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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : Simplifying Expressions

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

Possible Answers:

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

$\frac{p}{5}$

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

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

$5p^{3}$

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 #1 : Simplifying Expressions

Simplify the following:

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

Possible Answers:

2x(2-3x)

2+3x

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

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

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

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:

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

$\frac{5}{9}$

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

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

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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Example Question #472 : Variables

Simplify the rational expression.

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

Possible Answers:

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

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

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

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

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 #123 : Basic Single Variable Algebra

Divide the fractions.

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

Possible Answers:

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

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

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

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

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

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 #473 : Variables

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

Possible Answers:

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

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

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

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

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 #11 : How To Divide Monomial Quotients

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

Possible Answers:

$\frac{1}{2}x$

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

2x^2

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 #4711 : Algebra 1

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

Possible Answers:

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

$\frac{1}{x}$

x^3

-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 #13 : How To Divide Monomial Quotients

Find the result of

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

Possible Answers:

12x^3

$24x^{12}$

8x^2

$8x^{7/5}$

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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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Simplifying Expressions

Example Question #1 : Simplifying Expressions

Example Question #2 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #472 : Variables

Example Question #123 : Basic Single Variable Algebra

Example Question #473 : Variables

Example Question #11 : How To Divide Monomial Quotients

Example Question #4711 : Algebra 1

Example Question #13 : How To Divide Monomial Quotients

All Algebra 1 Resources

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