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Algebra 1 : Variables

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Example Questions

Example Question #521 : Variables

Simplify the following:

$\frac{8a^2b^3}{-2ab}$

Possible Answers:

-6a^2b^2

-4a^3b^4

-4a^2b^2

-4ab^2

-6ab^2

Correct answer:

-4ab^2

Explanation:

Given the problem

$\frac{8a^2b^3}{-2ab}$

we will write it like

$(\frac{8}{-2})(\frac{a^2b^3}{ab})$

We can easily simplify the first part

$(-4)(\frac{a^2b^3}{ab})$

Now, when dividing, to simplify monomials containing the same base, you substract their exponents. We get

$(-4)(a^{2-1}b^{3-1})$

(-4)(a^1b^2)

(-4)(ab^2)

-4ab^2

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Example Question #522 : Variables

Solve: $\frac{5x^2y}{15xy^6}$

Possible Answers:

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

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

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

$\frac{1}{3xy^5}$

$\frac{xy^4}{3}$

Correct answer:

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

Explanation:

In order to solve this expression, we need to write out the factors of the numerator and denominator.

$\frac{5x^2y}{15xy^6} = \frac{5\cdot x \cdot x \cdot y}{5 \cdot 3 \cdot x \cdot y \cdot y^5}$

We can then cancel out the common terms.

The answer is: $\frac{x}{3y^5}$

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Example Question #523 : Variables

Divide: $\frac{6ab^2}{6b^3}$

Possible Answers:

$\frac{1}{ab}$

$\frac{12a}{b^3}$

$\frac{1}{6ab}$

$\frac{6}{ab}$

$\frac{a}{b}$

Correct answer:

$\frac{a}{b}$

Explanation:

In order to divide, we should split the top and bottom into their factors.

$\frac{6ab^2}{6b^3} = \frac{6 \times a \times b^2}{6 \times b \times b^2}$

The six and b^2 terms can be cancelled in the numerator and denominator.

The answer is: $\frac{a}{b}$

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Example Question #524 : Variables

Divide: $\frac{18x^2y^3}{36x^5y^{-3}}$

Possible Answers:

$\frac{y^6}{2x^3}$

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

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

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

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

Correct answer:

$\frac{y^6}{2x^3}$

Explanation:

When similar bases of a certain power are divided, their powers can be subtracted.

Evaluate each term.

$\frac{18}{36} = \frac{1}{2}$

When dealing with negative exponents, they can be rewritten as the reciprocal of the positive exponent.

$\frac{x^2}{x^5} = x^{2-5} = x^{-3} = \frac{1}{x^3}$

$\frac{y^3}{y^{-3}} = y^{3-(-3)} = y^6$

Multiply all the terms together.

$\frac{1}{2}\cdot\frac{1}{x^3}\cdot y^6 = \frac{y^6}{2x^3}$

The answer is: $\frac{y^6}{2x^3}$

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Example Question #525 : Variables

Divide the monomials: $\frac{3x^3y}{6xy^2z}$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Rewrite both the numerator and denominator by factors.

$\frac{3x^3y}{6xy^2z} = \frac{3 \times x \times x \times x \times y}{3 \times 2 \times y \times y \times z}$

Cancel all the common terms on the top and bottom.

The answer is: $\frac{x^2}{2yz}$

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Example Question #526 : Variables

Divide the monomials: $\frac{3x^2y^5z}{3x^2y^{-5}z^3}$

Possible Answers:

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

$\frac{y^{10}}{z^2}$

$\frac{1}{y^{10}z^2}$

$y^{10}z^2$

$\frac{z^2}{y^{10}}$

Correct answer:

$\frac{y^{10}}{z^2}$

Explanation:

Some of the terms of the given expression can already be simplified.

Cancel out the 3x^2 terms.

$\frac{y^5z}{y^{-5}z^3}$

When we are dividing powers of a similar base, it is the same as subtracting the exponents.

$\frac{y^5}{y^{-5}} = y^{5-(-5)}= y^{10}$

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

A negative exponent can be written as one over the base's positive exponent.

Multiply both terms together.

