}$$ or 59% is greater? Explain.

(3/5) is greater.

Explanation:
(3/5) = 0.6, 59% = 0.59 so 0.6 is greater than 0.59

COMPARING NUMBERS

Tell which number is greater.

Question 8.
33%, 0.34

0.34 is greater.

Explanation:
0.34 = (34/100). 34 is greater than 33.

Question 9.
0.85, $$\frac{4}{5}$$

0.8 is greater.

Explanation:
0.85 = (85/100)

Question 10.
$$\frac{9}{50}$$, 17%

(9/50) is greater.

Explanation:
17% = (17/100) = 0.17,(9/50) = (18/100) = 0.18. So 0.18 is greater.

ORDERING NUMBERS
Order the numbers from least to greatest.

Question 11.
12%, 0.1, $$\frac{4}{25}$$

0.1,12%,4/25.

Explanation:
12% = 0.12, (4/25) = 0.16

Question 12.
1.35, 125%, $$\frac{6}{5}$$, 1.5, 130%

0.2, 1.25, 1.3, 1.35, 1.5.

Explanation:
125% = 1.25, (6/5) = 0.2, 130% = 1.3

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 13.
The table shows the portions of copper in three rings. Which ring has the highest portion of copper?

All the 3 rings are approximately equal.

Explanation:
25% = 0.25, 0.2, (9/40) = 0.225. So the 3 rings has approximately equal values.

Question 14.
DIG DEEPER!
The table shows the results of ﬁve teams competing in a scavenger hunt. List the ﬁve teams in order by the portion of items collected from least to greatest. What is the minimum number of items in the scavenger hunt? Explain.

Team 5, team 1, team 3, team 2, team 4.

Explanation:
(13/20) = 0.65, (3/4) = 0.75, 77.5% = 0.775,  0.8, 0.825. So the minimum number of items in scavenger hunt is 5.

### Comparing and Ordering Fractions, Decimals, and Percents Homework & Practice 4.3

Review & Refresh

Write the percent as a decimal.

Question 1.
12%

0.12

Explanation:
(12/100) = 0.12

Question 2.
98.37%

0.9837

Explanation:
(98.37/100) = 0.9837

Question 3.
0.046%

0.00046

Explanation:
(0.046/100) = 0.00046

Find the missing value(s) in the ratio table. Then write the equivalent ratios.

Question 4.

45

Explanation:
(4 x 9) = 36, (5 x 9) = 45

Question 5.

Multiply.

Question 6.

(5.3 x 6) = 31.8

Explanation:

Question 7.

162.9

Explanation:

Question 8.
12.43 × 1.51

(12.43 x 1.51) = 18.7693

Explanation:

Question 9.
0.852 × 6.7

(0.852 x 6.7) = 5.7084

Explanation:

Find the GCF of the numbers.

Question 10.
15, 36

3

Explanation:
(36/15) = 6 . (15/6) =3, (6/3) = 0

Question 11.
51, 85

17

Explanation:
(85/51) = 34,(51/34) = 17, (34/17) = 0

Question 12.
88, 112

8

Explanation:
(112/88) = 24, (88/24) = 16, (24/16) = 8, (16/8) = 0

Concepts, Skills, & Problem Solving

USING A NUMBER LINE
Use a number line to order the numbers from least to greatest. (See Exploration 1, p. 175.)

Question 13.
80%, 0.65, $$\frac{3}{10}$$, 40%

Explanation:
(3/10) = (3/10) x 100 = (3 x 10)/(10 x 10) = (30/100) =30%
0.65 = (0.65/100) x 100 = 65%

Question 14.
0.27, 20%, $$\frac{1}{25}$$, 9%

Explanation:
0.27 = (0.27/100) x 100 = 27%
(1/25) = (1/25) x 100 = (1 x 4/25 x 4) = (4/100) = 4%

Question 15.
$$\frac{1}{8}$$, 0.25, 15%, $$\frac{27}{100}$$

Explanation:
(1/8) = (1/8) x 100 = (1 x 50/4 x 50) = (50/200) = 0.25 = 25%
0.25 = (0.25 x 100) = 25%
(27/100) = (27/100) x 100 = 27%

COMPARING NUMBERS
Tell which number is greater.

Question 16.
0.9, 95%

95%

Explanation:
95% = (95/100) = 0.95

Question 17.
20%, 0.02

20%

Explanation:
20% = 0.2

Question 18.
$$\frac{37}{50}$$, 37%

(37/50)

Explanation:
(37/50) = 0.74, 37% = 0.37. So (37/50) is greater.

Question 19.
50%, $$\frac{13}{25}$$

(13/25)

Explanation:
50% = (50/100) = 0.5, (13/25) = 0.52

Question 20.
0.086, 86%

86%

Explanation:
86% = 0.86, 0.086 so 0.86 is greater

Question 21.
76%, 0.67

76%

Explanation:
76% = 0.76, 67% = 0.67

Question 22.
60%, $$9\frac{5}{8}$$

(5/8)

Explanation:
(5/8) = 0.625, 60% = 0.6

Question 23.
0.12, 1.2%

0.12

Explanation:
0.12 = 12%, 1.2%

Question 24.
17%, $$\frac{4}{25}$$

17%

Explanation:
17% = 0.17, (4/25) = 16% = 0.16

Question 25.
140%, 0.14

140%

Explanation:
140% = 1.4

Question 26.
$$\frac{3}{8}$$, 30%

0.375

Explanation:
30% = 0.3, (3/8) = 0.375

Question 27.
80%, $$\frac{7}{10}$$

80%

Explanation:
80% = 0.8, (7/10) = 0.7

ORDERING NUMBERS
Order the numbers from least to greatest.

