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Algebra 1 : Monomials

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

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Example Question #21 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{42x^{3}y^{2}}{6xy}$

Possible Answers:

7xy

$6xy^{2}$

$7x^{2}y$

14xy

Correct answer:

$7x^{2}y$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{42}{6}=7$

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

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

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

Combine these to get the final answer:

$7x^{2}y$

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Example Question #22 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{40x^{3}}{5x}$

Possible Answers:

$8x^{2}$

$7x^{2}$

$8x^{4}$

Correct answer:

$8x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{40}{5}=8$

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:

$8x^{2}$

Report an Error

Example Question #21 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{33x^{2}}{11x}$

Possible Answers:

$3x^{2}$

11x

$3x^{3}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{33}{11}=3$

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

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

Combine these to get the final answer:

Report an Error

Example Question #492 : Variables

Divide the following monomial quotients:

$\frac{x^{3}y^{2}z}{xy}$

Possible Answers:

xyz

$xyz^{2}$

$x^{2}yz$

Correct answer:

$x^{2}yz$

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.

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

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

$\frac{z}{1}=z$

Combine these to get the final answer:

$x^{2}yz$

Report an Error

Example Question #31 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{6xy}{3y}$

Possible Answers:

2xy

$6xy^{2}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{6}{3}=2$

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

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

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

Combine these to get the final answer:

Report an Error

Example Question #32 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$\frac{z}{xy}$

$\frac{z}{y}$

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

xyz

Correct answer:

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

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.

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

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

$\frac{z^{2}}{1}=z^{2}$

Combine these to get the final answer:

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

Report an Error

Example Question #31 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{12x^{2}}{3}$

Possible Answers:

$36x^{2}$

$4x^{2}$

12x

Correct answer:

$4x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{12}{3}=4$

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

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

Combine these to get the final answer:

$4x^{2}$

Report an Error

Example Question #32 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$x^{3}$

$x^{8}$

$x^{2}$

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:

$x^{3}$

Report an Error

Example Question #35 : 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:

$5x^{2}$

Report an Error

Example Question #32 : 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:

$7x^{3}$

Report an Error

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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #21 : How To Divide Monomial Quotients

Example Question #22 : How To Divide Monomial Quotients

Example Question #21 : How To Divide Monomial Quotients

Example Question #492 : Variables

Example Question #31 : How To Divide Monomial Quotients

Example Question #32 : How To Divide Monomial Quotients

Example Question #31 : How To Divide Monomial Quotients

Example Question #32 : How To Divide Monomial Quotients

Example Question #35 : How To Divide Monomial Quotients

Example Question #32 : How To Divide Monomial Quotients

All Algebra 1 Resources

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