Fractions - GRE Quantitative Reasoning

Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.

Quantity A: .1 * 45 = $4.50

Quantity B: .45 * 10 = $4.50

Therefore the two quantities are equal. This is always true: a% of $b = b% of $a.

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 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:

First, consider each quantity separately.

Quantity A

These two fractions do not have a common factor. Their common denominator is . Thus, we multiply the fractions as follows to give them a common denominator:

This is the same as:

Quantity B

The common denominator of these two values is . Therefore, you multiply the fractions as follows to give them a common denominator:

This is the same as:

Since Quantity A is larger than and Quantity B is a positive fraction less than , we know that Quantity A is larger without even using a calculator.

One remote is defective for every 199 non-defective remotes.

One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

estimate or calculate decimals after simplifying

The trick here is to set 1/2 as a baseline; all other choices are greater than 1/2.

Next is to see how much the difference is between each numerator and denominator (if you multiply 8/11 by 2/2, it will become 16/22) - each fraction besides 1/2 has a numerator that is 6 units less than the denominator. The trick is that the largest numerator will be the largest fraction when the numerator and denominator are the same units apart on all fractions.

First, you must find the total amount of solution. This is , or .

Now, the percentage of the solution that is blood can be represented:

, or

This is the same as % Rounded, it is %

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.

First, consider each quantity separately.

Quantity A

These two fractions do not have a common factor. Their common denominator is . Thus, we multiply the fractions as follows to give them a common denominator:

This is the same as:

Quantity B

The common denominator of these two values is . Therefore, you multiply the fractions as follows to give them a common denominator:

This is the same as:

Since Quantity A is larger than and Quantity B is a positive fraction less than , we know that Quantity A is larger without even using a calculator.

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

estimate or calculate decimals after simplifying

The trick here is to set 1/2 as a baseline; all other choices are greater than 1/2.

Next is to see how much the difference is between each numerator and denominator (if you multiply 8/11 by 2/2, it will become 16/22) - each fraction besides 1/2 has a numerator that is 6 units less than the denominator. The trick is that the largest numerator will be the largest fraction when the numerator and denominator are the same units apart on all fractions.

Begin by simplifying all terms inside the parentheses. Begin with the innermost set. Find a common denominator for the two terms. In this case, the common denominator will be twenty:

Simplify to and convert to not a mixed fraction:

Multiply the two fractions in the parentheses by multiplying straight across (A quick shortcut would be to factor out the 10 on top and bottom).

Now convert to a non-mixed fraction. It will become .

In order to subtract the two fractions, find a common denominator. In this case, it will be 70.

Now subtract, and find the answer!

is the answer