Question 28.
38%, $$\frac{8}{25}$$, 0.41

(8/25) , 38%, 0.41

Explanation:
38% = 0.38, (8/25) = 0.32, 0.41

Question 29.
68%, 0.63, $$\frac{13}{20}$$

0.63, (13/20), 68%

Explanation:
68% = 0.68, (13/20) = 0.65

Question 30.
$$\frac{43}{50}$$, 0.91, $$\frac{7}{8}$$, 84%

84%, (43/50), (7/8) , 0.91

Explana;tion:
(43/50) = 0.86, (7/8) = 0.875, 84% = (84/100) = 0.84

Question 31.
0.15%, $$\frac{3}{20}$$, 0.015

0.15%, 0.015, (3/20)

Explanation:
0.15% =(0.15/100) = 0.0015, (3/20) = 2.5

Question 32.
2.62, 2$$\frac{2}{5}$$, 26.8%, 2.26, 271%

2 x (2/5) ,26.8%, 2.26, 2.62, 2.71

Explanation:
2 x (2/5) = 0.024, 26.8% = 0.268, 271% = 2.71
So 0.024, 0.268, 2.26, 2.62, 2.71

Question 33.
$$\frac{87}{200}$$, 0.44, 43.7%, $$\frac{21}{50}$$

(21/50),0.44, 43.7%, (87/200)

Explanation:
(21/50) = 0.42, (87/200) = 0.435, 43.7% = 0.437

Question 34.
NUMBER SENSE
You answer 21 out of 25 questions correctly on a test. Do you reach your goal of answering at least 80% of the questions correctly?

yes we reach our goal of answering .

Explanation:
We answer 21 out of 25 questions correctly on a test. Yes we reach our goal of answering 80%.

Question 35.
MODELING REAL LIFE
The table shows the approximate portions of the world population that live in four countries. Order the countries by population from least to greatest.

PRECISION
Order the numbers from least to greatest.

Russia, Brazil, India, United States.

Explanation:
Brazil = 2.8%
India = (7/40) = (7/40) x 100 = 17.5%
Russia = (1/50) = (1/50) x 100 = 2%
United States = 0.044 = (444/1000) x 100 = 44.4%

Question 36.
66.1%, 0.66, $$\frac{133}{200}$$, 0.667

0.66, 66.1%, (133/200), 0.667

Explanation:
66.1% = 0.661, (13/200) = 0.665

Question 37.
$$\frac{111}{500}$$, 21%, 0.211, $$\frac{11}{50}$$

21%, 0.211, (11/50), (111/500)

Explanation:
21% = 0.21, (11/50) = 0.22, (111/500) = 0.222

MATCHING
Tell which letter shows the graph of the number.

Question 38.
$$\frac{2}{5}$$

Question 39.
45.2%

Question 40.
0.435

Question 41.
$$\frac{89}{200}$$

Question 42.
PRECISION
The Tour de France is a bicycle road race. The whole race is made up of 21 small races called stages. The table shows how several stages compare to the whole Tour de France in a recent year. Order the stages by distance from shortest to longest.

Stage21, Stage 8, Stage1, Stage17, Stage7

Explanation:
Stage 1 = (11/200 x 100) = 5.5%
Stage 7 = (444/1000 x 100 )  = 44.4%
Stage 8 = (6/125 x 100) = 4.8%
Stage 17 = (6/100 x 100) = 6%
Stage 21 = 4%

Question 43.
PRECISION
The table shows the portions of the day that several animals sleep.
a. Order the animals by sleep time from least to greatest.
b. Estimate the portion of the day that you sleep.
c. Where do you ﬁt on the ordered list?

a : Dolphin, Rabbit, Lion, Squirrel,Tiger
b : 8 hours
c : Dolhpin:

Explanation:
a : dolphin = 43.3%, rabbit = (19/40 x 100) = 47.5%, squirrel = (31/50 x 100) = 62
b : I will sieep 8 hours per a day
c : Dolhpin

Question 44.
NUMBER SENSE
Tell what whole number you can substitute for a in each list so the numbers are ordered from least to greatest. If there is none, explain why.
a. $$\frac{1}{a}$$, $$\frac{a}{20}$$, 28%
b. $$\frac{3}{a}$$, $$\frac{a}{5}$$, 75%

a : 0.1

### Lesson 4.4 Solving Percent Problems

EXPLORATION 1

Using Percent Models
Work with a partner
a. Find the missing values. What does the model represent?

The missing values of 15= 16.6%, (100/3) = 22.5, 40 = 62.5, 75% = 50

Explanation:
The missing value of 15 = (0+33.5)/2 = 16.6%
The missing value of 33.5 = (15 + 30)/2 = 22.5%
The missing value of 40 = (50 + 75)/2 = 62.5%
The missing value of 75 = (40 + 60)/2 = 50%

b. Label atleast three percents and their corresponding numbers on the model below. How do you know you are correct?

