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Algebra 1 : Monomials

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Example Questions

Example Question #61 : Monomials

Divide: $\frac{x}{x^3}$

Possible Answers:

$x^{2}$

$\frac{1}{2x}$

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

$\frac{1}x{}$

Correct answer:

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

Explanation:

Notice that both bases are the same. The power of the base in the numerator is one.

Since the bases are divided, simply subtract the powers.

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

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Example Question #62 : Monomials

Divide the following monomial quotients:

$\frac{6x^{2}}{2x}$

Possible Answers:

$3x^{2}$

$12x^{3}$

12x

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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:

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Example Question #17 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{10x^{4}y}{5xy}$

Possible Answers:

$2x^{3}$

$2x^{3}y$

$x^{2}$

2xy

Correct answer:

$2x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{10}{5}=2$

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

$\frac{x^{4}}{x} =x^{4-1}=x^{3}$

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

Combine these to get the final answer:

$2x^{3}$

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Example Question #63 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$\frac{y}{x}$

$\frac{1}{x}$

$\frac{x}{y}$

Correct answer:

$\frac{y}{x}$

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.

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

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

Combine these to get the final answer:

$\frac{y}{x}$

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Example Question #64 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$24y^{3}$

$2y^{3}$

$6x^{3}$

$6y^{3}$

Correct answer:

$6y^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{12}{2}=6$

2. Combine this with the lone variable to get the final answer:

$6y^{3}$

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Example Question #22 : How To Divide Monomial Quotients

Divide the folloiwng monomial quotients:

$\frac{36x^{2}y^{3}}{12xy}$

Possible Answers:

$3x^{2}y^{2}$

$6x^{3}y$

4xy

$3xy^{2}$

Correct answer:

$3xy^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{36}{12}=3$

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

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

$\frac{y^{3}}{y}=y^{2}$

Combine these to get the final answer:

$3xy^{2}$

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Example Question #23 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{25xy^{2}}{5y}$

Possible Answers:

5xy

$5x^{2}y$

Correct answer:

5xy

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{25}{5}=5$

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

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

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

Combine these to get the final answer:

5xy

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Example Question #24 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{15xy^{3}}{5x}$

Possible Answers:

$y^{3}$

$3y^{3}$

3xy

$3x^{2}y$

Correct answer:

$3y^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

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

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

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

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

Combine these to get the final answer:

$3y^{3}$

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Example Question #25 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{7x^{2}}{14x}$

Possible Answers:

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

$\frac{x}{2}$

$2x^{2}$

Correct answer:

$\frac{x}{2}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{7}{14}=\frac{1}{2}$

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:

$\frac{x}{2}$

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Example Question #65 : Monomials

Divide the following monomial quotients:

$\frac{8xy}{2x}$

Possible Answers:

$\frac{4}{y}$

8xy

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{8}{2}=4$

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

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

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

Combine these to get the final answer:

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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #61 : Monomials

Example Question #62 : Monomials

Example Question #17 : How To Divide Monomial Quotients

Example Question #63 : Monomials

Example Question #64 : Monomials

Example Question #22 : How To Divide Monomial Quotients

Example Question #23 : How To Divide Monomial Quotients

Example Question #24 : How To Divide Monomial Quotients

Example Question #25 : How To Divide Monomial Quotients

Example Question #65 : Monomials

All Algebra 1 Resources

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