Percentage - SAT Math

Card 0 of 1440

Question

The population of Town A is 12,979 people in 1995. The population, when measured again in 2005, is 22,752. What was the change in population to the nearest whole percentage point?

Answer

Since we are looking for the change, we must take the

(Ending Point – Starting Point)/Starting Point * 100%

(22752 – 12979)/12979 * 100%

9773/12979 * 100%

0.753 * 100%

75%

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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

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

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

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:

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

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

The pie chart illustrates how Carla allocates her money each week.

If she spends \$200 on groceries each week, how much does she spend on rent?

Answer

1. 20% of Carla's whole budget is equal to \$200. With this information, one can find Carla's weekly budget.

Set up the equation: 0.2b = 200 (b = budget).

b = 200/0.2 = 1000 = Carla's weekly budget

2. To find the amount Carla spends for rent, one needs to find what 35% of \$1000 is.

0.35 x 1000 = 350

3. Because Carla spends 35% of her total budget on rent, she spends \$350 on rent.

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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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