EXPLORATION 2
Solving a Percent Problem

Work with a partner. You purchase a national parks annual pass for 75% of the full price of the pass.
a. Suppose you know the full price or the discounted price. How can you ﬁnd the other price? Compare your answers with other students in your class.
b. Suppose the full price of the pass is $80. How can you use a percent model to ﬁnd the purchase price? Answer: If we purchase national parks annual pass for 75% = (75 x 80)/100 = 6 if they give 25% discount = (25 x 80)/100 = 20 Explanation: We purchase a national parks annual pass for 75% of the full price . If the full price is 100% then the discounted price is 25% = 100%-25% = 75% So if we purchase annual pass for 80% = (75 x 80)/100 = 6 If we purchase it for 25% = (25 x 80) /100 = 20 4.4 Lesson Try It Find the percent of the number. Question 1. 90% of 20 Answer: 18 Explanation: 90% = (90/100) x 20 = 18 Question 2. 75% of 32 Answer: 24 Eplanation: (75/100) x 32 = 24 Because n% means n per 100, you can also solve percent problems using part-to-whole ratios. Try It Find the percent of the number. Question 3. 10% of 110 Answer: 11 Explanation: (10/100) x 110 = 11 Question 4. 30% of 75 Answer: 22.5 Explanation: (30/100) x 75 = 22.5 Try It Find the whole. Question 5. 15% of what number is 9? Answer: 60 Explanation: (15/100) x 60 = 9 Question 6. 5% of what number is 10? Answer: 200 Explanation: (5/100) x 200 = 10 Try It Question 7. 62% of what number is 31? Answer: 50 Explanation: (62/100) x 50 = 31 Question 8. 125% of what number is 50? Answer: 40 Explanation: (120/100) x 40 = 50 Try It Question 9. The width of a rectangular stage is 55% of its length. The stage is 120 feet long. What is the area of the stage? Self-Assessment for Concepts & Skills Solve each exercise. Then rate your understanding of the success criteria in your journal. Question 10. DIFFERENT WORDS, SAME QUESTION Which is different? Find “both” answers. Answer: Twenty percent of what number is 30 is different. Explanations: 1 : (20/100) x 150 = 30 2 : (20/100) x ? = 30 then 30 x (100/20) = 150 Question 11. FINDING THE PERCENT OF A NUMBER Find 12% of 75. Answer: 9 Explanation: (12/100) x 75 = 9 Question 12. FINDING THE WHOLE 35% of what number is 21? Answer: 60 Explanation: (35/100) x 60 = 21 Question 13. NUMBER SENSE If 52 is 130% of a number, is the number greater than or less than 52? Explain. Answer: The number is less than 52 Explanation: (130/100) x 40 = 52. So 40 is less than 52 Question 14. STRUCTURE How can you ﬁnd 10% of any number without multiplying or dividing? Explain your reasoning. Answer: (10/100) = (1/10) = 0.1 Explanation: First, we have canceled zeros we got (1/10) automatically the point moves to the front then we get 0.1 Self-Assessment for Problem Solving Solve each exercise. Then rate your understanding of the success criteria in your journal. Question 15. You raise$420 during a fundraising event. The amount of money that you raise is 120% of your goal. How much more did you raise than your goal?

70$I raise more than my goal Explanation: If i raise 120% of our goal for$420
So for 100% i raise more than 20%
(420 x 20)/120 = 70$Question 16. A shirt is on sale for 60% of the original price. The original price is$28 more than the sale price. What was the original price?

The original price is 70

Explanation:
A shirt is on sale for 60% that  means for 100% 40% is remaining.
The original price is $28 more than the sale price. (100 x 28)/40 = 70 Question 17. You have a meal at a restaurant. The sales tax is 8%. You leave a tip for the waitress that is 20% of the pretax price. You spend a total of$23.04. What is the pretax price of the meal?

The pretax price of the meal =

### Solving Percent Problems Homework & Practice 4.4

Review & Refresh

Order the numbers from least to greatest.

Question 1.
latex]\frac{1}{8}[/latex], 35%, 0.33

(1/8), 0.33, 35%

Explanation:
(1/8) = 0.125, 35% = 0.35, 0.33 so 0.125, 0.33, 0.35

Question 2.
0.3, latex]\frac{9}{25}[/latex], 0.35, 33%

0.3, 33%, 0.35, (9/25)

Explanation:
33% = 0.33, (9/25) = 0.36 . So 0.3, 0.33, 0.35, 0.36

Question 3.
latex]\frac{13}{50}[/latex], 22%, 0.28, latex]\frac{1}{5}[/latex], 0.41

(1/5), 22%, 0.28, 0.41, (13/50)

Explanation:
(13/50) = 2.66, 22% = 0.22, (1/5) = 0.2 so (1/5), 22%, 0.28, 0.41,2.66 is from least to greatest.

Write the percent as a fraction or mixednumber in simplest form.

Question 4.
65%

(65/100)

Explanation:
65% = (65/100)

Question 5.
0.45%

(45/100)

Explanation:
0.45% = (45/100)

Question 6.
110%

(110/100)

Explanation:
110% = (110/100)

Divide.

Question 7.
19.2 ÷ 1.6

12

Explanation:
(19.2 % 1.6) = 12

Question 8.

10.2459016

Explanation:
(0.244 x 0.244) = 0.059536
0.61/0.244 = 10.2459016

Question 9.

2.89050757
Explanation:
(0.558 x 0.558) = 0.311364
0.9/0.311364 = 2.89050757

Question 10.
4.65 ÷ 0.003

1550

Explanation:
(4.65 % 0.003) = 1550

The tape diagram represents the ratio of the time you spend online to the time your friend spends online. You are online for 30 minutes. How many minutes does your friend spend online?

