Fractions and Percentage - SAT Math

Card 0 of 20

Question

When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?

Answer

The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.

If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.

Now, we set these two expressions equal to one another.

(9/10)y = (3/20)x

Multiply both sides by 20 to eliminate fractions.

18_y_ = 3_x_

The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.

18_y_ = 3_x_

Divide both sides by 3.

6_y_ = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

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Question

Write 7.5% as a fraction.

Answer

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

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Question

Write as a fraction: 22%

Answer

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

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Question

25% of 64 is equal to 5% of what number?

Answer

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$65%\rightarrow \frac{65}{100}$

From here, simplify the fraction as necessary:

$\frac{65}{100}\div \frac{5}{5}=\frac{13}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$22%\rightarrow \frac{22}{100}$

From here, simplify the fraction as necessary:

$\frac{22}{100}\div \frac{2}{2}=\frac{11}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$46%\rightarrow \frac{46}{100}$

From here, simplify the fraction as necessary:

$\frac{46}{100}\div \frac{2}{2}=\frac{23}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$55%\rightarrow \frac{55}{100}$

From here, simplify the fraction as necessary:

$\frac{55}{100}\div \frac{5}{5}=\frac{11}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$72%\rightarrow \frac{72}{100}$

From here, simplify the fraction as necessary:

$\frac{72}{100}\div \frac{2}{2}=\frac{36}{50}\div \frac{2}{2}=\frac{18}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$88%\rightarrow \frac{88}{100}$

From here, simplify the fraction as necessary:

$\frac{88}{100}\div \frac{4}{4}=\frac{22}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$44%\rightarrow \frac{44}{100}$

From here, simplify the fraction as necessary:

$\frac{44}{100}\div \frac{4}{4}=\frac{11}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$15%\rightarrow \frac{15}{100}$

From here, simplify the fraction as necessary:

$\frac{15}{100}\div \frac{5}{5}=\frac{3}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$2%\rightarrow \frac{2}{100}$

From here, simplify the fraction as necessary:

$\frac{2}{100}\div \frac{2}{2}=\frac{1}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$28%\rightarrow \frac{28}{100}$

From here, simplify the fraction as necessary:

$\frac{28}{100}\div \frac{4}{4}=\frac{7}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$92%\rightarrow \frac{92}{100}$

From here, simplify the fraction as necessary:

$\frac{92}{100}\div \frac{2}{2}=\frac{46}{50}\div \frac{2}{2}=\frac{23}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$36%\rightarrow \frac{36}{100}$

From here, simplify the fraction as necessary:

$\frac{36}{100}\div \frac{4}{4}=\frac{9}{25}$

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Question

What is the fractional equivalent to 30% of a given a is 12.

Answer

First write the question out in equation form.

$30% \times a$

Since the question states that

the equation becomes,

$30%\times 12$ .

From here, convert 30% into a fraction.

$30%\Rightarrow\frac{30}{100}=\frac{3}{10}$

Substituting the fraction in for the percentage the equation becomes,

$\frac{3}{10}\times 12$

$\frac{3\times12}{10}=\frac{36}{10}=\frac{18}{5}$

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Question

Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?

Answer

The first hen lays 8 brown eggs: 2/5 * 20 = 8

The second lays 5 brown eggs: 1/4 * 20 = 5

The third lays 6 brown eggs: 3/10 * 20 = 6

Add up the brown eggs and divide by 60, the total number of eggs:

19/60 = 0.31666667 = 31.67%, or 32%.

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Question

What is $\frac{7}{5}$ as a percentage?

Answer

Convert the improper fraction $\frac{7}{5}$ to the mixed numeral $1\frac{2}{5}$ or as the decimal . as a percentage is

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Question

A family with 6 children, aged 4, 4, 5, 7, 12, and 13 are moving to a new home. They all want the same bedroom, so the parents have a lottery. Each child places their name in once for every year of age (the four year olds each put their name in 4 times, the seven year old puts his name in 7 times, etc.) What is the probability of the chosen child being 4 years old?

Answer

First, we will determine the total number of ballots:

$4+4+5+7+12+13=45\hspace{1 mm}ballots$

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

$\frac{4+4}{45}=\frac{8}{45}=0.1\overline{7}=17.\overline{7}%$

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