Fractions and Percentage - SSAT Upper Level Quantitative

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Question

Which of the following operations is equivalent to taking of a number?

Answer

Let's just pick a number at random, for example .

of this number is , which is divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

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Question

Convert into a fraction.

Answer

Put the number over and drop the percent sign. Then, reduce to simplest form.

$14%=\frac{14}{100}=\frac{7}{50}$

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Question

Convert into a fraction.

Answer

Put the number over and drop the percent sign. Then, reduce to simplest form.

$23%=\frac{23}{100}$

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Question

Convert into a fraction.

Answer

Put the number over and drop the percent sign. Then, reduce to simplest form.

$62%=\frac{62}{100}=\frac{31}{50}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$14.5%=\frac{14.5}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{14.5\times10}{100\times10}=\frac{145}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{145}{1000}=\frac{29}{200}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$87.4%=\frac{87.4}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{87.4\times10}{100\times10}=\frac{874}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{874}{1000}=\frac{437}{500}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$25.6%=\frac{25.6}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{25.6\times10}{100\times10}=\frac{256}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{256}{1000}=\frac{32}{125}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$94.6%=\frac{94.6}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{94.6\times10}{100\times10}=\frac{946}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{946}{1000}=\frac{473}{500}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$32.9%=\frac{32.9}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{32.9\times10}{100\times10}=\frac{329}{1000}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$58.4%=\frac{58.4}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{58.4\times10}{100\times10}=\frac{584}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{584}{1000}=\frac{73}{125}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$24.2%=\frac{24.2}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{24.2\times10}{100\times10}=\frac{242}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{242}{1000}=\frac{121}{500}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$65.8%=\frac{65.8}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{65.8\times10}{100\times10}=\frac{658}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{658}{1000}=\frac{329}{500}$

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Question

What is as a fraction?

Answer

Put the number over and drop the percent sign.

$33.6%=\frac{33.6}{100}$

Multiply the numerator and denominator by to get rid of the decimal.

$\frac{33.6\times10}{100\times10}=\frac{336}{1000}$

Finally, reduce the fraction to get it in simplest form.

$\frac{336}{1000}=\frac{42}{125}$

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Question

What percent of 12,000 is 3,300?

Answer

To find out what percent a part is of a whole , evaluate the expression

$\frac{P}{W} \cdot 100 = \frac{3,300}{12,000} \cdot 100 = 27.5$

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Question

Convert into a percent.

Answer

First evaluate .

To convert a decimal to a percentage, multiply by 100 percent.

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Question

Convert into a percent.

Answer

To convert a decimal number into a percent, multiply the decimal number by .

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Question

Which of the following best represents $\frac{1}{6}%$ ?

Answer

The true value of the percentage $\frac{1}{6}%$ can be converted by dividing .

The correct value of $\frac{1}{6}%$ is $\frac{1}{600}$ .

$\frac{1}{600}= 0.001\overline{6}=0.0017$

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Question

Find the sum of $\frac{1}{3}+45%$ . Express the final answer as a fraction.

Answer

Convert the into fraction form by dividing this by .

$\frac{45%}{100%} = \frac{9}{20}$

Add the two fractions.

First find the common denominator by multiplying the current denominators together.

$3\cdot 20=60$

Now convert each fraction into an equivalent fraction with the new, common denominator.

$\frac{1\cdot 20}{3\cdot 20}+\frac{9\cdot 3}{20\cdot 3} =\frac{20}{60}+\frac{27}{60}=\frac{47}{60}$

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Question

What percentage of is ? Round to the nearest hundredth.

Answer

Set up a mathematical equation such that the percentage of the number is divided by 100. Solve for the unknown value.

$\left(\frac{x}{100}\right)(97)=4$

$x=4\left(\frac{100}{97}\right)=\frac{400}{97}= 4.1237$

The correct answer is .

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Question

Each of a set of balls is marked with a letter of the English alphabet. Each vowel is represented by five balls; each consonant, three. What percent of the balls are marked with vowels? (Nearest whole percent)

Note: For purposes of this problem, "Y" is considered a consonant.

Answer

There are five vowels, each represented by five balls; this is a total of

$5 \times 5 = 25$

balls with vowels.

There are twenty-one consonants, each represented by three balls; this is a total of

$21 \times 3 = 63$

balls with consonants.

There are balls total of which 25 out of 88 are marked with vowels. This represents

$\frac{25}{88} \times 100 % \approx 28.4 %$

of the balls, so 28% is the correct choice.

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