Question 11.

2 hrs

Explanation:
I spend it online for 30 minutes and my friend spends it online for 2 hrs. The above diagram shows that 1:4 ratio that is 120 minutes.

Question 12.

45 minutes

Explanation:
1 spend it online for 30 minutes and my friend spends it online for 45 minutes. The above diagram shows that my friend spends 45 minutes in online.

Concepts, Skills, & Problem Solving

USING TOOLS
An annual pass to a park costs $120. Use a percent model to ﬁnd the given percent of the full price of the annual pass. (See Exploration 2, p. 181.) Question 13. 25% Answer: 30$

Explanation:
(25/100) x 120 = 30$Question 14. 50% Answer:: 60$

Explanation:
(50/100) x 120 = 60$Question 15. 200% Answer: 240$

Explanation:
(200/100) x 120 = 240$FINDING THE PERCENT OF A NUMBER Find the percent of the number. Explain your method. Question 16. 20% of 60 Answer: 12 Explanation: (20/100) x 60 = 12 Question 17. 10% of 40 Anwer: 4 Explanation: (10/100) x 40 = 4 Question 18. 50% of 70 Answer: 35 Explanation: (50/100) x 70 = 35 Question 19. 30% of 30 Answer: 9 Explanation: (30/100) x 100 = 9 Question 20. 10% of 90 Answer: 9 Explanation: (10/100) x 90 = 9 Question 21. 15% of 20 Answer: 3 Explanation: (15/100) x 20 = 3 Question 22. 25% of 50 Answer: 12.5 Explanation: (25/100) x 50 = 12.5 Question 23. 5% of 60 Answer: 3 Explanation: (5/100) x 60 = 3 Question 24. 30% of 70 Answer: 21 Explanation: (30/100) x 70 = 21 Question 25. 75% of 48 Answer: 36 Explanation: (75/100) x 48 = 36 Question 26. 45% of 45 Answer: 20.25 Explanation: (45/100) x 45 = 20.25 Question 27. 92% of 19 Answer: 17.48 Explanation: (92/100) x 19 = 17.48 Question 28. 40% of 60 Answer: 24 Explanation: (40/100) x 60 = 24 Question 29. 38% of 22 Answer: 8.36 Explanation: (38/100) x 22 = 8.36 Question 30. 70% of 20 Answer: 14 Explanation: (70/100) x 20 = 14 Question 31. 87% of 55 Answer: 47.85 Explanation: (87/100) x 55 = 47.85 Question 32. 140% of 60 Answer: 84 Explanation: (140/100) x 60 = 84 Question 33. 120% of 33 Answer: 39.6 Explanation: (120/100) x 33 = 39.6 Question 34. 175% of 54 Answer: 94.5 Explanation: (175/100) x 54 = 94.5 Question 35. 250% of 146 Answer: 365 Explanation: (250/100) x 146 = 365 Question 36. MODELING REAL LIFE The tail of the spider monkey is 64% of the length shown. What is the length of the tail? Answer: 28 Explanation: The length of the tail is 28 Question 37. PROBLEM SOLVING A family pays$45 each month for cable television. The cost increases 7%.
a. How many dollars is the increase?

3.15$Explanation: (7/100) x 45 = 3.15$
b. What is the new monthly cost?

3.15$Explanation: The cost increases by 7% so we have to pay 3.15$ for the new month.

Question 38.
YOU BE THE TEACHER
Your friend ﬁnds 40% of 75. Is your friend correct? Explain your reasoning.

correct

Explanation:
40% = 0.4 so (40/100) x 75 = 0.4 x 75 = 30. Yes my friend is correct.

FINDING THE WHOLE
Find the whole. Explain your method.

Question 39.
10% of what number is 14?

1.4

Explanation:
(14/10) = 1.4

Question 40.
20% of what number is 18?

0.9

Explanation:
(18/20) = 0.9

Question 41.
25% of what number is 21?

0.84

Explanation:
(21/25) = 0.84

Question 42.
75% of what number is 27?

0.36

Explanation:
(27/75) = 0.36

Question 43.
15% of what number is 12?

0.8

Explanation:
(12/15) = 0.8

Question 44.
85% of what number is 17?

0.2

Explanation:
(17/85) = 0.2

Question 45.
140% of what number is 35?

0.25

Explanation:
(35/140) = 0.25

Question 46.
160% of what number is 32?

0.2

Explanation:
(32/160) = 0.2

Question 47.
125% of what number is 25?

0.2

Explanation:
(25/125) = 0.2

Question 48.
175% of what number is 42?

0.24

Explanation:
(42/175) = 0.24

Question 49.
YOU BE THE TEACHER
Your friend answers the question “20% of what number is 5?” Is your friend correct? Explain your reasoning.

correct

Explanation:
(5/20) = 0.25 = (1/4)

Question 50.
PROBLEM SOLVING
You have a coupon for a restaurant. You save $3 on a meal. What was the original cost of the meal? Answer: 12$

Explanation:
The original cost of the meal is 12$because they save 3$ on a meal.

Question 51.
PROBLEM SOLVING
The results of a survey are shown at the right. In the survey, 12 students said that they would like to learn French. How many of the students surveyed would like to learn Spanish?

