Fractions - SAT Math

Card 0 of 1832

Question

Car X used 4 gallons of gas in one week, and gets 10 miles to the gallon. If car Y went the same number of miles but only gets 8 miles to the gallon, how much gas did car Y use?

Answer

We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.

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Question

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

Answer

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

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Question

Bob and Sally are doing chores. It takes them 10 hours to do one of their chores. Assuming everyone works at the same rate, how many of their friends would they need to get to help them to do their chores in 2 hours?

Answer

Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.

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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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Question

Convert the following fraction to a percent, rounding to the nearest tenth:

$\frac{12}{18}$

Answer

Reduce the fraction.

$\frac{12}{18} = \frac{6\times 2}{6\times 3}= \frac{2}{3}$

Set up the proportion such that some number is over 100.

$\frac{2}{3}=\frac{x}{100}$

Solve for , which is the percent.

$x=\frac{200}{3}= 66.7%$

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Question

What is the closest percent equal to the fraction $\frac{5}{12}$ ?

Answer

The percent is a number over 100. Set up the proportion to find the unknown value.

$\frac{5}{12}=\frac{x}{100}$

$x=\frac{500}{12}=41.67%$

The closest answer is .

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Question

Express $\frac{3}{15}$ as a percent.

Answer

To turn this fraction into a percent, let's write it as a decimal first.

$\frac{3}{15} = 0.20$

Now, let's set up a proportion to make this a percent.

$\frac{0.2}{1} = \frac{x}{100}$

Therefore, our answer is .

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Question

0.3 < 1/3

4 > √17

1/2 < 1/8

–|–6| = 6

Which of the above statements is true?

Answer

The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.

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Question

Which of the following numbers is between 1/5 and 1/6?

Answer

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

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Question

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

Answer

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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Question

$\frac{1}{10}\times \frac{3}{5}\div \frac{6}{7}= {?}}$

Answer

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Question

How much less is $\frac{1}{16}$ than ?

Answer

$\frac{1}{16}=.0625$

$.0665-.0625=.004=\frac{4}{1000}=\frac{1}{250}$

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Question

Approximate the fraction to decimal and round to three decimal places: $\frac{2}{7}$

Answer

In order to estimate this fraction, set up a proportion equal to where the denominator is something of 100 parts.

$\frac{2}{7} = \frac{x}{100}$

Cross multiply.

$2 \cdot 100 = 7x$

Divide seven on both sides.

$x = \frac{200}{7 }= 28.571$

Rewrite the proportion.

$\frac{2}{7} = \frac{28.571}{100}$

To find the decimal, simply move the decimal place of the numerator back two spaces, and the denominator two spaces back as well.

$\frac{28.571}{100} = \frac{0.28571}{1} =0.286$

The answer is:

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Question

Find the decimal equivalent to the following fraction:

$\frac{5}{7}$

Answer

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is within the division symbol.

$7)\overline{5.0}$

From here, because the inside value is less than the outside value make sure to add a decimal and a zero.

$7)\overline{5.0}$

Now, evaluate how many times 7 goes into 50. Since seven times seven is 49 and that is the closest values to 50 without going over, that is the first value in the decimal. From here subtract 49 from 50.

$7)\overline{5.0}$

$\underline{-4.9}$

Now, evaluate how many times 7 goes into 10. In this case it is only once. Multiply one by seven and subtract this product from 10.

$7)\overline{5.00}$

$\underline{-4.9}$

$\underline{-0.07}$

Now, evaluate how many times seven goes into 30. Since seven times four is 28, this is the closest value to 30 without exceeding it and thus is the value we choose.

$7)\overline{5.000}$

$\underline{-4.9}$

$\underline{-0.07}$

$\underline{-0.028}$

Since all the answer choices stop at three digits we are done.

Therefore the answer is,

$\frac{5}{7}=5\div7=0.7143=0.714$

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Question

A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L

Answer

1 gallon = 3.785L = 3785mL, half of the tank = 2503785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr60min=1440min, the number of days =94625min/(1440min/day)=6.5 days

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Question

Find the decimal equivalent of the fraction:

$\frac{15}{16}$

Answer

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is in the division symbol.

$16)\overline{15.0}$

From here, we need to add a decimal point and zero because the inside value is less than the outside value.

$16)\overline{15.0}$

Now, evaluate how many times 16 goes into 150. Since 16 times 9 is 144 and that is the closest value to 150 without going over, that is the first value in the decimal. From here subtract 144 from 150.

$16)\overline{15.0}$

$\underline{-14.4}$

Now, evaluate how many times 16 goes into 60. Since 3 times 16 is 48, subtract that number from 60.

$16)\overline{15.00}$

$\underline{-14.4}$

$\underline{-0.48}$

Now, evaluate how many times 16 goes into 120. Since 16 times 7 is is 112, this is the closest value to 120 without exceeding it which means it the value we need to choose.

$7)\overline{5.000}$

$\underline{-14.4}$

$\underline{-0.48}$

$\underline{-0.112}$

Since all the answer choices stop at three digits we are done.

Therefore the answer is,

$\frac{15}{16}=15\div16=0.9375=0.938$

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Question

Find the decimal equivalent of the fraction:

$\frac{1}{8}$

Answer

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is in the division symbol.

$8)\overline{1.0}$

From here, we need to add a decimal point and zero because the inside value is less than the outside value.

$8)\overline{1.0}$

Now, evaluate how many times 8 goes into 10. In this case, it is only once, so multiply 1 by 8 to get 8. From here subtract 8 from 10.

$8)\overline{1.0}$

$\underline{-0.8}$

Now, evaluate how many times 8 goes into 20. Since 2 times 8 is 16, subtract that number from 20.

$8)\overline{1.00}$

$\underline{-0.8}$

$\underline{-0.16}$

Now, evaluate how many times 8 goes into 40. Since 8 times 5 is is 40, this is the value we need to choose.

$8)\overline{1.000}$

$\underline{-0.8}$

$\underline{-0.16}$

$\underline{-0.040}$

Since our final answer after subtracting is zero, we are done.

Therefore the answer is,

$\frac{1}{8}=1\div8=0.1250=0.125$

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Question

Find the decimal equivalent of the fraction:

$\frac{12}{23}$

Answer

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is in the division symbol.

$23)\overline{12.0}$

From here, we need to add a decimal point and zero because the inside value is less than the outside value.

$23)\overline{12.0}$

Now, evaluate how many times 23 goes into 120. In this case, since 5 times 23 is 115, this is largest number possible without exceeding 120. From here subtract 115 from 120.

$23)\overline{12.0}$

$\underline{-11.5}$

Now, evaluate how many times 23 goes into 50. Since 2 times 23 is 46, subtract that number from 50.

$23)\overline{12.00}$

$\underline{-11.5}$

$\underline{-0.46}$

Now, evaluate how many times 23 goes into 40, which in this case is only once. So multiply 1 times 23 to get 23, then subtract it from 40.

$23)\overline{12.000}$

$\underline{-11.5}$

$\underline{-0.46}$

$\underline{-0.023}$

Since our answer choices only go to three decimal places, we are done.

Therefore the answer is,

$\frac{12}{23}=12\div23=0.521$

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