SSAT Middle Level Math : How to find a ratio

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

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Example Question #1 : How To Find A Ratio

Which ratio is equivalent to  ?

Possible Answers:

Correct answer:

Explanation:

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

Rewrite as

 

or 

Example Question #2 : 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:

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 #3 : How To Find A Ratio

Rewrite this ratio in the simplest form: 

Possible Answers:

Correct answer:

Explanation:

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

The ratio, in simplest form, is 

Example Question #4 : How To Find A Ratio

Rewrite this ratio in the simplest form:

Possible Answers:

Correct answer:

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 #5 : How To Find A Ratio

Rewrite this ratio in the simplest form:

Possible Answers:

Correct answer:

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 #6 : How To Find A Ratio

Rewrite this ratio in the simplest form: 

Possible Answers:

Correct answer:

Explanation:

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

In simplest form, the ratio is 

 

Example Question #7 : How To Find A Ratio

Squares

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:

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 #8 : How To Find A Ratio

Squares

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:

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 #9 : How To Find A Ratio

Express the following ratio in simplest form: 

Possible Answers:

Correct answer:

Explanation:

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

The ratio, simplified, is .

Example Question #10 : How To Find A Ratio

Express this ratio in simplest form: 

Possible Answers:

Correct answer:

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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