# SSAT Upper Level Math : Rational Numbers

## Example Questions

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

Simplify.

Explanation:

Don't try to find the least common denominator as it will take a lot of time and a definite mistake in arithmetic. Instead try to see if these quadratics can simplify.

Upon inspection, we get

.

Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b.

With the cancellations, we should get

.

The common denominator will be

Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. The left fraction numerator is multiplied by  and the right fraction numerator is multiplied by .

Overall, the new fraction should read

.

After simplification, answer should be .

### Example Question #2 : How To Add Complex Fractions

Simplify.

None of the above are correct.

Explanation:

Try to simplify the fraction rather than finding the least common denominator. By breaking the quadratic equation into its factors, it becomes:

.

Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b. Also, if the values of a, b, and c in the quadratic equation can be reduced, then factor out that divisor to make the quadratic easier to factor.

Upon cancelling, we should get

.

The common denominator is  or  or Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. Then multiply the numerator of left fraction by  and the numerator of right fraction by  and the new fraction should look like,

.

Upon distributing the four and simplifying the fraction, answer is shown.

### Example Question #1201 : Ssat Upper Level Quantitative (Math)

Simplify.

Explanation:

Least common denominator is . Just multiply the left fraction numerator by  and solve.

### Example Question #1202 : Ssat Upper Level Quantitative (Math)

Simplify.

Explanation:

Try to simplify the fractions rather than trying to find the least common denominator. It should look like this:

.

Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b. The  may not be easy to factor but when put into the quadratic formula

, we get roots of  and . Then set equations equal to  so that when solving for , the answer is the root.

Now after cancellations, we get .

The common denominator is  or  or .

Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. For the left fraction numerator you multiply by what it's lacking and same with the right fraction numerator.

The overall fraction should look like

Once simplified, the answer will be shown.

### Example Question #1203 : Ssat Upper Level Quantitative (Math)

Explanation:

Rewrite the fractions using a division sign.

To change the division sign to a multiplication sign, take the reciprocal of the second terms.

Simplify.

Find the LCD, and rewrite the fractions to add the numerators.

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

Simplify:

Explanation:

Add the fractions in the numerator, then divide the sum by the denominator:

### Example Question #2 : How To Find A Complex Fraction

Simplify:

Explanation:

Simplify the sum in the numerator, then divide by the denominator:

### Example Question #3 : How To Find A Complex Fraction

Simplify:

Explanation:

Rewrite this as a division problem, then solve:

### Example Question #4 : How To Find A Complex Fraction

Simplify:

Explanation:

Rewrite this as a division problem, then solve:

Simplify: