# SSAT Upper Level Math : Rational Numbers

## Example Questions

### Example Question #81 : Rational Numbers

Simplify:

The correct answer is not given among the other responses.

The correct answer is not given among the other responses.

Explanation:

This is not among the given responses.

Simplify:

Explanation:

### Example Question #1 : How To Find A Complex Fraction

Simplify, writing as a proper fraction.

Explanation:

Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

### Example Question #32 : Complex Fractions

Simplify.

Explanation:

Find the least common denominator which is .

Just multiply the right fraction top and bottom by

Finally, subtract.

.

### Example Question #33 : Complex Fractions

Simplify.

Explanation:

Lets try to factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

Next cancel out the like terms.

Now combine the numerator. Remember to distribute the negative sign.

.

### Example Question #143 : Number Concepts And Operations

Simplify.

Explanation:

Turn the  into a fraction that has a common denominator with the other fraction. To do this multiply .

This results in the following expression:

With the same denominator, just subtract and remember to distribute the negative sign.

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### Example Question #87 : Rational Numbers

Solve and simplify.

Explanation:

Lets try to reduce the fraction. When factoring a difference of squares, the form is . When you foil, the middle terms cancel out.

So when doing that, we have:

.

Cancel out like terms and we get this:

.

Distribute the negative sign and we should get .

### Example Question #88 : Rational Numbers

Solve for .

Explanation:

First find the least common denominator. That will be   .

Multiply top and bottom of the left fraction by  .

Then subtract the numerator and then cross-multiply to get this:

Then combine like terms. To get rid of the square root,

square both sides to get  as the final answer.

### Example Question #1 : How To Subtract Complex Fractions

Solve for .

Both  and .

Both  and .

Explanation:

Find the least common denominator which is . Then multiply the left fraction numerator by  and multiply the right numerator by  inorder for each fraction to share the common denominator.

Distribute and be careful of the negative sign.

Cross-multiply and create the quadratic equation.

Lets factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

If you check these answers back into the question, none of the fractions are undefined so these are the final answers.

### Example Question #90 : Rational Numbers

Solve for .

Explanation:

Find the least common denominator which is . Then multiply the left fraction numerator by  and multiply the right numerator by  in order to make each fraction share the common denominator.

Distribute and be careful of the negative sign.

Simplify the numerator and cross multiply. Because there is an absolute value bar, we need to split this expression into two different equations.

Equation one:

By inspection, these values pass and don't violate the fractions being undefined.

Equation two:

This answer is imaginary and not in the choices leaving  as the answers.