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ACT Math : Monomials

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Example Questions

Example Question #1 : Variables

Mike wants to sell candy bars for a $50\%$ $\displaystyle 50\%$ profit. If he sells each bar for $\$1.20$ $\displaystyle \$1.20$, how much did each bar cost him?

Possible Answers:

$\$0.75$ $\displaystyle \$0.75$

$\$0.80$ $\displaystyle \$0.80$

$\$1.00$ $\displaystyle \$1.00$

$\$0.60$ $\displaystyle \$0.60$

Correct answer:

$\$0.80$ $\displaystyle \$0.80$

Explanation:

In order to solve this problem, set up the following equation:

$\frac{1.20}{x}=\frac{150\%}{100\%}$ $\displaystyle \frac{1.20}{x}=\frac{150\%}{100\%}$

Cross multiply:

$\displaystyle 150x = 120$

Divide:

$\frac{150x}{150} = \frac{120}{150} = 0.80$ $\displaystyle \frac{150x}{150} = \frac{120}{150} = 0.80$

The original cost of the of each candy bar is $\$0.80$ $\displaystyle \$0.80$

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Example Question #1 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$ $\displaystyle \frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$

Possible Answers:

3ax $\displaystyle 3ax$

2yp $\displaystyle 2yp$

3yp $\displaystyle 3yp$

12xp $\displaystyle 12xp$

2xy $\displaystyle 2xy$

Correct answer:

2yp $\displaystyle 2yp$

Explanation:

$\frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$ $\displaystyle \frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$

To divide monomial quotients, simply invert the divisor and multiply:

$\frac{12x^3y^2p}{4ab} *\frac{2ab}{3x^3y} = \frac{24x^3y^2pab}{12abx^3y}$ $\displaystyle \frac{12x^3y^2p}{4ab} *\frac{2ab}{3x^3y} = \frac{24x^3y^2pab}{12abx^3y}$

Then, reduce:

$\frac{24yp}{12} = 2yp$ $\displaystyle \frac{24yp}{12} = 2yp$

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Example Question #1 : Monomials

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$ $\displaystyle \frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$

Possible Answers:

$\frac{20x^3}{9y}$ $\displaystyle \frac{20x^3}{9y}$

$\frac{20n^3}{9m}$ $\displaystyle \frac{20n^3}{9m}$

$\frac{20p^3n}{9m}$ $\displaystyle \frac{20p^3n}{9m}$

$\frac{20m^3n}{9p}$ $\displaystyle \frac{20m^3n}{9p}$

$\frac{9p}{20m^3n}$ $\displaystyle \frac{9p}{20m^3n}$

Correct answer:

$\frac{20m^3n}{9p}$ $\displaystyle \frac{20m^3n}{9p}$

Explanation:

$\frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$ $\displaystyle \frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$

To find your answer, you have to invert the divisor and multiply across:

$\frac{10m^2np}{3xy} * \frac{2xym}{3p^2} = \frac{20m^3npxy}{9p^2xy}$ $\displaystyle \frac{10m^2np}{3xy} * \frac{2xym}{3p^2} = \frac{20m^3npxy}{9p^2xy}$

Then, reduce:

$\frac{20m^3n}{9p}$ $\displaystyle \frac{20m^3n}{9p}$

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Example Question #2 : Monomials

Multiply: $2x\ast(4x+3)$ $\displaystyle 2x\ast(4x+3)$

Possible Answers:

$6x^{2}+8x$ $\displaystyle 6x^{2}+8x$

$8x^{2}+6$ $\displaystyle 8x^{2}+6$

8x+6 $\displaystyle 8x+6$

$8x^{2}+6x$ $\displaystyle 8x^{2}+6x$

6x+8 $\displaystyle 6x+8$

Correct answer:

$8x^{2}+6x$ $\displaystyle 8x^{2}+6x$

Explanation:

To solve you must multiply $\displaystyle 2x$ by both terms in (4x+3) $\displaystyle (4x+3)$

$2x\ast4x=8x^{2}$ $\displaystyle 2x\ast4x=8x^{2}$

$2x\ast3=6x$ $\displaystyle 2x\ast3=6x$

$8x^{2}+6x$ $\displaystyle 8x^{2}+6x$

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Example Question #1 : Monomials

Multiply:

$4x\cdot(5x+7)$ $\displaystyle 4x\cdot(5x+7)$

Possible Answers:

20x+11 $\displaystyle 20x+11$

$9x^{2}+28$ $\displaystyle 9x^{2}+28$

$20x^{2}+28x$ $\displaystyle 20x^{2}+28x$

$9x^{2}+28x$ $\displaystyle 9x^{2}+28x$

Correct answer:

$20x^{2}+28x$ $\displaystyle 20x^{2}+28x$

Explanation:

Multiply $\displaystyle 4x$ by both terms in (5x+7) $\displaystyle (5x+7)$

$4x\cdot5x=20x^{2}$ $\displaystyle 4x\cdot5x=20x^{2}$

$4x\cdot7=28x$ $\displaystyle 4x\cdot7=28x$

$20x^{2}+28x$ $\displaystyle 20x^{2}+28x$

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Example Question #593 : Algebra

Multiply $\left (7x^{2}-12x+4 \right ) \cdot 3x$ $\displaystyle \left (7x^{2}-12x+4 \right ) \cdot 3x$

Possible Answers:

$21x^{3}+36x^{2}+12x$ $\displaystyle 21x^{3}+36x^{2}+12x$

$21x^{3}-36x^{2}+12x$ $\displaystyle 21x^{3}-36x^{2}+12x$

$21x^{2}-36x+12$ $\displaystyle 21x^{2}-36x+12$

$7x^{3}-12x^{2}+4x$ $\displaystyle 7x^{3}-12x^{2}+4x$

None of the other answers

Correct answer:

$21x^{3}-36x^{2}+12x$ $\displaystyle 21x^{3}-36x^{2}+12x$

Explanation:

When multiplying a polynomial by a monomial, each term in the polynomial gets multiplied by the monomial. Calculate each term one at a time, then add the results to get the final answer. In this case, we start by multiplying $7x^{2}\cdot3x$ $\displaystyle 7x^{2}\cdot3x$. $7\cdot3=21$ $\displaystyle 7\cdot3=21$ and $x^{2}\cdot x=x^{3}$ $\displaystyle x^{2}\cdot x=x^{3}$, thus we get $21x^{3}$ $\displaystyle 21x^{3}$. For the second term of the polynomial, we multiply $-12\cdot3=-36$ $\displaystyle -12\cdot3=-36$ and $x\cdot x= x^{2}$ $\displaystyle x\cdot x= x^{2}$, resulting in $-36x^{2}$ $\displaystyle -36x^{2}$. Finally, we multiply $4\cdot3 = 12$ $\displaystyle 4\cdot3 = 12$ and $1\cdot x = x$ $\displaystyle 1\cdot x = x$, resulting in 12x $\displaystyle 12x$. Adding the three terms that we just found, we come to the answer of $21x^{3}-36x^{2}+12x$ $\displaystyle 21x^{3}-36x^{2}+12x$.

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Example Question #4 : Monomials

Choose the answer that is the best solution to the following expression of monomial quotients:

$\frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$ $\displaystyle \frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$

Possible Answers:

$\frac{8xp^3}{36ny}$ $\displaystyle \frac{8xp^3}{36ny}$

$\frac{4xp}{11n^2y}$ $\displaystyle \frac{4xp}{11n^2y}$

$\frac{2xp}{9n^2y}$ $\displaystyle \frac{2xp}{9n^2y}$

$\frac{4xp^3}{5ny}$ $\displaystyle \frac{4xp^3}{5ny}$

$\frac{2xp^3}{9ny}$ $\displaystyle \frac{2xp^3}{9ny}$

Correct answer:

$\frac{2xp^3}{9ny}$ $\displaystyle \frac{2xp^3}{9ny}$

Explanation:

$\frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$ $\displaystyle \frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$

To multiply monomial quotients, treat them as you would any other fraction. Combine like terms wherever possible:

$\frac{8x^2p^3mn}{36mn^2xy}$ $\displaystyle \frac{8x^2p^3mn}{36mn^2xy}$

Then, you need to reduce:

$\frac{2xp^3}{9ny}$ $\displaystyle \frac{2xp^3}{9ny}$

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Example Question #595 : Algebra

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$ $\displaystyle \frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$

Possible Answers:

$\frac{13x^2y^3p}{100z}$ $\displaystyle \frac{13x^2y^3p}{100z}$

$\frac{8x^2y^3p}{25z^2}$ $\displaystyle \frac{8x^2y^3p}{25z^2}$

$\frac{2x^2y^3p}{25z}$ $\displaystyle \frac{2x^2y^3p}{25z}$

$\frac{2xyp}{15z}$ $\displaystyle \frac{2xyp}{15z}$

$\frac{2p}{25z}$ $\displaystyle \frac{2p}{25z}$

Correct answer:

$\frac{2x^2y^3p}{25z}$ $\displaystyle \frac{2x^2y^3p}{25z}$

Explanation:

$\frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$ $\displaystyle \frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$

To simplify, first multiply across:

$\frac{8x^3y^4z^2p}{100z^3xy}$ $\displaystyle \frac{8x^3y^4z^2p}{100z^3xy}$

Then, reduce:

$\frac{2x^2y^3p}{25z}$ $\displaystyle \frac{2x^2y^3p}{25z}$

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ACT Math : Monomials

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Variables

Example Question #1 : Variables

Example Question #1 : Monomials

Example Question #2 : Monomials

Example Question #1 : Monomials

Example Question #593 : Algebra

Example Question #4 : Monomials

Example Question #595 : Algebra

All ACT Math Resources

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