18

Explanation:
The students who would like to learn French is 12. The students who would like  to learn spanish is 18

Question 52.
MODELING REAL LIFE
A sixth grader weighs 90 pounds, which is 120% of what he weighed in fourth grade. How much did he weigh in fourth grade?

60

Explanation:

Question 53.
LOGIC
In an asteroid ﬁeld, 75% of the asteroids are carbonaceous asteroids. There are 375,000 carbonaceous asteroids in the asteroid ﬁeld. How many asteroids are not carbonaceous?

281250

Explanation:
(75/100) x  375,000 = 281250

Question 54.
DIG DEEPER!
A bottle contains 20 ﬂuid ounces of lotion and sells for $5.80. The 20-ﬂuid-ounce bottle contains 125% of the lotion in the next smallest size, which sells for$5.12. Which is the better buy? Explain.

COMPARING PERCENTS
Copy and complete the statement using <, >, or =

Question 55.

equals to

Explanation:
80% = 0.8, (80/100) x 60 = 48
60% = 0.6, (60/100) x 80 = 48 so both the values are equal.

Question 56.

6 is less than 12

Explanation:
20% = 0.2, (20/100) x 30 = 6
30% = 0.3, (30/100) x 40 = 12 so 6 is less than 12

Question 57.

6 is greater than 2

Explanation:
120% = 1.2, (120/100) x 5 = 6
0.8% = 0.008, (0.8/100) x 250 = 2 so 6 is greater than 2.

Question 58.

equals to

Explanation:
85% = 0.85, (85/100) x 40 = 34
25% = 0.25, (25/100) x 136 = 34 so both the values are equal

Question 59.
Time
How many minutes is 40% of 2 hours?

48 minutes

Explanation:
120 x (40/100) = 48

Question 60.
LENGTH
How many inches is 78% of 3 feet?

Explanation:

Question 61.
GEOMETRY
The width of the rectangle is 75% of its length.
a. What is the area of the rectangle?

108

Explanation:
Area of the Rectangle = L x W, width =( 75/100) x 24 = 18, L = (25/100) x 24 = 6 so (18 x 6 ) = 108
b. The length of the rectangle is doubled. What percent of the length is the width now? Explain your reasoning.

Question 62.
PRECISION
To pass inspection, a new basketball should bounce between 68% and 75% of the starting height. A new ball is dropped from 6 feet and bounces back 4 feet 1 inch. Does the ball pass inspection? Explain.

Yes the ball passes the inspection.

Explanation:
If the ball is dropped from 6 feet and it bounces back 4 feet 1 inch so it bounces 68% then it satisfies the condition.

Question 63.
REASONING
You know that 15% of a number n is 12. How can you use this to ﬁnd 30% of n? 45% of n? Explain.

To find 30% = 24
To find 45% = 36

Explanation:
(15/100) x 80 = 12 = n
(30/100) x 80 = 24
(45/100) x 80 = 36

Question 64.
REASONING
You have a coupon for 10% off the sale price of a surfboard. Which is the better buy? Explain your reasoning.

• 40% off the regular price
• 30% off the regular price and then 10% off the sale price

40% of the regular price is better to buy.

Explanation:
40% is the better buy because they are giving more discount than the other.

Question 65.
CRITICAL THINKING
Consider two different numbers x and y. Is x% of y the same as y% of x? Justify your answer

same

Explanation:
X = 10 and Y = 50 then X% of Y = (10/100) x 50 = 5
Y% of X = (50/100) x 10 =5

Question 66.
GEOMETRY
Square ABCD and Square EFGH both have side lengths of 8 inches. The squares overlap and form Rectangle ABGH, which has a length of 10 inches. What percent of Rectangle ABGH is shaded purple?

60%

Explanation:
In the above figure, the square ABCD and EFGH have 8 inches. The percent of Rectangle ABGH shaded purple is 60%. Total percent is 100% so 100-40 = 60

Question 67.
NUMBER SENSE
On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The ﬁnal test is worth 250 points. What percent do you need on the ﬁnal to earn 93% of the total points on all tests?

97.2%

Explanation:
(88 + 94 +90) x 150 + p x 250 = 93 x (3 x 150 + 250)
40800 + 250p = 65100
250p = 24300
p = 24300/250
p = 97.2%

### Percents Connecting Concepts

4 Connecting Concepts

Using the Problem-Solving Plan

Question 1.
During a football game, a total of 63 points are scored by the two teams. Team A scores 80% of the number of points that Team B scores. What is the ﬁnal score of the game?

Understand the Problem
You know that Team A’s score is 80% of Team B’s score, and the total points scored is 63. You are asked to ﬁnd the ﬁnal score of the football game.
Make a Plan
Because 80% means 80 per 100, write the relationship between the scores of the teams as a ratio. Then represent the situation using a tape diagram. Use the total points to ﬁnd the value of each part of the tape diagram and the ﬁnal score of the game.
Solve and check
Use the plan to solve the problem.

Question 2.
A pen at a pet store contains male and female guinea pigs. The ratio of female guinea pigs to male guinea pigs is 7 to 3. Find the percent of guinea pigs in the pen that is male. Justify your answer.

30

Explanation:
(7/10) x 100 =  30. 30 % of guinea pigs are male

Question 3.
You multiply two numbers. The ﬁrst number, 21, is 6.25% of the product. What is the second number? Justify your answer.

