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Algebra 1 : Monomials

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Example Questions

Example Question #22 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$6xy^{2}$ $\displaystyle 6xy^{2}$

$7x^{2}y$ $\displaystyle 7x^{2}y$

14xy $\displaystyle 14xy$

7xy $\displaystyle 7xy$

Correct answer:

$7x^{2}y$ $\displaystyle 7x^{2}y$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

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

Combine these to get the final answer:

$7x^{2}y$ $\displaystyle 7x^{2}y$

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Example Question #21 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$7x^{2}$ $\displaystyle 7x^{2}$

$8x^{4}$ $\displaystyle 8x^{4}$

$\displaystyle 6x$

$8x^{2}$ $\displaystyle 8x^{2}$

Correct answer:

$8x^{2}$ $\displaystyle 8x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

Combine these to get the final answer:

$8x^{2}$ $\displaystyle 8x^{2}$

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Example Question #71 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$3x^{2}$ $\displaystyle 3x^{2}$

$\displaystyle 3x$

11x $\displaystyle 11x$

$3x^{3}$ $\displaystyle 3x^{3}$

Correct answer:

$\displaystyle 3x$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

Combine these to get the final answer:

$\displaystyle 3x$

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Example Question #72 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$xyz^{2}$ $\displaystyle xyz^{2}$

$\displaystyle yz$

$x^{2}yz$ $\displaystyle x^{2}yz$

xyz $\displaystyle xyz$

Correct answer:

$x^{2}yz$ $\displaystyle x^{2}yz$

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.

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

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

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

Combine these to get the final answer:

$x^{2}yz$ $\displaystyle x^{2}yz$

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Example Question #72 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

2xy $\displaystyle 2xy$

$6xy^{2}$ $\displaystyle 6xy^{2}$

$\displaystyle 2x$

$\displaystyle 3y$

Correct answer:

$\displaystyle 2x$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

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

Combine these to get the final answer:

$\displaystyle 2x$

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Example Question #73 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

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

$\frac{z}{xy}$ $\displaystyle \frac{z}{xy}$

xyz $\displaystyle xyz$

$\frac{z}{y}$ $\displaystyle \frac{z}{y}$

Correct answer:

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

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.

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

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

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

Combine these to get the final answer:

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

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Example Question #72 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$\displaystyle 4x$

$36x^{2}$ $\displaystyle 36x^{2}$

$4x^{2}$ $\displaystyle 4x^{2}$

12x $\displaystyle 12x$

Correct answer:

$4x^{2}$ $\displaystyle 4x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

Combine these to get the final answer:

$4x^{2}$ $\displaystyle 4x^{2}$

Report an Error

Example Question #71 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$x^{2}$ $\displaystyle x^{2}$

$x^{3}$ $\displaystyle x^{3}$

$x^{8}$ $\displaystyle x^{8}$

$\displaystyle 2x$

Correct answer:

$x^{2}$ $\displaystyle x^{2}$

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.

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

Combine these to get the final answer:

$x^{3}$ $\displaystyle x^{3}$

Report an Error

Example Question #31 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$\displaystyle 5x$

$4x^{2}$ $\displaystyle 4x^{2}$

10x $\displaystyle 10x$

$5x^{2}$ $\displaystyle 5x^{2}$

Correct answer:

$5x^{2}$ $\displaystyle 5x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

Combine these to get the final answer:

$5x^{2}$ $\displaystyle 5x^{2}$

Report an Error

Example Question #33 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$\displaystyle 7x$

$3x^{2}$ $\displaystyle 3x^{2}$

$7x^{3}$ $\displaystyle 7x^{3}$

$\displaystyle 6x$

Correct answer:

$7x^{3}$ $\displaystyle 7x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

Combine these to get the final answer:

$7x^{3}$ $\displaystyle 7x^{3}$

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 #22 : How To Divide Monomial Quotients

Example Question #21 : How To Divide Monomial Quotients

Example Question #71 : Monomials

Example Question #72 : Monomials

Example Question #72 : Monomials

Example Question #73 : Monomials

Example Question #72 : Monomials

Example Question #71 : Monomials

Example Question #31 : How To Divide Monomial Quotients

Example Question #33 : How To Divide Monomial Quotients

All Algebra 1 Resources

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