GRE Math : Decimals with Fractions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1011 : Gre Quantitative Reasoning

Choose the answer below which best expresses the following fraction as a decimal (round to the nearest hundredth, if necessary):

Possible Answers:

Correct answer:

Explanation:

To convert, first divide the numerator (twelve), by the denomenator (eleven), and you will yield:

 repeating.  

Then, you may round to the nearest hundredth, which gives you 

Since the value in the thousandths place is less than four this means the the value in the hundredths place will remain the same.

Example Question #1 : Decimals

Possible Answers:

0.07

0.04

0.01

0.05

0.10

Correct answer:

0.07

Explanation:

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.

Example Question #11 : Decimals With Fractions

Simplify.

Possible Answers:

Correct answer:

Explanation:

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:

.

Example Question #21 : Fractions

Simplify.

Possible Answers:

Correct answer:

Explanation:

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 .

Example Question #22 : Fractions

Simplify.

Possible Answers:

Correct answer:

Explanation:

Since there are four decimal places, we shift the decimal point in the numerator four places to the right.

For the denominator, since there is no decimal point, we just add four more zeroes.

Then reduce by dividing top and bottom by .

Example Question #11 : Decimals With Fractions

What is  of ?

Possible Answers:

Correct answer:

Explanation:

We need to convert the sentence into a math expression. Anytime there is "of" means we need to multiply. Let's first convert the decimal to a fraction. We need to move the decimal point two places to the right.

Since  is the same as  we can add two more zeroes to the denominator.

 

We can reduce the  to a  and the  to a .

Then reduce the  to  and the  to .

.

Then dividing  into  and we get 

Example Question #433 : Arithmetic

 of  is . What is ?

Possible Answers:

Correct answer:

Explanation:

We need to convert this sentence into a math expression. Anytime there is "of" in a sentence it means we need to multiply. Let's convert  into a decimal which is .

Thus our mathematical expression becomes:

.

 Divide both sides by .

 

Move decimal point two places to the right. The numerator will become . Then simplify by dividing top and bottom by .

 

Example Question #11 : Decimals With Fractions

Solve for .

Possible Answers:

Correct answer:

Explanation:

Let's convert the decimal into a fraction.

 

If we multiply everything by , we should have an easier quadratic.

 

Remember, we need to find two terms that are factors of the c term that add up to the b term. 

 This is the only value.

Example Question #12 : Decimals With Fractions

Evaluate.

Possible Answers:

Correct answer:

Explanation:

Let's actually simplify the top of the fraction.  divides into .

We should have: 

.

Then move the decimal two spots to the right and add two zeroes to the denominator.

 

Let's actually multiply top and bottom by  to get:  .

Now we want to eliminate those zeroes. By dividing, the decimal point in the numerator moves to the left three places to get an answer of  or .

Example Question #27 : Fractions

Evaluate and express in a fraction.

Possible Answers:

Correct answer:

Explanation:

Since each decimal has two digits, we can convert easily to integers.

 

Then multiply top and bottom by  to get: 

 is reduced to  and  is reduced to  

Then  and  can be divided by  to get  and  respectively.

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