Decimals with Fractions - GRE Quantitative Reasoning
Card 0 of 408
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
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Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the 
can be removed, leaving: 
, which can be reducted to:
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the
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Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
Compare your answer with the correct one above
Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the can be removed, leaving: , which can be reducted to:
To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:
The zero in front of the
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0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
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.
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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Convert 
to a mixed number fraction. Then simplify your answer.
Convert
Both decimals and fractions represent part of a whole. To convert this decimal number to a mixed number fraction, use the following steps:
(because the decimal number has a 
in the ones place value and an 
in the hundredths place value).
Then simplify 
.
Thus, the correct answer is 
Both decimals and fractions represent part of a whole. To convert this decimal number to a mixed number fraction, use the following steps:
(because the decimal number has a
Then simplify
Thus, the correct answer is
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Convert 
to a fraction. Then simplify.
Convert
Both decimals and fractions represent part of a whole. Since this decimal number has a value of 
in the tenths place and a value of 
in the hundredths place, it can be re-written as:
.
Then, simplify the fraction by dividing both the numerator and denominator by a divisor of 
Thus, the solution is:
Both decimals and fractions represent part of a whole. Since this decimal number has a value of
Then, simplify the fraction by dividing both the numerator and denominator by a divisor of
Thus, the solution is:
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Find the fractional equivalent to 
.
Find the fractional equivalent to
This problem requires several conversions. First, convert 
into a mixed number fraction. This means, the new fraction will have a whole number of 
and a fraction that represents 
thousandths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.
Thus, the solution is:
This problem requires several conversions. First, convert
Thus, the solution is:
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Convert 
to an improper fraction.
Convert
This problem requires two conversions. First convert 
to a mixed number fraction. This must equal a whole number of 
and a fraction that represents a value of 
tenths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.
Thus, the solution is:
This problem requires two conversions. First convert
Thus, the solution is:
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Find the fractional equivalent to 
. Then reduce the fraction if possible.
Find the fractional equivalent to
To solve this problem, make a mixed number fraction with a whole number of 
and a fraction that represents 
hundredths. Then simplify the fraction portion of the mixed number by dividing the numerator and denominator by their largest common divisor.
To solve this problem, make a mixed number fraction with a whole number of
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Convert 
to an equivalent decimal number.
Convert
To convert this fraction to a decimal number, divide the numerator by the denominator. Since this fraction has a larger numerator than denominator, the fraction is classified as an improper fraction. This means that the fraction represents a value greater than one whole. Thus, the solution must be greater than one.
Note that 
fits into 
evenly 
times, and has a remainder for of 
To convert this fraction to a decimal number, divide the numerator by the denominator. Since this fraction has a larger numerator than denominator, the fraction is classified as an improper fraction. This means that the fraction represents a value greater than one whole. Thus, the solution must be greater than one.
Note that
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Find the fractional equivalent to 
. Then simplify.
Find the fractional equivalent to
This problem requires you to first convert the decimal number to a mixed number fraction that has a whole number of 
and a fraction that represents 
thousandths. Then reduce the numerator and denominator by common divisors until you can no longer simplify the fraction.
This problem requires you to first convert the decimal number to a mixed number fraction that has a whole number of
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Convert 
to a fraction. Then simplify.
Convert
Both fractions and decimals represent part of a whole. The value of this decimal number reaches the ten-thousandths place value. Thus, the fraction must represent 
ten-thousandths. Then reduce the numerator and denominator by the common divisor of 
.
Both fractions and decimals represent part of a whole. The value of this decimal number reaches the ten-thousandths place value. Thus, the fraction must represent
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Find the decimal equivalent of 
.
Find the decimal equivalent of
Fractions and decimals both represent part of a whole. To solve this problem you may divide 
by 
, or you can reduce the fraction by dividing the numerator and denominator by the common factor of 
This will equal a fraction of 
hundredths, which can be written as the decimal number "zero and 
hundredths."
Note: both 
and 
equal 
Fractions and decimals both represent part of a whole. To solve this problem you may divide
Note: both
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Convert 
to an improper fraction.
Convert
First convert this decimal number to a mixed number fraction, then covert the mixed number to an improper fraction. The mixed number fraction must have a whole number of 
and a fraction that represents 
tenths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.
First convert this decimal number to a mixed number fraction, then covert the mixed number to an improper fraction. The mixed number fraction must have a whole number of
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Find the fractional equivalent for 
.
Find the fractional equivalent for
Decimal numbers and fractions both represent part of a whole. This decimal number has a value of 
in the tenths and thousandths place values. Since the decimal number reaches the thousandths place, the correct answer is 
over 
--which represents 
thousandths.
Decimal numbers and fractions both represent part of a whole. This decimal number has a value of
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Convert the mixed fraction 
to a decimal number.
Convert the mixed fraction
Since the starting number is a mixed number fraction, the decimal number must also have a value in the ones place. Since the denominator in the fraction has a value that is a factor of 
, both the numerator and denominator can be multiplied by a factor of 
to form 
tenths. (Note, the first decimal place value is the tenths place).
Since the starting number is a mixed number fraction, the decimal number must also have a value in the ones place. Since the denominator in the fraction has a value that is a factor of
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A retailer can only order wristbands in bulk cases. Each case has 300 wristbands and costs $1172.
Quantity A: The number of wristbands that can be bought for $10547.
Quantity B: The number of wristbands that can be bought for $10560.
A retailer can only order wristbands in bulk cases. Each case has 300 wristbands and costs $1172.
Quantity A: The number of wristbands that can be bought for $10547.
Quantity B: The number of wristbands that can be bought for $10560.
The key to this problem is to realize that the store cannot buy partial crates of wristbands--it's all or nothing. Calculate how many crates can be bought with each sum of money by dividing the sum by the price of a crate.
Quantity A:
Although oh so close, only eight crates can be bought with this sum of money. Don't round up!
Quantity B:
There's just enough to buy nine crates.
Quantity B is greater.
The key to this problem is to realize that the store cannot buy partial crates of wristbands--it's all or nothing. Calculate how many crates can be bought with each sum of money by dividing the sum by the price of a crate.
Quantity A:
Although oh so close, only eight crates can be bought with this sum of money. Don't round up!
Quantity B:
There's just enough to buy nine crates.
Quantity B is greater.
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Simplify.
Simplify.
Whenever there are decimals in fractions, we remove them by shifting the decimal place over however many it takes to make number an integer.
In this case we have to move the decimal in the numerator to the right one place.
Then, we add just one zero to the denominator.
Final answer becomes:
.
Whenever there are decimals in fractions, we remove them by shifting the decimal place over however many it takes to make number an integer.
In this case we have to move the decimal in the numerator to the right one place.
Then, we add just one zero to the denominator.
Final answer becomes:
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Simplify.
Simplify.
With the numerator having more decimal spots than the denominator, we need to move the decimal point in the numerator two places to the right.
Then in the denominator, we move the decimal point also two to the right. Since there's only one decimal place we just add one more zero.
Then we can reduce by dividing top and bottom by 
.
With the numerator having more decimal spots than the denominator, we need to move the decimal point in the numerator two places to the right.
Then in the denominator, we move the decimal point also two to the right. Since there's only one decimal place we just add one more zero.
Then we can reduce by dividing top and bottom by
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