ISEE Middle Level Math : How to multiply variables

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #61 : Variables

Simplify the following expression: 

Possible Answers:

The expression is already reduced. 

Correct answer:

Explanation:

When you multiple variables, the constants will be multiplied together and the variables will be combined.  

So that means that 

 

and 

 

so that leaves us with a final answer of 

.

Example Question #62 : Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

We can simplify this by combining like terms. We need to multiply the two pieces in parentheses. 

We can only combine variables with the same base. 

To multiply variables we must add their exponents.

The integers (whole numbers) can be combined via standard multiplication.

So, we should get the following:

So our answer is:

Example Question #63 : Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve    distribute the  to each term in the parenthesis. Remember: When multiplying variables add the exponents.

Rewrite:

 

Example Question #64 : Variables

Possible Answers:

Correct answer:

Explanation:

Multiply the coefficients of the variable 

Then multiply the variables by adding the exponents:

 is the correct answer.

Example Question #65 : Operations

Possible Answers:

Correct answer:

Explanation:

First distribute the  to all terms in the parenthesis.

  (When multiplying variables with exponents, the exponents are added together).

Example Question #66 : Operations

Possible Answers:

Correct answer:

Explanation:

To solve 

Separate the parts of the terms.  Multiply the coefficients:

Multiply the terms with  as the variable. When multiplying, the exponents get added.

Multiply the terms with  as the variable. When multiplying, the exponents get added.

Put it all together:

 

 

 

Example Question #67 : Operations

The length of a rectangle is  and the width is  What is the area of this rectangle?

Possible Answers:

Correct answer:

Explanation:

The formula for the Area of a rectangle is length times width or l x w.  Multiply the length which is  times the width which is 

First multiply

Then multiply the variables; add the exponents:

Area or A of the rectangle is

Example Question #65 : Variables

The length of a rectangular prism is  centimeters.  The width is  centimeters. The height is  centimeters. Find the volume of this rectangular prism.

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is determined by using the formula

V = length x width x height

Example Question #69 : Operations

Multiply the following:

Possible Answers:

Correct answer:

Explanation:

When multiplying variables, we multiply them together just like we would integers.  We have

 

The first term isn't showing a coefficient, so it is automatically 1.  So,

 

Now, we will multiply the coefficients together, then we multiply the variables together.

So, we get

Example Question #66 : Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

Let's begin by rewriting the expression with similar terms next to each other.

Next, multiply the terms out.

Our first pair of terms is just like regular multiplication.

For the next two terms, we need to add the exponents. 

In doing so, we get:

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