29.76

Explanation:
The first number x second number = product of two numbers.
21 x X = (625/100) x 100
X = 625/21= 29.76

Question 4.
You have a bag containing dollar coins, dimes, and pennies. The bag contains 40 coins. The number of dollar coins is 20% of the total number of coins. The number of pennies is $$\frac{7}{9}$$ of the number of dimes. How much money is in the bag?

8 rs  are there in the bag

Explanation:
The bag contains 40 coins.
The number of dollar coins is 20% of the total number of coins that is 40 coins.

Genetic Ancestry
At the beginning of this chapter, you watched a STEAM video called “Chargaff’s Rules.” You are now ready to complete the performance task for this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.

### Percents Chapter Review

Review Vocabulary
Write the deﬁnition and give an example of the vocabulary term.
percent, p. 164

A part of a whole expressed in hundredths.
(42/100) = 0.42

Graphic Organizers

You can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as deﬁnition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph, or equation. Here is an example of a Four Square for ﬁnding the percent of a number.

Choose and complete a graphic organizer to help you study the concept.

1. percent
2. writing percents as fractions
3. writing fractions as percents
4. writing percents as decimals
5. writing decimals as percents
6. ﬁnding the whole

Chapter Self-Assessment

As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.

4.1 Percents and Fractions (pp. 163 – 168)

Question 1.
12%

(12/100)

Explanation:
(12/100) = 12%

Question 2.
88%

(88/100)

Explanation:
(88/100) = 88%

Question 3.
0.8%

(0.8/100)

Explanation:
(0.8/100) = 0.8%

Question 4.
127%

(127/100)

Explanation:
(127/100) = 127%

Question 5.
2.5%

(2.5/100)

Explanation:
(2.5/100) = 2.5%

Question 6.
18%

(18/100)

Explanation:
(18/100) = 18%

Write the fraction or mixed number as a percent.

Question 7.
$$\frac{3}{5}$$

Question 8.
1$$\frac{18}{25}$$

72%

Explanation:
(18/25) = 0.72 x 100 = 72

Question 9.
1$$\frac{21}{50}$$

42%

Explanation:
(21/50) = 0.42 x 100 = 42

Question 10.
$$\frac{14}{35}$$

0.04%

Explanation:
(14/35) = 0.4 x 100 = 0.04%

Question 11.
5$$\frac{7}{25}$$

5.28

Explanation:
5 x (7/25) = (132/25) = 5.28

Question 12.
$$\frac{7}{400}$$

1.75

Explanation:
(7/400) x 100 = (7/4) = 1.75

Question 13.
Write a fraction in simplest form that is greater than 43% and less than 47%.

(9/20)

Explanation:
45% is greater than 43% and 47%
45% = (45/100) = (9/20)

Question 14.
Write a percent thatis greater than 3$$\frac{3}{4}$$ and less than 3$$\frac{4}{5}$$.

Question 15.

23:50
Explanation:
In the above figure it displays 46% and the remaining 54% is downloading. So (46/100) = (23/50).

Question 16.
You complete 40% of your homework problems before dinner. What fraction of the problems did you complete before dinner?

2:5
Explanation:
40% = (40/100) = (2/5) = 2:5

Question 17.
There are nine different colonies of bacteria on the Petri dish. What percent of the bacteria on the Petri dish is from Colony 3?

33.3

Explanation:
(3/9) x 100 = 33.3

4.2 Percent and Decimals

Write the percent as a decimal.

Question 18.
76%

0.76

Explanation:
76% = (76/100) = 0.76

Question 19.
6%

0.06

Explanation:
6% = (6/100) = 0.06

Question 20.
17%

0.17

Explanation:
17% = (17/100) = 0.17

Question 21.
0.8%

0.008

Explanation:
0.8% = (0.8/100) = 0.008

Question 22.
0.016%

0.00016

Explanation:
0.016 = (0.016/100) 0.00016

Question 23.
334%

3.34

Explanation:
334% = (334/100) = 3.34

Write the decimal as a percent.

Question 24.
0.15

15%

Explanation:
(15/100) = 0.15

Question 25.
0.77

77%

Explanation:
(77/100) = 0.77

Question 26.
0.56

56%

Explanation:
(56/100) = 0.56

Question 27.
1.06

106%

Explanation:
(106/100) = 1.06

Question 28.
1.24

124%

Explanation:
(124/100) = 1.24

Question 29.
0.097

Question 30.
Write a decimal that is greater than 0.62% and less than 0.64%.

63

Explanation:
0.63% is greater than 0.64% and less than 0.62%
0.63% = (0.63/100) = 63

Question 31.
Write a percent that is greater than 0.026 and less than 0.028.

2.7

Explanation:
2.7 is greater than 0.026 and less than 0.028
(0.027/100) = 2.7

Question 32.
On a ﬁshing trip, 38% of the ﬁsh that you catch are perch. Write this percent as a decimal.

0.38

Explanation:
(38/100) = 0.38

4.3 Comparing and Ordering Fractions, Decimals, and Percents (pp. 175 – 180)

Tell which number is greater.

Question 33.
$$\frac{1}{2}$$, 52%

52%

Explanation:
52% = (52/100) =0.52, (1/2) = 0.5. So 52% is greater

Question 34.
$$\frac{12}{5}$$, 245%

245%

Explanation:
245% = 2.45. (12/5) = 2.4 so 245% is greater

Question 35.
0.46, 43%

0.46

Explanation:
43% = 0.43, 0.46 = 46%

Question 36.
0.023, 22%

22%

Explanation:
22% = 0.22, 0.023

Order the numbers from least to greatest.