$y^{10} \cdot \frac{1}{z^2}= \frac{y^{10}}{z^2}$

The answer is: $\frac{y^{10}}{z^2}$

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Example Question #51 : How To Divide Monomial Quotients

Simplify: $\frac{8xz^3}{2z}$

Possible Answers:

4z^2

4xz^2

4x^2z^2

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

4x-z^2

Correct answer:

4xz^2

Explanation:

In order to simplify this fraction, we will need to rewrite the numerator using factors.

$\frac{8xz^3}{2z}=\frac{2\cdot 4 \cdot x \cdot z^3}{2z}$

Cancel the common terms in the numerator and denominator.

The answer is: 4xz^2

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Example Question #61 : How To Divide Monomial Quotients

Divide the monomials: $\frac{3x^6yz^3}{3x^{-6}y^6z^5}$

Possible Answers:

y^5z^2

$\frac{1}{y^5z^2}$

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

$\frac{y^5}{z^2}$

Correct answer:

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

Explanation:

When powers of a similar base are divided, the powers can be subtracted.

The coefficients will cancel.

Subtract each power for each variable.

$x^{6-(-6)}=x^{12}$

$y^{1-6}= y^{-5} = \frac{1}{y^5}$

$z^{3-5}= z^{-2} = \frac{1}{z^2}$

Multiply and combine each of these terms together.

$x^{12} \times \frac{1}{y^5} \times \frac{1}{z^2}$

The answer is: $\frac{x^{12}}{y^5z^2}$

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Example Question #522 : Variables

Divide: $\frac{9ab^6}{36a^3b^6}$

Possible Answers:

$\frac{1}{27a^2}$

4a^2

$\textup{Cannot be solved.}$

$\frac{1}{4a^2}$

Correct answer:

$\frac{1}{4a^2}$

Explanation:

Rewrite the numerator and denominator in factors.

$\frac{9ab^6}{36a^3b^6} = \frac{9\times a \times b^6}{9 \times 4 \times a\times a^2 \times b^6}$

Cancel out the common terms in the numerator and denominator. Since all the terms in the numerator cancels out, the numerator becomes a one.

The answer is: $\frac{1}{4a^2}$

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Example Question #107 : Monomials

Simplify the following expression:

Which of the following expressions is equivalent to this one:

$\frac{4a^{3}b^{2}}{6a}\cdot\frac{8c^{4}b^{3}}{2b}$

Possible Answers:

$\frac{16a^2b^3c^4}{3}$

$\frac{8a^{2}b^{4}c^{4}}{3}$

$\frac{8a^{2}b^{3}c^{4}}{3}$

$\frac{32a^3b^3 c^4}{12}$

$\frac{8a^2bc^4}{6}$

Correct answer:

$\frac{8a^{2}b^{4}c^{4}}{3}$

Explanation:

First, simplify each term individually. Let's start with the term on the left. We can factor out from both the numerator and denominator.

$\frac{4a^{3}b^{2}}{6a}\rightarrow \frac{2a^2b^2}{3}$

Next, factor out from the numerator and denominator of the term on the right.

$\frac{8c^{4}b^{3}}{2b}\rightarrow \frac{4c^4b^2}{1}$

Combine and multiply. Remember that when we are multiplying terms with exponents, we need to add their exponential values. Likewise, when we divide exponents, we will subtract their exponential values.

$\frac{4a^3b^2}{6a}\cdot\frac{8c^4b^3}{2b} = \frac{2a^2b^2}{3}\cdot\frac{4c^4b^2}{1}$

$\frac{2a^2b^2}{3}\cdot\frac{4c^4b^2}{1}=\frac{(2a^2b^2)(4c^4b^2)}{3}$

Simplify.

$\frac{(2a^2b^2)(4c^4b^2)}{3}=\frac{8a^2b^4c^4}{3}$

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #521 : Variables

Example Question #522 : Variables

Example Question #523 : Variables

Example Question #524 : Variables

Example Question #525 : Variables

Example Question #526 : Variables

Example Question #51 : How To Divide Monomial Quotients

Example Question #61 : How To Divide Monomial Quotients

Example Question #522 : Variables

Example Question #107 : Monomials

All Algebra 1 Resources

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