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7.8: Exercise Supplement

Last updated

Jun 8, 2024
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- 7.7: Summary of Key Concepts
- 7.9: Proficiency Exam

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Ratios and Rates

Exercise $\PageIndex{1}$

Compare 250 watts to 100 watts by subtraction.

Answer: 250 watts are 150 watts more than 100 watts

Exercise $\PageIndex{2}$

Compare 126 and 48 by subtraction.

Exercise $\PageIndex{3}$

Compare 98 radishes to 41 radishes by division.

Answer: 98 radishes are 2.39 times as many radishes as 41 radishes

Exercise $\PageIndex{4}$

Compare 144 to 9 by division.

Exercise $\PageIndex{5}$

Compare 100 tents to 5 tents by division.

Answer: 100 tents are 20 times as many tents as 5 tents

Exercise $\PageIndex{6}$

Compare 28 feet to 7 feet by division.

Exercise $\PageIndex{7}$

Comparison, by division, of two pure numbers or two like denominate numbers is called a .

Answer: ratio

Exercise $\PageIndex{8}$

A comparison, by division, of two unlike denominate numbers is called a .

For problems 9-12, express each ratio or rate as a fraction.

Exercise $\PageIndex{9}$

15 to 5

Answer: $\dfrac{3}{1}$

Exercise $\PageIndex{10}$

72 to 12

Exercise $\PageIndex{11}$

8 millimeters to 5 milliliters

Answer: $\dfrac{\text{8ml}}{\text{5ml}}$

Exercise $\PageIndex{12}$

106 tablets to 52 tablets

For problems 13-16, write each ratio in the form " $a$ to $b$ ".

Exercise $\PageIndex{13}$

$\dfrac{9}{16}$

Answer: 9 to 16

Exercise $\PageIndex{14}$

$\dfrac{5}{11}$

Exercise $\PageIndex{15}$

$\dfrac{\text{1 diskette}}{\text{8 diskettes}}$

Answer: 1 diskette to 8 diskettes

Exercise $\PageIndex{16}$

$\dfrac{\text{5 papers}}{\text{3 pens}}$

For problems 17-21, write each ratio or rate using words.

Exercise $\PageIndex{17}$

$\dfrac{9}{16} = \dfrac{18}{32}$

Answer: 9 is to 16 as 18 is to 32

Exercise $\PageIndex{18}$

$\dfrac{1}{4} = \dfrac{12}{48}$

Exercise $\PageIndex{19}$

$\dfrac{\text{8 items}}{\text{4 dollars}} = \dfrac{\text{2 items}}{\text{1 dollar}}$

Answer: 8 items are to 4 dollars as 2 items are to 1 dollar

Exercise $\PageIndex{20}$

150 milligrams of niacin is to 2 tablets as 300 milligrams of niacin is to 4 tablets.

Exercise $\PageIndex{21}$

20 people is to 4 seats as 5 people is to 1 seat.

Answer

$\dfrac{20}{4} = \dfrac{5}{1}$

20 people are to 4 seats as 5 people are to 1 seat

Proportions

For problems 22-27, determine the missing number in each proportion.

Exercise $\PageIndex{22}$

$\dfrac{x}{3} = \dfrac{24}{9}$

Exercise $\PageIndex{23}$

$\dfrac{15}{7} = \dfrac{60}{x}$

Answer: 28

Exercise $\PageIndex{24}$

$\dfrac{1}{1} = \dfrac{x}{44}$

Exercise $\PageIndex{25}$

$\dfrac{3}{x} = \dfrac{15}{50}$

Answer: 10

Exercise $\PageIndex{26}$

$\dfrac{\text{15 bats}}{\text{16 balls}} = \dfrac{\text{x bats}}{\text{128 balls}}$

Exercise $\PageIndex{27}$

$\dfrac{\text{36 rooms}}{\text{29 fans}} = \dfrac{\text{504 rooms}}{\text{x fans}}$

Answer: 406

Applications of Proportions

Exercise $\PageIndex{28}$

On a map, 3 inches represents 20 miles. How many miles does 27 inches represent?

Exercise $\PageIndex{29}$

A salt solution is composed of 8 parts of salt to 5 parts of water. How many parts of salt are there in a solution that contains 50 parts of water?

Answer: 80

Exercise $\PageIndex{30}$

A model is built to $\dfrac{4}{15}$ scale. If a particular part of the model measures 8 inches in length, how long is the actual structure?

Exercise $\PageIndex{31}$

The ratio of ammonia to air in a container is $\dfrac{3}{40}$ . How many milliliters of air should be in a container that contains 8 milliliters of ammonia?

