Pre-Algebra

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Questions 1 - 10
1

The area of a particular rectangle is . If the length of the rectangle is twice the width, what is the width of the rectangle?

Explanation

The forumla for the area of a rectangle is Length X Width. Here, that would be Width X 2Width (length). Solving for width, you get

. Dividing by 2 and taking the square root of each side gives us

. Thus, the width of the rectangle is units.

2

What is the perimeter of a triangle with side lengths of

Explanation

To find the perimeter of a triangle you must add all of the side lengths together.

In this case our equation would look like

Add the numbers together to get the answer .

3

What is the perimeter of a triangle with side lengths of , , and ?

Explanation

To find the perimeter of a triangle, add the lengths of all sides together:

4

What is the perimeter of a triangle with side lengths of , , and ?

Explanation

To find the perimeter of a triangle you must add the three side lengths together.

In this case our equation would look like

Add the numbers together to get the answer .

5

Reduce the fraction .

Explanation

To reduce any fraction, you must find the greatest common factor (GCF) of both the numerator and denominator. In this case, the biggest number that can be divided into both 18 and 24 evenly is 6. Divide both 18 and 24 by 6 to solve.

The solution is .

6

Evaluate the following expression:

Explanation

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

Next, we complete the multiplication:

Finally, we evaluate the addition and subtraction from left to right in the expression:

7

What is the volume of a cone with a height of meters and a base diameter of meters?

Explanation

The formula for the volume of a cone is .

Notice that we are given the diameter, meters, not the radius; thus, we have to solve for the radius by dividing the diameter by two. The radius is therefore 3 meters. Then, we plug this value into the formula for volume:

8

What is the volume of a pyramid with a base area of 9 sqaure centimeters and a height of 4 centimeters?

Explanation

The volume of a pyramid can be determined using the following equation:

9

Multiply:

Explanation

Multiply the ones digits together.

The ones digit of the final answer is .

Carry over the to the next calculuation.

Multiply the with the tens digit of the first number, and add the carryover .

The answer is:

10

Multiply:

Explanation

Eliminate the absolute value sign before proceeding to multiply all the terms.

A value inside the absolute value will result into a positive value.

From here, first multiply , when doing so remember when a negative number is multiplied by a positive number the resulting product is negative.

Therefore we get,

.

Now we will need to multiply with .

First multiply six with nine to get . Keep the four in the ones place and carry the five to the tens place. Now multply nine with three . Since we carried the five over we need to add . Combine this value with the value that was found for the ones spot to get, . Finally, place a negative sign in front of it to arrive at the final answer.

.

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