### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : Simplifying Fractions

Rewrite the mixed fraction as an improper fraction in lowest terms, and call the product of the numerator and the denominator of the simplified improper fraction. How many digits does have?

**Possible Answers:**

**Correct answer:**

, so simplifies to .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore,

Multiply the numerator and the denominator: ,

a three-digit number.

### Example Question #2 : Simplifying Fractions

Reduce to lowest terms, call the sum of the numerator and the denominator. Which statement is true of ?

**Possible Answers:**

**Correct answer:**

Add the numerator and the denominator:

The correct response is therefore .

### Example Question #3 : Simplifying Fractions

Consider a fraction , where the numerator is unknown. How many of the following values of would yield a fraction *not* in lowest terms?

I)

II)

III)

IV)

**Possible Answers:**

**Correct answer:**

The prime factorization of is , so the fraction is reducible if and only if is a multiple of 5 or 13.

We can immediately tell that 115 is the only multiple of 5, so we test the other numbers to see if there is a multiple of 13. We soon see that

, so 116 and 118 cannot be multples of 13.

115 and 117 are the only values of that yield reducible fractions, so the correct response is two.

### Example Question #4 : Simplifying Fractions

Reduce the fraction to lowest terms, and call the product of the numerator and the denominator of the simplified fraction. Give the value of .

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator:

The product is a three-digit number.

### Example Question #5 : Simplifying Fractions

Put the fraction in the simplest form.

**Possible Answers:**

**Correct answer:**

To put a fraction in simplest form, keep dividing the numerator and denominator by the same number until you cannot go any further.

### Example Question #6 : Simplifying Fractions

Put the fraction in simplest form.

**Possible Answers:**

**Correct answer:**

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

### Example Question #7 : Simplifying Fractions

Put the fraction in simplest form.

**Possible Answers:**

**Correct answer:**

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

### Example Question #8 : Simplifying Fractions

Put the fraction in simplest form.

**Possible Answers:**

**Correct answer:**

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

### Example Question #9 : Simplifying Fractions

Put the fraction in simplest form.

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Simplifying Fractions

Put the fraction in simplest form.

**Possible Answers:**

**Correct answer:**

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