Question 37.
$$\frac{9}{4}$$, 220%, 2.15, 218%

220%, 2.15, 218%,(9/4)

Explanation:
220% = 2.2, (9/4) = 2.25, 218% = 2.18

Question 38.
0.88, $$\frac{7}{8}$$, 92%, 0.89

(7/8), 0.88, 0.89, 92%

Explanation:
(7/8) = 0.875, 92% = 0.92

Question 39.
Write a percent that is greater than $$\frac{13}{25}$$ and less than 0.54.

Question 40.
The table shows the portions of students in your grade who participate in ﬁve activities. List the activities in order by number of students from least to greatest.

4.4 Solving Percent Problems (pp. 181–188)

Find the percent of the number. Explain your method.

Question 41.
60% of 80

48

Explanation:
60% = (60/100) x 80 = 0.6 x 80 =48

Question 42.
80% of 55

44

Explanation:
80% = (80/100) x 55 = 0.8 x 55 = 44

Question 43.
150% of 48

72

Explanation:
150% = (150/100) x 48 = 1.5 x 48 = 72

Question 44.
42% of 150

63

Explanation:
42% = (42/100) x 150 = 0.42 x 150 = 63

Question 45.
112% of 75

84

Explanation:
112% = (112/100) x 75  = 1.12 x 75 = 84

Question 46.
45% of 42

18.9

Explanation:
45% = (45/100) x 42 = 0.45 x 42 = 18.9

Find the whole. Explain your method.

Question 47.
70% of what number is 35?

0.5

Explanation:
(35/70) = 0.5

Question 48.
28% of what number is 21?

0.75

Explanation:
(21/28) = 0.75

Question 49.
56% of what number is 84?

1.5

Explanation:
(84/56) = 1.5

Question 50.
20% of what number is 96?

4.8

Explanation:
(96/20) = 4.8

Question 51.
140% of what number is 56?

0.4

Explanation:
(56/140) = 0.4

Question 52.
175% of what number is 112?

0.64

Explanation:
(112/175) = 0.64

Question 53.
Each cell of a dog contains 78 chromosomes. Exactly 50% of the chromosomes are inherited from the father. How many chromosomes in each cell of the dog are inherited from the father?

