# SSAT Upper Level Math : Rational Numbers

## Example Questions

### Example Question #61 : Rational Numbers

Solve for .

Both  and

Both   and

Both   and

Explanation:

Lets factor as this is an easier approach especially with the absolute value present. Remember, we need to find two terms that are factors of the c term that add up to the b term. We get:

The  cancels and now with the absolute vaue present, we need to split into two different equations. Remember, absolute value means there is a positive value and a negative value. So for the first equation:

Now the second equation:

Double check that these answers don't create undefined answers. In this case, it doesn't so  and  are the answers to this question.

### Example Question #61 : Rational Numbers

Multiply:

Explanation:

Multiply the numerator and denominator.

Rewrite the complex fraction using a division sign.

### Example Question #63 : Rational Numbers

Explanation:

First, add the fractions found in the numerator and denominator of the complex fraction. To add two fractions, they need to have a common denominator. You can create a common denominator by multiplying the numerator and denominator of one fraction by  as a fraction made up of the denominator of the other fraction. For example, if you need to create a common denominator for  and , you would multiply  by  and  by . Since this just multiplies each fraction by , it doesn't change the fractions' values, just the way in which they are represented.

Now, divide those two fractions.

### Example Question #64 : Rational Numbers

Solve.

Explanation:

Find the least common denominator between the two fractions. In our case both  and  go into  thus, this is our common denominator.

The top is multiplied by 2x for the left fraction and to get:

.

For the right fraction, the top is multiplied by 7.

To solve we need to add these two fractions together.

.

### Example Question #65 : Rational Numbers

Solve.

Explanation:

By inspection, the denominator of the left fraction is a perfect square . Since the right fraction already has a , just multiply top and bottom by  so the denominators of both fraction are the same.

The top should read  with a bottom of .

After simplification, the answer is revealed.

### Example Question #66 : Rational Numbers

Simplify.

Explanation:

If you can recognize that  is -1 then the answer is quick.

Otherwise just find the least common denominator which is .

The numerator of the new fraction will be . It may be tempting to think  should have been the right answer, however, the question does say simplify and yes this can be simplified. If you factor the  out of the numerator, it's . The bottom does look very similar to the top only the signs are flipped. This means if you factor out a  on the bottom, the quadratic equation should match and cancel out leaving you with the answer of

### Example Question #61 : Rational Numbers

Solve.

Explanation:

First focus on the big fraction specificall,y the numerator. We need to find a common denominator in the numerator in order to add the two fractions and simplify the expression.

The top should have a common denominator of .

Therefore the top should become .

Now lets look at the denominator of the big fraction. We again need to find a common denominator for the two components. In this case it will be .

Therefore the bottom should become .

Since we need to have a single fraction added to a , we need to multiply top and bottom by  so we can add the fractions easier.

So far, the new equation to solve is .

Same thing, find the least common denominator and solve to arrive at the final answer.

### Example Question #68 : Rational Numbers

Solve.

Explanation:

Although intimidating, just focus on the inner fraction and work your way up.

Common denominator is  so that should lead to

.

By multiplying everything by  this should lead to .

Common denominator is now  and this should arrive at,

which is the final answer when everything is simplified.

### Example Question #69 : Rational Numbers

Simplify.

Explanation:

Work on each fraction and start from the bottom and work your way up.

For the left fraction, it should be

since  is the common denominator.

Then multiply by the inverse to get .

For the right, it's the same concept as the final fraction to get is .

Finally find the common denominator of these new complex fractions and solve to get the final answer.

### Example Question #121 : Number Concepts And Operations

Simplify.

Explanation:

By careful inspection, the fractions all reduce to .

All the fractions have values in the numerator and denominator that cancel out.

There are five of these so multiply  by  to get the final answer.