Monomials - ACT Math

Card 0 of 72

Question

Mike wants to sell candy bars for a profit. If he sells each bar for , how much did each bar cost him?

Answer

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

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

Cross multiply:

Divide:

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

The original cost of the of each candy bar is

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Question

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

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

Answer

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

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

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

Then, reduce:

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

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Question

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

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

Answer

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

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

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

Then, reduce:

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

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Question

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

Answer

To solve you must multiply by both terms in

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

$2x\ast3=6x$

$8x^{2}+6x$

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Question

Multiply:

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

Answer

Multiply by both terms in

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

$4x\cdot7=28x$

$20x^{2}+28x$

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Question

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

Answer

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 $7x^{2}\cdot3x$ . $7\cdot3=21$ and $x^{2}\cdot x=x^{3}$ , thus we get $21x^{3}$ . For the second term of the polynomial, we multiply $-12\cdot3=-36$ and $x\cdot x= x^{2}$ , resulting in $-36x^{2}$ . Finally, we multiply $4\cdot3 = 12$ and $1\cdot x = x$ , resulting in . Adding the three terms that we just found, we come to the answer of $21x^{3}-36x^{2}+12x$ .

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Question

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

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

Answer

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

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

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

Then, you need to reduce:

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

Compare your answer with the correct one above

Question

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

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

Answer

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

To simplify, first multiply across:

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

Then, reduce:

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

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Question

Mike wants to sell candy bars for a profit. If he sells each bar for , how much did each bar cost him?

Answer

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

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

Cross multiply:

Divide:

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

The original cost of the of each candy bar is

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Then, reduce:

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

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Then, reduce:

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

Compare your answer with the correct one above

Question

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

Answer

To solve you must multiply by both terms in

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

$2x\ast3=6x$

$8x^{2}+6x$

Compare your answer with the correct one above

Question

Multiply:

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

Answer

Multiply by both terms in

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

$4x\cdot7=28x$

$20x^{2}+28x$

Compare your answer with the correct one above

Question

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

Answer

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 $7x^{2}\cdot3x$ . $7\cdot3=21$ and $x^{2}\cdot x=x^{3}$ , thus we get $21x^{3}$ . For the second term of the polynomial, we multiply $-12\cdot3=-36$ and $x\cdot x= x^{2}$ , resulting in $-36x^{2}$ . Finally, we multiply $4\cdot3 = 12$ and $1\cdot x = x$ , resulting in . Adding the three terms that we just found, we come to the answer of $21x^{3}-36x^{2}+12x$ .

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Then, you need to reduce:

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

Compare your answer with the correct one above

Question

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

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

Answer

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

To simplify, first multiply across:

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

Then, reduce:

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

Compare your answer with the correct one above

Question

Mike wants to sell candy bars for a profit. If he sells each bar for , how much did each bar cost him?

Answer

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

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

Cross multiply:

Divide:

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

The original cost of the of each candy bar is

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Then, reduce:

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

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Then, reduce:

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

Compare your answer with the correct one above

Question

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

Answer

To solve you must multiply by both terms in

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

$2x\ast3=6x$

$8x^{2}+6x$

Compare your answer with the correct one above

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