# ISEE Middle Level Quantitative : How to divide variables

## Example Questions

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

What is the value of ?

Explanation:

(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)

Therefore, 90 is the correct answer.

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

What is the value of ?

Explanation:

(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)

Therefore, 30 is the correct answer.

### Example Question #23 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Simplify:

Explanation:

Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

### Example Question #22 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Simplify:

Explanation:

Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

### Example Question #23 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Simplify:

Explanation:

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:

Now, since all of the variables are positive powers, this is easy. Normally, you would begin by reducing the numeric coefficient. This is not necessary since there is only a 5 in the numerator. Therefore, combine the like variables first:

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

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

Simplify:

Explanation:

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction.  When you do this, you make the exponent's sign positive:

Next, go ahead and reduce the numeric coefficient:

Then, combine the like variables first:

Finally, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

### Example Question #23 : Variables

Solve for :

Explanation:

To start, notice that the left side of the equation has a common factor of . You can factor this out:

becomes

Next, you can divide both sides by  since you know that it does not equal :

Simplifying the right side, you get:

Finally, subtract  from both sides:

### Example Question #23 : Algebraic Concepts

Solve for :

Explanation:

To start, notice that the left side of the equation has common factors of  and . You can factor these out:

becomes...

Next, you can divide both sides by  since you know that it does not equal :

Simplify the right side by canceling the  and reducing the :

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

is the multiplicative inverse of . Which is the greater quantity?

(a)

(b)

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity