# ISEE Middle Level Math : How to divide variables

## Example Questions

### Example Question #1 : How To Divide Variables

Explanation:

First convert each mixed number into and improper fraction

Then convert the operation to multiplication and flip the second fraction

Reduce where possible and multiply to solve:

Simplify:

Explanation:

### Example Question #72 : Variables

Solve for B

Not enough information provided.

Explanation:

This problem looks strange since it mostly contains variables, in particular unknown variables. Still remember the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. We still use those operations in this case. All we must do is move the variables around to solve for .

In this case we can subtract (additive inverse)  to the other side first.

Rewrite our problem.

Stop for a moment and look at the progress. Go back to the original question, solve for . Our problem shows  about to be multiplied to , but we do not necessarily have to multiply because we can divide by  to both sides of the equation, which would save us a step as well as have B by itself.

### Example Question #4 : How To Divide Variables

Suppose you know the values of , and , and you want to evaluate the expression below.

Which of the following is the first step you must complete?

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Explanation:

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square  first.

Divide:

Explanation:

### Example Question #6 : How To Divide Variables

Simplify:

Explanation:

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

Replace the denominator with this value and simplify.

### Example Question #7 : How To Divide Variables

Simplify:

Explanation:

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

We can write:

and

Replace the fraction with these values and simplify.

### Example Question #1 : How To Divide Variables

Which of the following numbers is divisible by 7?

Explanation:

The number 756 can be segmented into 700 and 56. Given that 700 is divisble by 7 (700 divided by 7 is 100) and that 56 is divisible by 7 (56 divided by 7 is 8), 756, as the aggregate of 700 and 56, is also divisble by 7.

### Example Question #2 : How To Divide Variables

What is the equivalent of this expression?

The square root of 64 divided by the square of 2.

Explanation:

The mathematical translation of the square root of 64 divided by the square of 2 is:

### Example Question #3 : How To Divide Variables

Which of the following is divisible by 3?