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Algebra 1 : Monomials

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Example Questions

Example Question #47 : How To Divide Monomial Quotients

Divide the monomials: $\frac{9x}{81x^2}$

Possible Answers:

$\frac{9}{x}$

$\frac{1}{9x}$

$\frac{x}{9}$

$\frac{1}{9x^3}$

$\frac{1}{9x^2}$

Correct answer:

$\frac{1}{9x}$

Explanation:

In order to simplify this expression, write out the factors of the numerator and denominator.

$\frac{9x}{81x^2} = \frac{9\cdot x}{9 \cdot 9 \cdot x \cdot x}$

Cancel out the common terms on the numerator and denominator.

The answer is: $\frac{1}{9x}$

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Example Question #45 : How To Divide Monomial Quotients

Simplify the following:

$\frac{15x^8}{3x^2}$

Possible Answers:

$5x^{16}$

5x^4

$5x^{10}$

5x^6

12x^6

Correct answer:

5x^6

Explanation:

When dividing monomials, we divide the coefficients, and if the base is the same, we subtract the exponents. So

$\frac{15x^8}{3x^2}$

can be simplified to

$5 x^{(8 - 2)}$

5x^6

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Example Question #49 : How To Divide Monomial Quotients

Divide the monomials: $\frac{3x^4}{6x^5}$

Possible Answers:

$\frac{2}{x}$

$\frac{x}{2}$

$\frac{1}{2x}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2x}$

Explanation:

The terms in the numerator and denominator can be expanded.

Write out the terms and factors in order to see what can be cancelled on the numerator and denominator.

$\frac{3x^4}{6x^5} = \frac{3\cdot x \cdot x \cdot x \cdot x}{2\cdot 3 \cdot x\cdot x\cdot x\cdot x\cdot x}$

After cancelling out the common terms, we are left with $\frac{1}{2x}$ .

The answer is: $\frac{1}{2x}$

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Example Question #46 : How To Divide Monomial Quotients

Divide the following monomials: $\frac{5x^5}{35x^7}$

Possible Answers:

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

$\frac{1}{5x^2}$

$\frac{5}{7x^2}$

$\frac{1}{7x^2}$

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

Correct answer:

$\frac{1}{7x^2}$

Explanation:

In order to solve this, we will need to split the numerator and denominator into their factors.

Write out the factors of the fraction.

$\frac{5x^5}{35x^7}= \frac{5 \cdot x^5}{5\cdot 7\cdot x^5 \cdot x\cdot x}$

Notice that the 5x^5 term can cancel. The fraction will reduce to: $\frac{1}{7x^2}$

The answer is: $\frac{1}{7x^2}$

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Example Question #511 : Variables

Divide: $\frac{13x^6}{26x^6}$

Possible Answers:

$\frac{1}{2}$

$\frac{1}{2x}$

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

Correct answer:

$\frac{1}{2}$

Explanation:

To simplify the monomial, simply write out the terms of the common factors for the numerator and denominator.

$\frac{13x^6}{26x^6}=\frac{13 \times x^6}{2 \times 13 \times x^6}$

The terms and x^6 can be divided easily, resultiing to one.

Simplify the fraction.

$\frac{13 \times x^6}{2 \times 13 \times x^6} = \frac{1}{2}$

The answer is: $\frac{1}{2}$

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Example Question #512 : Variables

Divide: $\frac{x^3 yz^2}{x^5yz^3}$

Possible Answers:

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

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

$\textup{The denominator cannot be zero.}$

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

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

Correct answer:

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

Explanation:

Each variable in this expression can be solved separately. When we are dividing the powers of the same base, we can simply subtract the powers.

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

The negative exponent can be converted to: $\frac{1}{x^2}$

Dividing the terms on the numerator and denominator will give us .

$\frac{y}{y} = \frac{y^1}{y^1} = y^{1-1}= y^0 = 1$

Divide $\frac{z^2}{z^3}$ and simplify to a fraction.

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

Multiply all the terms.

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

The answer is: $\frac{1}{x^2z}$

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Example Question #513 : Variables

Divide: $\frac{3xy^2}{9x^2y^4}$

Possible Answers:

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

$\frac{3}{xy}$

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

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

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

Correct answer:

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

Explanation:

Write out the factors for the numerator and denominator.

$\frac{3xy^2}{9x^2y^4}= \frac{3 \cdot x \cdot y^2}{3\cdot3\cdot x \cdot x \cdot y^2 \cdot y^2}$

Cancel the common factors on the top and bottom.

The answer is: $\frac{1}{3xy^2}$

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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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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #47 : How To Divide Monomial Quotients

Example Question #45 : How To Divide Monomial Quotients

Example Question #49 : How To Divide Monomial Quotients

Example Question #46 : How To Divide Monomial Quotients

Example Question #511 : Variables

Example Question #512 : Variables

Example Question #513 : Variables

Example Question #521 : Variables

Example Question #522 : Variables

Example Question #523 : Variables

All Algebra 1 Resources

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