ACT Math : Monomials

Example Questions

Example Question #1 : Variables

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

Explanation:

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

Cross multiply:

Divide:

The original cost of the of each candy bar is

Example Question #2 : Variables

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

Explanation:

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

Then, reduce:

Example Question #3 : Variables

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

Explanation:

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

Then, reduce:

Example Question #4 : Variables

Multiply:

Explanation:

To solve you must multiply  by both terms in

Example Question #5 : Variables

Multiply:

Explanation:

Multiply  by both terms in

Example Question #6 : Variables

Multiply

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  and , thus we get . For the second term of the polynomial, we multiply  and , resulting in . Finally, we multiply  and , resulting in . Adding the three terms that we just found, we come to the answer of .

Example Question #7 : Variables

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

Explanation:

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

Then, you need to reduce:

Example Question #8 : Variables

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