# SSAT Middle Level Math : How to find a ratio

## Example Questions

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

Which ratio is equivalent to  ?

Explanation:

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

Rewrite as

or

### Example Question #1 : Numbers And Operations

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

Explanation:

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 #1 : Numbers And Operations

Rewrite this ratio in the simplest form:

Explanation:

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

The ratio, in simplest form, is

### Example Question #1 : Numbers And Operations

Rewrite this ratio in the simplest form:

Explanation:

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 #1 : Numbers And Operations

Rewrite this ratio in the simplest form:

Explanation:

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 #1 : Numbers And Operations

Rewrite this ratio in the simplest form:

Explanation:

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

In simplest form, the ratio is

### Example Question #1 : 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-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?

Explanation:

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 #1 : 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?

Explanation:

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 #1 : How To Find A Ratio

Express the following ratio in simplest form:

Explanation:

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

The ratio, simplified, is .

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

Express this ratio in simplest form:

Explanation:

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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