### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : Compound Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

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 .

The answer then should be .

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

Convert into a fraction.

**Possible Answers:**

**Correct answer:**

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 #1 : Compound Fractions

Convert to an improper fraction.

**Possible Answers:**

**Correct answer:**

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 #1 : Compound Fractions

Simplify.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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

Solve and simplify.

**Possible Answers:**

**Correct answer:**

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.

.

Then add it all up to get the final answer.

### Example Question #1 : Compound Fractions

Simplify.

**Possible Answers:**

**Correct answer:**

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.

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