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Algebra 1 : Variables

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Example Questions

Example Question #42 : How To Divide Monomial Quotients

Evaluate:

$\frac{64x^{6}y^{-3}z^7}{12x^{4}y^{-2}z^9}$

Possible Answers:

$\frac{16x^{2}}{3y^{-1}z^2}$

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

$\frac{16x^{2}}{3yz^2}$

$\frac{3z^3}{16x^{2}y}$

$\frac{3x^{2}y}{16z^2}$

Correct answer:

$\frac{16x^{2}}{3yz^2}$

Explanation:

To evaluate, we must cancel out like values on the numerator and denominator:

$\frac{64x^{6}y^{-3}z^7}{12x^{4}y^{-2}z^9}=\frac{64x^{6}y^{2}z^7}{12x^{4}y^{3}z^9}=\frac{16x^{2}}{3yz^2}$

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Example Question #45 : How To Divide Monomial Quotients

Divide the following

$\frac{24a^4bc^5}{2abc^2}$

Possible Answers:

12a^5b^2c^7

12a^3c^3

12abc

12a^3bc^3

24a^3c^3

Correct answer:

12a^3c^3

Explanation:

To solve, we will divide the monomials using the quotient of powers.

SOLUTION A

We have

$\frac{24a^4bc^5}{2abc^2}$

We know

$a^4 = a \cdot a \cdot a \cdot a$

and

$c^5 = c \cdot c \cdot c \cdot c \cdot c$

and so on.

Let's expand the original problem. We get

$\frac{24 \cdot a \cdot a \cdot a \cdot a \cdot b \cdot c \cdot c \cdot c \cdot c \cdot c}{2 \cdot a \cdot b \cdot c \cdot c}$

Now, we know we can look at the numerator and cancel anything in the denominator. So,

$\frac{24 \cdot {\color{Red} a} \cdot a \cdot a \cdot a \cdot {\color{Blue} b} \cdot {\color{Green} c} \cdot {\color{Green} c} \cdot c \cdot c \cdot c}{2 \cdot {\color{Red} a} \cdot {\color{Blue} b} \cdot {\color{Green} c} \cdot {\color{Green} c}}$

We can cancel the variables that have been highlighted. So, we get

$\frac{24 \cdot a \cdot a \cdot a \cdot c \cdot c \cdot c}{2}$

We can divide the integers, leaving us with

$12 \cdot a \cdot a \cdot a \cdot c \cdot c \cdot c}$

Which equals

12a^3c^3

SOLUTION B

We can solve this a different way by using a shortcut. When dividing monomials, simply subtract the quotients with the same base.

$\frac{24{\color{Red} a^4}{\color{Blue} b}{\color{Green} c^5}}{2{\color{Red} a}{\color{Blue} b}{\color{Green} c^2}}$

The different variables have been highlighted. Now, we subtract.

$\frac{24a^{4-1}b^{1-1}c^{5-2}}{2}$

$\frac{24a^3c^3}{2}$

12a^3c^3

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Example Question #44 : How To Divide Monomial Quotients

Find the quotient of the following

$\frac{36x^3y^2}{9xy^2}$ .

Possible Answers:

4x^2

6x^2y

6x^4y^4

4xy

4x^4y^4

Correct answer:

4x^2

Explanation:

When dividing polynomials, you subtract the powers with the same base.

$\frac{36x^3y^2}{9xy^2}$

$\frac{36}{9}x^{3-1}y^{2-2}$

$\frac{36}{9}x^2y^0$

We know that anything raised to the zero power equals 1.

So we get

$\frac{36}{9}x^2$

We simplify the integers.

We get

4x^2

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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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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #42 : How To Divide Monomial Quotients

Example Question #45 : How To Divide Monomial Quotients

SOLUTION A

SOLUTION B

Example Question #44 : How To Divide Monomial Quotients

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

All Algebra 1 Resources

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