# SSAT Upper Level Math : How to find a solution to a compound fraction

## Example Questions

### Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

Explanation:

Simplify into a complex fraction for the numerator and denominator.

For the numerator, we need to multiply  then the top should read .

For the bottom, we need to multiply  in order to add the components. Thus the bottom should read .

Dividing fractions is the same as multiplying the numerator by the reciprocal of the denominator.

Therefore, multiply top and bottom by  and then you should see that if you factor a  on the bottom, the  cancels along with the .

### Example Question #2 : How To Find A Solution To A Compound Fraction

Convert  into a fraction.

Explanation:

The whole number  is multipled by the denominator . Then we add the numerator . This value is divided by the denominator. Final answer is .

### Example Question #3 : How To Find A Solution To A Compound Fraction

Convert  to an improper fraction.

Explanation:

To convert into an improper fraction, take the whole number  and multiply that with the denominator .

Then, we add that to the numerator which is .

Then we take that sum and put it over th denominator  which gives us an answer of:

### Example Question #4 : How To Find A Solution To A Compound Fraction

Simplify.

Explanation:

Lets focus on the left fraction. Lets try to have three fractions multipled altogether. To acheive this, we can multiply the numerator of the left fraction with the reciprocal of the denominator.

Thus, mutliple the numerator and denominator by .

Now we have . We can simplify this by crossing out the  to a  and the  to a .

Then, cross out the  into a  and the  into a . It should look like this:

.

Multiply it out and you will get the answer.

### Example Question #5 : How To Find A Solution To A Compound Fraction

Solve and simplify.

Explanation:

Convert both numerator and denominators into fractions. Convert the integers first to fractions.

Now that our numerator and denominator have a common denominator between their fractions we can subtract them.

Then multiply top and bottom by  as that is the reciprocal of the denominator and when dividing fractions, it is the same as multiplying the numerator by the reciprocal of the denominator.

Then reduce by crossing out the  into a  and the  into a .

Then multiply to get the answer.

### Example Question #6 : How To Find A Solution To A Compound Fraction

Solve and simplify.

Explanation:

Remember PEMDAS, the order of operations for dealing with expressions which is the acronym that stands for (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Multiplication has priority over addition. Looking at the fractions that are multiplied together we can see the  is reduced to  and the  into a .

The new fraction becomes:

Then find least common denominator. In our case it will be 70.

.

### Example Question #7 : How To Find A Solution To A Compound Fraction

Simplify.

Explanation:

Remember PEMDAS. Take care of the parentheses first and find least common denominator of the fractions. Next distribute, then add and finally, subtract.

Working with the parentheses we get:

Reduce the  to  and the  to . Then reduce  to  and  to .

Multiply first then subtract.

If I divide the left fraction by , I should be able to match the denominator of the right fraction and also I can subtract easily.