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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #4731 : Algebra 1

Divide the following monomial quotients:

$\frac{x^{5}}{x^{3}}$

Possible Answers:

$x^{2}$

$x^{3}$

$x^{8}$

Correct answer:

$x^{2}$

Explanation:

To solve this problem, divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x^{5}}{x^{2}} =x^{5-2}=x^{3}$

Combine these to get the final answer:

$x^{3}$

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Example Question #33 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{20x^{3}}{4x}$

Possible Answers:

10x

$4x^{2}$

$5x^{2}$

Correct answer:

$5x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{20}{4}=5$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x^{3}}{x} =x^{3-1}=x^{2}$

Combine these to get the final answer:

$5x^{2}$

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Example Question #34 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{21x^{5}}{3x^{2}}$

Possible Answers:

$7x^{3}$

$3x^{2}$

Correct answer:

$7x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{21}{3}=7$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x^{5}}{x^{2}} =x^{5-2}=x^{3}$

Combine these to get the final answer:

$7x^{3}$

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Example Question #4733 : Algebra 1

Divide the following monomial quotients:

$\frac{32y^{3}}{4x}$

Possible Answers:

$\frac{8y^{3}}{x}$

12xy

$\frac{4y}{x^{2}}$

$\frac{8y}{x}$

Correct answer:

$\frac{8y^{3}}{x}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{32}{4}=8$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{1}{x} =x^{-1}=\frac{1}{x}$

$\frac{y^{3}}{1}=y^{3}$

Combine these to get the final answer:

$\frac{8y^{3}}{x}$

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Example Question #4732 : Algebra 1

Divide the following monomial quotients:

$\frac{28y^{2}}{7y}$

Possible Answers:

$\frac{4}{y}$

$3y^{2}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{28}{7}=4$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{y^{2}}{y}=y$

Combine these to get the final answer:

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Example Question #506 : Variables

Divide the following monomial quotients:

$\frac{16xy^{2}}{2xy}$

Possible Answers:

$\frac{y}{4}$

$\frac{y}{x}$

$8y^{2}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{16}{2}=8$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x}{x} =x^{1-1}=1$

$\frac{y^{2}}{y}=y^{2-1}=y$

Combine these to get the final answer:

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Example Question #507 : Variables

Divide the following monomial quotients:

$\frac{x^{15}y}{x^{3}y^{2}}$

Possible Answers:

$\frac{x^{3}}{y}$

$\frac{x^{5}}{y^{2}}$

$\frac{x^{12}}{y}$

$\frac{x^{18}}{y}$

Correct answer:

$\frac{x^{12}}{y}$

Explanation:

To solve this problem, divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x^{15}}{x^{3}} =x^{15-3}=x^{12}$

$\frac{y}{y^{2}}=y^{1-2}=\frac{1}{y}$

Combine these to get the final answer:

$\frac{x^{12}}{y}$

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Example Question #41 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{15xy}{3x^{2}}$

Possible Answers:

5xy

$\frac{5x}{y}$

$\frac{5y}{x}$

Correct answer:

$\frac{5y}{x}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{15}{3}=5$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x}{x^{2}} =x^{1-2}=\frac{1}{x}$

$\frac{y}{1}=y$

Combine these to get the final answer:

$\frac{5y}{x}$

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Example Question #41 : How To Divide Monomial Quotients

Divide: $\frac{9x}{33x^2}$

Possible Answers:

$-\frac{1}{24x}$

$\frac{3x}{11}$

24x

$\frac{3}{11x}$

$\frac{1}{24x}$

Correct answer:

$\frac{3}{11x}$

Explanation:

In order to simplify this fraction, write the factors out for the numerator and denominator.

$\frac{9x}{33x^2} = \frac{3\cdot 3\cdot x}{3\cdot 11 \cdot x \cdot x}$

Cancel out the common terms in the numerator and denominator.

$\frac{3\cdot 3\cdot x}{3\cdot 11 \cdot x \cdot x} = \frac{3}{11x}$

The answer is: $\frac{3}{11x}$

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Example Question #41 : How To Divide Monomial Quotients

Evaluate:

$\frac{21x+14x^2+28x^3}{7x}$

Possible Answers:

$\frac{4x+2}{7x}$

21x^2+7x+14

$\frac{4x^2}{2x+3}$

4x^2+2x+3

x^2+2x+7

Correct answer:

4x^2+2x+3

Explanation:

We can simplify this monomial by cancelling out like terms in the numerator and denominator:

$\frac{21x+14x^2+28x^3}{7x}=\frac{7x(3+2x+4x^2)}{7x}=4x^2+2x+3$

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #4731 : Algebra 1

Example Question #33 : How To Divide Monomial Quotients

Example Question #34 : How To Divide Monomial Quotients

Example Question #4733 : Algebra 1

Example Question #4732 : Algebra 1

Example Question #506 : Variables

Example Question #507 : Variables

Example Question #41 : How To Divide Monomial Quotients

Example Question #41 : How To Divide Monomial Quotients

Example Question #41 : How To Divide Monomial Quotients

All Algebra 1 Resources

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