Answer: $\dfrac{320}{3}$ or $106 \dfrac{2}{3}$

Exercise $\PageIndex{32}$

A 4-foot girl casts a 9-foot shadow at a particular time of the day. How tall is a pole that casts a 144-foot shadow at the same time of the day?

Exercise $\PageIndex{33}$

The odds that a particular event will occur are 11 to 2. If this event occurs 55 times, how many times would you predict it does not occur?

Answer: 10

Exercise $\PageIndex{34}$

Every $1\dfrac{3}{4}$ teaspoon of a multiple vitamin, in granular form, contains 0.85 the minimum daily requirement of vitamin A. How many teaspoons of this vitamin are required to supply 2.25 the minimum daily requirement?

Percent and Fractions of One Percent ([link],[link])

For problems 35-39, convert each decimal to a percent.

Exercise $\PageIndex{35}$

0.16

Answer: 16%

Exercise $\PageIndex{36}$

0.818

Exercise $\PageIndex{37}$

5.3536

Answer: 535.36%

Exercise $\PageIndex{38}$

0.50

Exercise $\PageIndex{39}$

Answer: 300%

For problems 40-48, convert each percent to a decimal.

Exercise $\PageIndex{40}$

62%

Exercise $\PageIndex{41}$

1.58%

Answer: 0.0158

Exercise $\PageIndex{42}$

9.15%

Exercise $\PageIndex{43}$

0.06%

Answer: 0.0006

Exercise $\PageIndex{44}$

0.003%

Exercise $\PageIndex{45}$

$5 \dfrac{3}{11}$ % to a three-place decimal

Answer: 0.053

Exercise $\PageIndex{46}$

$\dfrac{9}{13}$ % to a three-place decimal

Exercise $\PageIndex{47}$

$82 \dfrac{25}{29}$ % to a four-place decimal

Answer: 0.8286

Exercise $\PageIndex{48}$

$18 \dfrac{1}{7}$ % to a four-place decimal

For problems 49-55, convert each fraction or mixed number to a percent.

Exercise $\PageIndex{49}$

$\dfrac{3}{5}$

Answer: 60%

Exercise $\PageIndex{50}$

$\dfrac{2}{10}$

Exercise $\PageIndex{51}$

$\dfrac{5}{16}$

Answer: 31.25%

Exercise $\PageIndex{52}$

$\dfrac{35}{8}$

Exercise $\PageIndex{53}$

$\dfrac{105}{16}$

Answer: 656.25%

Exercise $\PageIndex{54}$

$45 \dfrac{1}{11}$

Exercise $\PageIndex{55}$

$6 \dfrac{278}{9}$

Answer: $3688.\overline{8}$ %

For problems 56-64, convert each percent to a fraction or mixed number.

Exercise $\PageIndex{54}$

95%

Exercise $\PageIndex{55}$

12%

Answer: $\dfrac{3}{25}$

Exercise $\PageIndex{54}$

83%

Exercise $\PageIndex{55}$

38.125%

Answer: $\dfrac{61}{160}$

Exercise $\PageIndex{54}$

$61.\overline{2}$ %

Exercise $\PageIndex{55}$

$\dfrac{5}{8}$ %

Answer: $\dfrac{1}{160}$

Exercise $\PageIndex{54}$

$6 \dfrac{9}{20}$ %

Exercise $\PageIndex{55}$

$15 \dfrac{3}{22}$ %

Answer: $\dfrac{2977}{19800}$

Exercise $\PageIndex{54}$

$106\dfrac{19}{45}$ %

Applications of Percents

For problems 65-72, find each solution.

Exercise $\PageIndex{55}$

What is 16% of 40?

Answer: 6.4

Exercise $\PageIndex{54}$

29.4 is what percent of 105?

Exercise $\PageIndex{55}$

$3\dfrac{21}{50}$ is 547.2% of what number?

Answer: 0.625 or $\dfrac{5}{8}$

Exercise $\PageIndex{54}$

0.09378 is what percent of 52.1?

Exercise $\PageIndex{55}$

What is 680% of 1.41?

Answer: 9.588

Exercise $\PageIndex{54}$

A kitchen knife is on sale for 15% off the marked price. If the marked price is $ 39.50, what is the sale price?

Exercise $\PageIndex{55}$

On an 80 question geology exam, a student gets 68 correct. What percent is correct?

Answer: 85

Exercise $\PageIndex{54}$

A salesperson makes a commission of 18% of her monthly sales total. She also receives a monthly salary of $1,600.00. If, in a particular month, she sells $4,000.00 worth of merchandise, how much will she make that month?

Ratios and Rates

Proportions

Applications of Proportions

Percent and Fractions of One Percent ([link],[link])

Applications of Percents

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