39 chromosomes in each cell of the dog are inherited from the father

Explanation:
50% = (78/2) = 39

Question 54.
You went to the mall with $80. You spent 25% of your money on a pair of shorts and 65% of the remainder on sandals. How much did you spend on the sandals? Which country would you most like to visit? Answer: Question 55. The results of the survey are shown at the left. In the survey, 7 students said that they would most like to visit Italy. How many of the students surveyed would most like to visit Ireland? Answer: 2 students Explanation: (8/4) = 2 Question 56. You answer 24 questions on a 100-point test correctly and earn a 96%. a. All of the questions are worth the same number of points. How many questions are on the test? How many points is each question worth? Answer: 25 questions are on the test b. Your friend earns a grade of 76% on the same test. How many questions did your friend answer correctly? Answer: 19 Explanation: My friend answer 19 questions correctly Percents Practice Test 4 Practice Test Write the fraction or mixed number as a percent. Question 1. $$\frac{21}{25}$$ Answer: 84% Explanation: (21/25) = 0.84 = 84 Question 2. $$\frac{17}{20}$$ Answer: 85% Explanation: (17/20) = 0.85 = 85 Question 3. 1$$\frac{2}{5}$$ Answer: 0.4% Explanation: (2/5) = 0.4 Write the decimal as a percent. Question 4. 0.42 Answer: 42% Explanation: 42% = (42/100) = 0.42 Question 5. 7.88 Answer: 788% Explanation: 788% = (788/100) = 7.88 Question 6. 0.5854 Answer: 5854% Explanation: 5854% = (5854/10000) = 0.5854 Write the percent as a fraction in simplest form and as a decimal. Question 7. 0.96% Answer: Fraction= 24:25, Decimal = 0.0096 Explanation: 0.96% = (0.96/100) = 0.0096 Question 8. 65% Answer: Fraction = 13:20, Decimal = 0.65 Explanation: 65% = 0.65, (65/100) = 13:20 Question 9. 25.7% Answer: Fraction = Tell which number is greater. Question 10. $$\frac{16}{25}$$, 65% Answer: 65% is greater Explanation: (16/25) = 0.64, 65% = (65/100) = 0.65. So 65% is greater Question 11. 56%, 5.6 Answer: 5.6 is greater Explanation: 56% = (56/100) = 0.56 . So 5.6 is greater Order the numbers from least to greatest. Question 12. 85%, $$\frac{7}{10}$$, 0.74, $$\frac{4}{5}$$ Answer: (7/10), 0.74, 0.8, 0.85 Explanation: 85% = 0.85, (7/10) = 0.7, (4/5) = 0.8 Question 13. 130%, 1.32, $$\frac{6}{5}$$, $$\frac{5}{4}$$, 1.28 Answer: (6/5), (5/4), 1.28, 130%, 1.32 Explanation: 130% = (130/100) = 1.3, (6/5) = 1.2, (5/4) = 1.25 Question 14. 80% of 90 is what number? Answer: 72 Explanation: 80% = (80/100) =0.8 x 90 =72 Question 15. 120% of 75 is what number? Answer: 112.5 Explanation: 120% = (120/100) = 1.2 x 112.5 Question 16. 40% of what number is 34? Answer: 0.34 Explanation: (34/40) = 0.34 Question 17. 130% of what number is 52? Answer: 0.4 Explanation: (52/130) = 0.4 Question 18. A goalie’s saves (.) and goals scored against (×) are shown. What percent of shots did the goalie save? Explain. Answer: 2% Explanation: Two dots are there. So 2% Question 19. About 62% of the human body is composed of water. Write this percent as a fraction in simplest form. Answer: 31:50 Explanation: 62% = (62/100) = 31:50 Question 20. You, your cousin, and a friend each take the same number of free throws at a basketball hoop. You make $$\frac{17}{20}$$ of your free throws, your cousin makes 0.8 of her free throws, and your friend makes 87.5% of his free throws. Who made the most free throws? Answer: Question 21. In a class of 20 students, 40% are boys. Twenty-ﬁve percent of the boys and 50% of the girls wear glasses. How many students in the class wear glasses? Answer: 15 students in the class wear glasses. Explanation: In the above given question there are 20 students. So 75% of students wear glasses that means the students who wear glasses is 15. Question 22. Eighty percent of the picture frame is glass. What is the area of the moulding? Answer: 91.375 Explanation: (17/2) = 8.5 (43/4) = 10.75 Area = l x b = 91.375 ### Percents Cumulative Practice Question 1. How many pints are in 8 quarts? A. 2 pints B. 4 pints C. 16 pints D. 32 pints Answer: 16 pints Explanation: 16 pints = 8 quarts Question 2. Which fraction is not equivalent to 25%? Answer: (2/5) is not equivalent to 25% Explanation: 25% = (25/100), 25% = (5/20), 25% = (1/4). So (2/5) is not equivalent to 25% Question 3. What is the missing value in the ratio table? Answer: 28 Explanation: In the above given table 2 x 2 x 2 = 8, 8 x 2 =16. 7 x 2 x 2 = 28, 28 x 2 = 56. The missing value in the ratio table is 28. Question 4. Your friend was ﬁnding the percent of a number in the box below. What should your friend do to correct the error? A. Divide 24 by 25. B. Divide $$\frac{1}{4}$$ by 24. C. Multiply 24 by 25. D. Multiply 24 by $$\frac{1}{4}$$. Answer: option b is correct Explanation: (25/100) x 24 = 6 Question 5. Which percent is equivalent to $$\frac{4}{5}$$? F. 20% G. 45% H. 80% I. 125% Answer: 80% is equivalent to (4/5) Explanation: 80% = (80/100) 0.8 , (4/5) = 0.8. So 80% is equivalent to (4/5) Question 6. Which pair of numbers does not have a least common multiple less than 100? A. 10, 15 B. 12, 16 C. 16, 18 D. 18, 24 Answer: Option c is correct Explanation: 16, 18 = 108 is least common multiple less than 100. Question 7. You are comparing the costs of buying bottles of water at the supermarket. Which of the following has the least cost per liter? F. 6 one-liter bottles for$1.80
G. 1 two-liter bottle for $0.65 H. 8 half-liter bottles for$1.50
I. 12 half-liter bottles for $1.98 Answer: one liter bottle for$1.80

Explanation:
one liter bottle for \$1.80

Question 8.
What is 75% of 36?

27

Explanation:
(75/100) x 36 = 27

Question 9.
Which number is equivalent to $$\frac{5}{12}$$ × $$\frac{4}{9}$$ ?
A. $$\frac{5}{27}$$
B. $$\frac{3}{7}$$
C. $$\frac{15}{16}$$
D. $$\frac{5}{3}$$

Option A is equivalent to (5/12) x (4/9)

Explanation:
(5/12) x (4/9) = 0.18518518. S0 (5/27) = 0.18518517. So both values are equal.

Question 10.
Which list of numbers is in order from least to greatest?
F. 0.8, $$\frac{5}{8}$$, 70%, 0.09
G. $$\frac{5}{8}$$, 70%, 0.8, 0.09
H. 0.09, $$\frac{5}{8}$$, 0.8, 70%
I. 0.09, $$\frac{5}{8}$$, 70%, 0.8

0.09, (5/8) , 70%, 0.8

Explanation:
(5/8) = 0.625, 70% = 0.7

Question 11.+
Which number is equivalent to 1.32 ÷ 0.006?
A. 2.2
B. 22
C. 220
D. 2200

220

Explanation:
(1.32 / 0.006) = 220

Question 12.
Which ratio is equivalent to 4 : 14?
F. 2 : 12
G. 10 : 35
H. 18 : 28
I. 8 : 18

Option G is correct

Explanation:
4 : 14 = 2 : 7 , 10 : 35 = 2 :7

Question 13.
For a party, you make a gelatin dessert in a rectangular pan and cut the dessert into equal-sized pieces, as shown below.

The dessert consists of 5 layers of equal height. Each layer is a different ﬂavor, as shown below by a side view of the pan.

Your guests eat $$\frac{3}{5}$$ of the pieces of the dessert.
Part A
Write the amount of cherry gelatin that your guests eat as a fraction of the total dessert. Justify your answer.
Part B
Write the amount of cherry gelatin that your guests eat as a percent of the total dessert. Justify your answer.

Conclusion:
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