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Algebra 1 : How to divide monomial quotients

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Example Question #11 : Multiplying And Dividing Exponents

Simplify the rational expression.

$\frac{12x^2y^4z^6}{6xz^{12}}$

Possible Answers:

$\frac{2xy^4}{z^6}$

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

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

$\frac{2xy^4}{z^2}$

Correct answer:

$\frac{2xy^4}{z^6}$

Explanation:

$\frac{12x^2y^4z^6}{6xz^{12}}$

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

$\frac{12}{6}(x^{2-1})(y^{4-0})(z^{6-12})=2xy^4z^{-6}=\frac{2xy^4}{z^6}$

Remember that negative exponents will eventually be moved back to the denominator.

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Example Question #31 : Simplifying Expressions

Divide the fractions.

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Possible Answers:

$\frac{5x^{4}}{12}$

$\frac{5x^{2}}{12y^{2}}$

$\frac{5y^{2}}{12x^{2}}$

$\frac{12y^{2}}{5x^{2}}$

$\frac{12x^{4}}{5}$

Correct answer:

$\frac{12y^{2}}{5x^{2}}$

Explanation:

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Dividing fractions is equal to multiplying by the reciprocal.

$\frac{30xy}{11} * \frac{22y}{25x^{3}}$

Cross-cancel the 30 with the 25, and the 22 with the 11.

$\frac{6xy}{1} *\frac{2y}{5x^{3}}$

Combine via multiplication and simplify.

$\frac{6xy* 2y}{5x^{3}}=\frac{6* 2*x* y*y}{5x^{3}}=\frac{12y^{2}}{5x^{2}}$

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Example Question #12 : Multiplying And Dividing Exponents

Simplify $\frac{a^{4}b^{2}}{6a^{3}b}\div \frac{2b^{5}}{12a^{7}}$

Possible Answers:

$\frac{b^4}{a^8}$

$\frac{2a^8}{b^4}$

$\frac{b^6}{36a^6}$

$\frac{a^8}{b^4}$

Correct answer:

$\frac{a^8}{b^4}$

Explanation:

Rewrite so that you are multiplying the reciprocal of the second fraction:

$\frac{a^{4}b^{2}}{6a^{3}b}\times \frac{12a^{7}}{2b^{5}}$

You can then simplify using rules of exponents:

$\frac{12a^{11}b^2}{12a^3b^6}=\frac{a^8}{b^4}$

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Example Question #51 : Monomials

Evaluate: $3x^3 \div 6x$

Possible Answers:

2x^2

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

$\frac{1}{2}x$

Correct answer:

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

Explanation:

First, divide the coefficients.

$3\div 6 = \frac{1}{2}$ .

Now consider the variables. x^3 means x times itself 3 times. Doing $x^3 \div x$ is the same as $\frac{x*x*x}{x}$ .

We see that an x from the top can cancel with the x on the bottom, leaving $\frac{x*x}{1}$ , or x^2 . Our answer then is $\frac{1}{2}x^2$ .

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Example Question #11 : How To Divide Monomial Quotients

Divide: $\frac{x^2}{x^{-1}}$

Possible Answers:

x^3

$\frac{1}{x^3}$

$\frac{1}{x}$

-x^3

Correct answer:

x^3

Explanation:

Dividing exponents by the same base allows the powers to be subtracted. Rewrite the exponents as one base.

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

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Example Question #53 : Monomials

Find the result of

$\frac{12x^3\cdot2x^4}{3x^5}$ .

Possible Answers:

$8x^{7/5}$

12x^3

8x^2

$24x^{12}$

Correct answer:

8x^2

Explanation:

The question asks for the quotient of $\frac{12x^3\cdot2x^4}{3x^5}$ .

We can rewrite the expression using the rules of multiplication and exponents to find the answer of 8x^2 .

$\frac{12\cdot2\cdot x\cdotx^{3+4}}{3x^5}= \frac{24}{3}\cdot x^{3+4-5}= 8x^2$

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Example Question #12 : How To Divide Monomial Quotients

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

Possible Answers:

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

$\frac{1}x{}$

$x^{2}$

$\frac{1}{2x}$

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 #13 : How To Divide Monomial Quotients

Divide the following monomial quotients:

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

Possible Answers:

$12x^{3}$

$3x^{2}$

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 #63 : Monomials

Divide the following monomial quotients:

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

Possible Answers:

$2x^{3}$

2xy

$x^{2}$

$2x^{3}y$

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 #14 : How To Divide Monomial Quotients

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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Algebra 1 : How to divide monomial quotients

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Multiplying And Dividing Exponents

Example Question #31 : Simplifying Expressions

Example Question #12 : Multiplying And Dividing Exponents

Example Question #51 : Monomials

Example Question #11 : How To Divide Monomial Quotients

Example Question #53 : Monomials

Example Question #12 : How To Divide Monomial Quotients

Example Question #13 : How To Divide Monomial Quotients

Example Question #63 : Monomials

Example Question #14 : How To Divide Monomial Quotients

All Algebra 1 Resources

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