### All SSAT Middle Level Math Resources

## Example Questions

### Example Question #1 : Numbers And Operations

Which ratio is equivalent to ?

**Possible Answers:**

**Correct answer:**

A ratio can be rewritten as a quotient; do this, and simplify it.

Rewrite as

or

### Example Question #1 : How To Find A Ratio

A soccer team played 20 games, winning 5 of them. The ratio of wins to losses is

**Possible Answers:**

**Correct answer:**

The ratio of wins to losses requires knowing the number of wins and losses. The question says that there are 5 wins. That means there must have been

losses.

The ratio of wins to losses is thus 5 to 15 or 1 to 3.

### Example Question #3 : Numbers And Operations

Rewrite this ratio in the simplest form:

**Possible Answers:**

**Correct answer:**

Rewrite in fraction form for the sake of simplicity, then divide each number by :

The ratio, in simplest form, is

### Example Question #2 : Ratio And Proportion

Rewrite this ratio in the simplest form:

**Possible Answers:**

**Correct answer:**

A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:

Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:

The ratio simplifies to

### Example Question #2 : How To Find A Ratio

Rewrite this ratio in the simplest form:

**Possible Answers:**

**Correct answer:**

A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:

Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:

The ratio simplifies to

### Example Question #6 : Numbers And Operations

Rewrite this ratio in the simplest form:

**Possible Answers:**

**Correct answer:**

Rewrite in fraction form for the sake of simplicity, then divide each number by :

In simplest form, the ratio is

### Example Question #7 : Numbers And Operations

Note: Figure NOT drawn to scale.

Refer to the above diagram. If one side of the smaller square is three-fifths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?

**Possible Answers:**

**Correct answer:**

Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 5; if this is the case, the smaller square has sidelength 3. The areas of the large and small squares are, respectively, and .

The white region is the small square and has area 9. The grey region is the small square cut out of the large square and has area . Therefore, the ratio of the area of the gray region to that of the white region is 16 to 9.

### Example Question #8 : How To Find A Ratio

Note: Figure NOT drawn to scale.

Refer to the above diagram. If one side of the smaller square is three-fourths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?

**Possible Answers:**

**Correct answer:**

Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength ; if this is the case, the smaller square has sidelength . The areas of the large and small squares are, respectively, and .

The white region is the small square and has area . The grey region is the small square cut out of the large square and has area . Therefore, the ratio of the area of the gray region to that of the white region is to .

### Example Question #9 : How To Find A Ratio

Express the following ratio in simplest form:

**Possible Answers:**

**Correct answer:**

Rewrite this in fraction form for the sake of simplicity, and divide both numbers by :

The ratio, simplified, is .

### Example Question #8 : Numbers And Operations

Express this ratio in simplest form:

**Possible Answers:**

**Correct answer:**

A ratio of fractions can best be solved by dividing the first number by the second. Rewrite the mixed fraction as an improper fraction, rewrite the problem as a multiplication by taking the reciprocal of the second fraction, and corss-cancel:

The ratio, simplified, is .

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