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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #62 : Proportions

Solve the proportion: $\frac{1}{6} = \frac{6}{5x}$

Possible Answers:

$\frac{5}{12}$

$\frac{1}{5}$

$\frac{36}{5}$

$\frac{5}{36}$

$\frac{12}{5}$

Correct answer:

$\frac{36}{5}$

Explanation:

To solve this proportion, cross multiply the terms.

5x=36

Divide by five on both sides.

$\frac{5x}{5}=\frac{36}{5}$

Simplify both sides.

The answer is: $\frac{36}{5}$

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Example Question #63 : Proportions

Solve the proportion: $\frac{1}{6} = \frac{6}{5x}$

Possible Answers:

$\frac{1}{5}$

$\frac{36}{5}$

$\frac{5}{36}$

$\frac{12}{5}$

$\frac{5}{12}$

Correct answer:

$\frac{36}{5}$

Explanation:

To solve this proportion, cross multiply the terms.

5x=36

Divide by five on both sides.

$\frac{5x}{5}=\frac{36}{5}$

Simplify both sides.

The answer is: $\frac{36}{5}$

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Example Question #1191 : Algebra 1

Adam cleaned 8 cars in 2 days. How many days will it take him to clean 12 cars? Assume the relationship is directly proportional.

Possible Answers:

3.5 days

4 days

3 days

2.5 days

6 days

Correct answer:

3 days

Explanation:

When solving a proportion, we will first set up two ratios and set them equal to each other. We know Adam cleaned 8 cars in 2 days. We create a ratio using that information.

$\frac{8 \text{ cars}}{2 \text{ days}}\ \ \text{or} \ \ \frac{8}{2}$

The question asks how many days does it take Adam to clean 12 cars. So, we know the number of cars. We do not know the number of days, so we will use a variable. We get

$\frac{12 \text{ cars}}{x} \ \ \text{or} \ \ \frac{12}{x}$

Now, we can set the two ratios equal to each other and solve.

$\frac{8}{2} = \frac{12}{x}$

To solve, we cross multiply. We get

8x = 24

Now, we solve for x.

$\frac{8x}{8} = \frac{24}{8}$

x = 3

Therefore, it will take Adam 3 days to clean 12 cars.

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Example Question #61 : Proportions

Solve the proportion: $\frac{7}{8} = \frac{x}{9}$

Possible Answers:

$\frac{72}{7}$

$\frac{7}{72}$

$\frac{63}{8}$

Correct answer:

$\frac{63}{8}$

Explanation:

Solve by cross multipling the terms of the fractions.

7(9) = 8x

Simplify and solve for x.

63=8x

Divide by eight on both sides.

$\frac{63}{8}=\frac{8x}{8}$

$x=\frac{63}{8}$

The answer is: $\frac{63}{8}$

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Example Question #62 : Proportions

Solve the proportion: $\frac{3}{8}= \frac{4}{x}$

Possible Answers:

$\frac{3}{32}$

$\frac{3}{2}$

$\frac{32}{3}$

$\frac{23}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{32}{3}$

Explanation:

Cross multiply the two fractions.

3x=32

Divide by three on both sides.

$\frac{3x}{3}=\frac{32}{3}$

The answer is: $\frac{32}{3}$

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Example Question #67 : Proportions

Solve the proportion: $\frac{2}{9} =\frac{x}{8}$

Possible Answers:

$\frac{9}{16}$

$\frac{16}{9}$

$\frac{1}{36}$

$\frac{8}{3}$

Correct answer:

$\frac{16}{9}$

Explanation:

To solve the proportion, we need to cross multiply.

16=9x

Divide by 9 on both sides.

$\frac{16}{9}=\frac{9x}{9}$

Simplify both sides.

$\frac{16}{9}=x$

The answer is: $\frac{16}{9}$

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Example Question #1192 : Algebra 1

Solve for : $\frac{2}{x} = \frac{x}{8}$

Possible Answers:

$\pm8$

$\pm4$

Correct answer:

$\pm4$

Explanation:

Cross multiply both fractions on each side.

(2)(8)=(x)(x)

16 =x^2

Square root both sides.

$\sqrt{16} =\sqrt{x^2}$

$x=\pm4$

Check both solutions to ensure that both answers will satisfy the original proportion.

The answer is: $\pm4$

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Example Question #69 : Proportions

Solve the proportion: $\frac{6}{x}= \frac{1}{7}$

Possible Answers:

$\frac{1}{13}$

$\frac{1}{3}$

$\frac{1}{42}$

Correct answer:

Explanation:

In order to solve for x, first cross multiply the fractions.

(6)(7) =(1)(x)

Simplify both sides of the equation.

42=x

The answer is .

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Example Question #70 : Proportions

Solve the proportion: $\frac{2+x}{6}= \frac{3x}{7}$

Possible Answers:

$\frac{7}{4}$

$\frac{23}{14}$

$\frac{14}{11}$

Correct answer:

$\frac{14}{11}$

Explanation:

Cross multiply the terms.

7(2+x)= 6(3x)

Distribute and simplify both sides of the equation.

14+7x=18x

Subtract on both sides.

14+7x-7x=18x-7x

14=11x

Divide by eleven on both sides.

$x=\frac{14}{11}$

The answer is: $\frac{14}{11}$

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Example Question #71 : Proportions

Solve the proportion: $\frac{2x}{9} = \frac{4}{3}$

Possible Answers:

$\frac{81}{2}$

$\frac{13}{6}$

$\frac{13}{5}$

$\frac{1}{6}$

Correct answer:

Explanation:

To solve the proportion, cross multiply the fractions.

(2x)(3)=(9)(4)

Simplify both sides.

6x=36

Divide by six on both sides.

$\frac{6x}{6}=\frac{36}{6}$

Simplify both sides.

The answer is: x=6

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #62 : Proportions

Example Question #63 : Proportions

Example Question #1191 : Algebra 1

Example Question #61 : Proportions

Example Question #62 : Proportions

Example Question #67 : Proportions

Example Question #1192 : Algebra 1

Example Question #69 : Proportions

Example Question #70 : Proportions

Example Question #71 : Proportions

All Algebra 1 Resources

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