How to find a ratio - SSAT Middle Level Quantitative

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Question

A 16-ounce bottle of Charlie's Fizzy Fizz Root Beer costs 89 cents. Give the price per ounce to the nearest tenth of a cent.

Answer

Divide 89 by 16:

$89 \div 16 = 5.5625 \approx 5.6$

The soda costs about 5.6 cents per ounce.

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Question

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:6\rightarrow \frac{3}{6}$

Reduce.

$\frac{3}{6}=\frac{1}{2}$

We know that candidate B received votes. Write a new ratio.

$A:320\rightarrow\frac{A}{255}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{255}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{255}{2}$

Solve.

$A=127\tfrac{1}{2}$

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Question

At a car production company, manufacturers place tires and transmission on every car in the production line. A manager orders tires, how many transmissions should he order?

Answer

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$4\ \text{tires}:1\ \text{transmission}$

We can use this ratio to make a table.

According to the table, the manager should order $6\ \text{transmissions}$ .

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Question

If candidate A receives vote for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every vote cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:5\rightarrow \frac{1}{5}$

We know that candidate B received votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{5}=\frac{A}{320}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{5A}{5}=\frac{320}{5}$

Solve.

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Question

If candidate A receives vote for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every vote cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:2\rightarrow \frac{1}{2}$

We know that candidate B received votes. Write a new ratio.

$A:300\rightarrow\frac{A}{300}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{300}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{300}{2}$

Solve.

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Question

Candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got vote. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$7:1\rightarrow \frac{7}{1}$

We know that candidate B received votes. Write a new ratio.

$A:134\rightarrow\frac{A}{134}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{7}{1}=\frac{A}{134}$

Cross multiply and solve for .

Simplify and solve.

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Question

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

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.

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Question

Which ratio is equivalent to $10 \frac{1}{2} : 1 \frac{1}{2}$ ?

Answer

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

$10 \frac{1}{2} : 1 \frac{1}{2}$

Rewrite as

$10 \frac{1}{2} \div 1 \frac{1}{2} = \frac{21}{2} \div \frac{3}{2} = \frac{21}{2} \cdot \frac{2}{3} = \frac{7}{1} \cdot \frac{1}{1} = \frac{7}{1}$

or

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Question

Rewrite this ratio in the simplest form:

Answer

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

$\frac{72}{42}= \frac{72\div 6}{42\div 6}= \frac{12}{7}$

In simplest form, the ratio is

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Question

Rewrite this ratio in the simplest form:

Answer

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

$\frac{90}{63} = \frac{90\div 9}{63\div 9} = \frac{10}{7}$

The ratio, in simplest form, is

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Question

Rewrite this ratio in the simplest form:

$\frac{4}{5} : \frac{3}{10}$

Answer

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

$\frac{\frac{4}{5}}{\frac{3}{10}} = \frac{4}{5} \div \frac{3}{10}$

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

$\frac{4}{5} \div \frac{3}{10} = \frac{4}{5} \times \frac{10}{3} = \frac{4}{1} \times \frac{2}{3} =\frac{8}{3}$

The ratio simplifies to

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Question

There are 50 orange cats and 20 black cats. What is the ratio of black to orange cats?

Answer

The number of black cats goes before the colon since this question is asking for the ratio of black to orange cats.

Therefore, there are $20:50=\textsl{ black}: \textsl{ orange cats}$ .

This can be simplified if you divide both numbers by 10. This gives a ratio of .

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Question

Rewrite this ratio in the simplest form:

$\frac{2}{3}: \frac{5}{12}$

Answer

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

$\frac{\frac{2}{3}}{\frac{5}{12}} = \frac{2}{3} \div \frac{5}{12}$

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

$\frac{2}{3} \div \frac{5}{12} = \frac{2}{3} \times \frac{12}{5} = \frac{2}{1} \times \frac{4}{5} =\frac{8}{5}$

The ratio simplifies to

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Question

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?

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, $5^{2} = 25$ and $3^{2} = 9$ .

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.

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Question

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?

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, $4^{2} = 16$ and $3^{2} = 9$ .

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 .

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Question

In Mrs. Jones' class, the ratio of boys to girls is 3:2. If there are 8 girls in the class, how many total students are in the class?

Answer

Using the ratio, we find that there are 12 boys in the class $\frac{3}{2}=\frac{12}{8}$ .

Summing 12 and 8 gives the total number of 20 students.

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Question

Express the following ratio in simplest form:

Answer

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

$\frac{150}{60}=\frac{150\div 30}{60\div 30} = \frac{5}{2}$

The ratio, simplified, is .

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Question

Express this ratio in simplest form: $6 \frac{2}{5} : \frac{4}{5}$

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:

$6 \frac{2}{5} \div \frac{4}{5} = \frac{32}{5} \div \frac{4}{5} = \frac{32}{5} \cdot \frac{5} {4} =\frac{8}{1} \cdot \frac{1} {1} =\frac{8}{1}$

The ratio, simplified, is .

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Question

Express this ratio in simplest form:

Answer

A ratio involving decimals can be simplified as follows:

First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:

$1.6 : 0.25 \Rightarrow 160 : 25$ (Note the addition of a zero at the end of the first number.)

Now, rewrite as a fraction and divide both numbers by :

$\frac{160}{25} = \frac{160 \div 5}{25 \div 5} = \frac{32}{5}$

The ratio, simplified, is .

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Question

Write as a unit rate: revolutions in minutes

Answer

Divide the number of revolutions by the number of minutes to get revolutions per minute:

$330\div 15 = 22$ ,

making revolutions per minute the correct choice.

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