# ISEE Upper Level Math : Operations

## Example Questions

### Example Question #9 : How To Divide Variables

Divide:

The expression cannot be simplified further.

Explanation:

To divide this problem we simplify it first. In this problem we can separate the big fraction into three smaller fractions.

Then from here, we can pull out a  from both the numerator and denominator of each smaller fraction.

Now we cancel terms and get the following result:

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

Simplify:

Explanation:

To simplify this problem we first separate the large fraction into three smaller fractions.

From here we can factor out  from the numerator and denominator of the first two fractions.

The  can be canceled out in the first two fractions. From here we can factor out a  from the numerator and denominator of the third fraction.

Thus becoming:

### Example Question #31 : Variables

Divide:

Explanation:

To divide this problem we start by simplify it. In this problem we can break the large fraction into three smaller fractions.

From here we can factor out a  from the numerator and denominator of each fraction.

Now we can cancel the  terms and are left with the following result:

### Example Question #32 : Variables

Simplify the following expression:

Explanation:

Simplify the following expression:

Let's begin by simplifying the coefficients

Next, complete the question by subtracting the exponents:

### Example Question #33 : Variables

Simplify the following expression:

Explanation:

Simplify the following expression:

Let's begin by simplifying the coefficients:

We have a 49 on top and a 7 on bottom. We can treat this just like a regular fraction:

Next, to deal with our variables, all we need to do is subtract the bottom exponent from the top exponent. If we get a negative number, we just put that number on the bottom.

So our answer will look like this:

Simplify:

Explanation:

### Example Question #31 : Operations

Simplify the expression:

Explanation:

Group and collect like terms:

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

Simplify:

The expression cannnot be simplified further.

Explanation:

Group and collect like terms:

### Example Question #31 : Variables

What is  ?

Insufficient information is given to answer this question.

Explanation:

Simplify: