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Algebra 1 : How to divide monomial quotients

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Example Questions

Example Question #1 : How To Divide Monomial Quotients

Evaluate

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

Possible Answers:

$2w^{2}+4w-5$

$-1+7w^{2}$

$2w^{2}-4w+5$

$7w^{2}+4w-5$

Correct answer:

$7w^{2}+4w-5$

Explanation:

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

When dividing a polynomial by a monomial, we can use a divison called, term-by-term, dividing each of the top terms by the monomial.

$\frac{12w^{2}}{3w}-\frac{15w}{3w}+\frac{21w^{3}}{3w}$

Simplify.

$4w-5+7w^{2}$

Rewrite it with the leading coefficent first,

Final Answer: $7w^{2}+4w-5$

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Example Question #1 : How To Divide Monomial Quotients

Simplify the fraction to its lowest terms:

$\frac{18x^4y^3z}{6xy^2z^3}$

Possible Answers:

$3x^3yz^{-2}$

3x^5y^5z^4

12x^3yz^2

3x^3yz^2

Correct answer:

$3x^3yz^{-2}$

Explanation:

The first step is to divide the constants, 18 and 6, by the LCM, 6, to get 3. When dividing variables, if the variable is present in the numerator and denominator, subtract the exponent found in the numerator by the exponent in the denominator.

For , you have 4-1=3 .

For , you have 3-2=1 .

For , you have 1-3=-2 .

Then write the simplified answer as one term:

$3x^3yz^{-2}$

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Example Question #3 : How To Divide Monomial Quotients

Divide:

$\frac{9x^4+6x^3-12x}{3x}$

Possible Answers:

3x^3+2x^2+4

6x^3+3x^2-9

6x^3+3x^2+9

3x^3+2x^2-4

Correct answer:

3x^3+2x^2-4

Explanation:

$\frac{9x^4+6x^3-12x}{3x}=\frac{9x^4}{3x}+\frac{6x^3}{3x}-\frac{12x}{3x}=3x^3+2x^2-4$

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Example Question #4 : How To Divide Monomial Quotients

Siimplify:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =\ ?$

Possible Answers:

$x^{2}y - 3xyz + 5x^{2}yz^{2}$

$xy^{2}-3xz+5xy$

$xy - yz+5xz^{2}$

$xy^{2}-3yz+5x^{2}z^{2}$

$xyz-3yz+5x^{2}yz^{2}$

Correct answer:

$xy^{2}-3yz+5x^{2}z^{2}$

Explanation:

For any polynomial division, divide each term in the numerator individually by the denominator:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =$ $\frac{2x^{2}y^{3}z}{2xyz} - \frac{6xy^{2}z^{2}}{2xyz} + \frac{10x^{3}yz^{3}}{2xyz}=$

$xy^{2}-3yz+5x^{2}z^{2}$

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Example Question #4 : How To Divide Monomial Quotients

Simplify:

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

Possible Answers:

$\frac{1}{2xy}$

98x^3y

98xy

2xy

Correct answer:

2xy

Explanation:

When dividing monomials, consider the coefficients and variables separately. Rewrite the expression as $\left(\frac{14}{7}\right)\left(\frac{x^2}{x}\right)\left(y\right)$ , grouping common bases. For the coeffiecients, we can divide normally: $\left(\frac{14}{7} \right )=2$ . For the variables, we can keep the common base and subtract the exponents: $\left(\frac{x^2}{x} \right )=x^{2-1}=x$ . Then, multiply each portion all back together to obtain 2xy .

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Example Question #1 : Simplifying Expressions

Simplify the expression.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Possible Answers:

$\small \frac{xy^3}{z^3}$

$\small \frac{z^3}{xy^3}$

$\small \frac{z^3}{x^2y^5}$

$\small \frac{x^2y^5}{z^3}$

Correct answer:

$\small \frac{xy^3}{z^3}$

Explanation:

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Because we are only multiplying terms in the numerator, we can disregard the parentheses.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}=\frac{x^2y^2x^3y^4z}{x^4y^3z^4}$

To combine like terms in the numerator, we add their exponents.

$\small \frac{x^5y^6z}{x^4y^3z^4}$

To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.

$x^{5-4}y^{6-3}z^{1-4}=xy^3z^{-3}$

Remember that any negative exponents stay in the denominator.

$\frac{xy^3}{z^3}$

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Example Question #1 : Simplifying Expressions

Simplify: $\frac{5p^{7}}{25p^{^{4}}}$

Possible Answers:

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

$\frac{p^{7/4}}{5}$

$\frac{p}{5}$

$\frac{p^{-3}}{5}$

$5p^{3}$

Correct answer:

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

Explanation:

$p^{7}$ and $p^{4}$ cancel out, leaving $p^{3}$ in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

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Example Question #2 : Simplifying Expressions

Simplify the following:

$\frac{4x+6x^2}{2x}$

Possible Answers:

2x(2-3x)

$\frac{2-3x}{2x}$

$\frac{2}{2x}-\frac{3}{2}$

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

2+3x

Correct answer:

2+3x

Explanation:

$\frac{4x+6x^2}{2x}$

First, let us factor the numerator:

4x+6x^2=x(4+6x)=2x(2+3x)

$\frac{2x(2+3x)}{2x}=2+3x$

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Example Question #2 : How To Divide Monomial Quotients

Simplify the following:

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}$

Possible Answers:

$\frac{5}{9}$

$\frac{-10lx}{27zp}$

$\frac{-18}{15xyz}$

$\frac{-18p^{3}l^{3}}{15xy^{2}z}$

Correct answer:

$\frac{-10lx}{27zp}$

Explanation:

First, flip the numerator and the denominator of the second fraction to turn the division into multiplication.

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}=\frac{-2pl^2}{3yz} * \frac{5xy}{9lp^2}=\frac{-2pl^25xy}{3yz9lp^2}$

We can then cancel like terms.

From both the numerator and denominator, remove one , remove one , and remove one :

$\frac{-2l5x}{3z9p}$

Then we finish by multiplying the constants:

$\frac{-10lx}{27zp}$

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Example Question #1 : How To Divide Monomial Quotients

Simplify this expression:

$\frac{x^{2}y^{-3}z^{4}}{x^{3}y^{-2}z^{2}}$

Possible Answers:

$xyz^{2}$

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

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

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

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

Correct answer:

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

Explanation:

When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:

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

For the above problem,

$\frac{x^{2}}{x^{3}} = \frac{1}{x} ; \frac{y^{-3}}{y^{-2}} = \frac{y^{2}}{y^{3}} = \frac{1}{y} ; \frac{z^{4}}{z^{2}} = z^{2}$

Therefore, the expression simplifies to:

$\left ( \frac{1}{x} \right ) \left ( \frac{1}{y} \right ) z^{2} = \frac{z^{2}}{xy}$

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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 #1 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #3 : How To Divide Monomial Quotients

Example Question #4 : How To Divide Monomial Quotients

Example Question #4 : How To Divide Monomial Quotients

Example Question #1 : Simplifying Expressions

Example Question #1 : Simplifying Expressions

Example Question #2 : Simplifying Expressions

Example Question #2 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

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