# ISEE Middle Level Quantitative : How to subtract variables

## Example Questions

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

What is the value of ?

Explanation:

To solve for , the fractions should first be converted to ones that share a common denominator. Given that , the common denominator is 12.

Thus,  can be converted to . This gives us:

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

Simplify:

Explanation:

It is easiest to begin by moving like terms together. Hence:

becomes

(Notice that  is its own term.)

Now, consider the coefficients for each term.

For , you have

For , you have

Hence, the expression simplifies to:

This can be moved around to get the correct answer (which means the same thing):

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

Simplify:

Explanation:

Begin by distributing the two groups. Notice that you must distribute the subtraction through the groups:

becomes

Next, you should move like terms next to each other:

(Notice that  is its own term.)

Now, combine terms.

For , you get

For , you get

Therefore, the final form of the expression is:

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

Solve for :

Explanation:

Begin by distributing. Thus,

becomes

(Don't forget that you have to distribute your subtraction for the second group.)

Combine like terms on the right side of the equation:

Next, move the  values to the left side of the equation and all of the other values to the right side:

Combine like terms on the left:

Finally, divide everything by :

This comes out to be:

or

### Example Question #5 : How To Subtract Variables

Simplify:

Explanation:

Begin by distributing the multiplied groups:

Next, move all similar factors together:

Now, combine each set of similar factors:

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

Simplify:

Explanation:

This problem is not too difficult. Begin by moving all common terms next to each other:

Next, simplify each group of terms that has the same set of variables:

And do not forget that you are left with  as well!

Now, combine all of these:

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

Simplify:

Explanation:

Begin by moving common factors next to each other. Thus,

becomes

Now, combine each set:

Remember, there still is  also.

Therefore, the simplified form of the expression is:

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

Which is the greater quantity?

(a)

(b) 9

(a) and (b) are equal

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

(b) is the greater quantity

(a) is the greater quantity

(b) is the greater quantity

Explanation:

also, since , it follows that

, and by the inequality properties,

making 9 the greater quantity.