Fractions - GRE Quantitative Reasoning

Card 1 of 1968

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)=?$

Tap to reveal answer

Answer

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:

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{5}{20}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{6}{20}\right)\right)$

Simplify $\frac{6}{20}$ to $\frac{3}{10}$ and convert $1\frac{3}{7}$ to not a mixed fraction:

$1\frac{3}{7}=\frac{10}{7}$

$2\frac{9}{10}-\left(\frac{10}{7}\cdot \frac{3}{10}\right)$

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).

$2\frac{9}{10}-\left(\frac{30}{70}\right)$

$2\frac{9}{10}-\left(\frac{3}{7}\right)$

Now convert $2\frac{9}{10}$ to a non-mixed fraction. It will become $\frac{29}{10}$ .

$\frac{29}{10}-\frac{3}{7}$

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

$\frac{203}{70}-\frac{30}{70}$

Now subtract, and find the answer!

$\frac{173}{70}$ is the answer

← Didn't Know|Knew It →

Question

Solve:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Tap to reveal answer

Answer

To simplify a complex fraction, simply invert the denomenator and multiply by the numerator:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Multiplying the numerator by the reciprocal of the denominator for each term we get:

$\frac{2}{3} \cdot\frac{5}{1} + \frac{9}{1}\cdot \frac{2}{3} =$

$\frac{10}{3} + \frac{18}{3} =$

Since we have a common denominator we can now add these two terms.

$\frac{28}{3}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{1}{2}}{8}+\frac{\frac{x}{4}}{4}$

Tap to reveal answer

Answer

Although you could look for the common denominator of the fraction as it has been written, it is probably easiest to rewrite the fraction in slightly simpler terms. Thus, recall that you can rewrite your fraction as:

$\frac{\frac{1}{2}}{\frac{8}{1}}+\frac{\frac{x}{4}}{\frac{4}{1}}$

Using the rule for dividing fractions, you can rewrite your expression as:

$\frac{1}{2} \cdot \frac{1}{8} + \frac{x}{4} \cdot \frac{1}{4}$

Then, you can multiply each set of fractions, getting:

$\frac{1}{16} + \frac{x}{16}$

This makes things very easy, for then your value is:

$\frac{1+x}{16}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{3}{5}}{\frac{3}{10}}+\frac{12}{5}$

Tap to reveal answer

Answer

For this problem, begin by rewriting the complex fraction, using the rule for dividing fractions:

$\frac{\frac{3}{5}}{\frac{3}{10}} = \frac{3}{5} \cdot \frac{10}{3}$

This is much easier to work on. Cancel out the s and the and the , this gives you:

$\frac{1}{1} * \frac{2}{1}$ , which is merely . Thus, your problem is:

$2+\frac{12}{5}$

The common denominator is , so you can rewrite this as:

$\frac{10}{5}+\frac{12}{5} = \frac{22}{5}$

← Didn't Know|Knew It →

Question

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)=?$

Tap to reveal answer

Answer

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:

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{5}{20}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{6}{20}\right)\right)$

Simplify $\frac{6}{20}$ to $\frac{3}{10}$ and convert $1\frac{3}{7}$ to not a mixed fraction:

$1\frac{3}{7}=\frac{10}{7}$

$2\frac{9}{10}-\left(\frac{10}{7}\cdot \frac{3}{10}\right)$

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).

$2\frac{9}{10}-\left(\frac{30}{70}\right)$

$2\frac{9}{10}-\left(\frac{3}{7}\right)$

Now convert $2\frac{9}{10}$ to a non-mixed fraction. It will become $\frac{29}{10}$ .

$\frac{29}{10}-\frac{3}{7}$

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

$\frac{203}{70}-\frac{30}{70}$

Now subtract, and find the answer!

$\frac{173}{70}$ is the answer

← Didn't Know|Knew It →

Question

Solve:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Tap to reveal answer

Answer

To simplify a complex fraction, simply invert the denomenator and multiply by the numerator:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Multiplying the numerator by the reciprocal of the denominator for each term we get:

$\frac{2}{3} \cdot\frac{5}{1} + \frac{9}{1}\cdot \frac{2}{3} =$

$\frac{10}{3} + \frac{18}{3} =$

Since we have a common denominator we can now add these two terms.

$\frac{28}{3}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{1}{2}}{8}+\frac{\frac{x}{4}}{4}$

Tap to reveal answer

Answer

Although you could look for the common denominator of the fraction as it has been written, it is probably easiest to rewrite the fraction in slightly simpler terms. Thus, recall that you can rewrite your fraction as:

$\frac{\frac{1}{2}}{\frac{8}{1}}+\frac{\frac{x}{4}}{\frac{4}{1}}$

Using the rule for dividing fractions, you can rewrite your expression as:

$\frac{1}{2} \cdot \frac{1}{8} + \frac{x}{4} \cdot \frac{1}{4}$

Then, you can multiply each set of fractions, getting:

$\frac{1}{16} + \frac{x}{16}$

This makes things very easy, for then your value is:

$\frac{1+x}{16}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{3}{5}}{\frac{3}{10}}+\frac{12}{5}$

Tap to reveal answer

Answer

For this problem, begin by rewriting the complex fraction, using the rule for dividing fractions:

$\frac{\frac{3}{5}}{\frac{3}{10}} = \frac{3}{5} \cdot \frac{10}{3}$

This is much easier to work on. Cancel out the s and the and the , this gives you:

$\frac{1}{1} * \frac{2}{1}$ , which is merely . Thus, your problem is:

$2+\frac{12}{5}$

The common denominator is , so you can rewrite this as:

$\frac{10}{5}+\frac{12}{5} = \frac{22}{5}$

← Didn't Know|Knew It →

Question

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)=?$

Tap to reveal answer

Answer

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:

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{1}{4}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{5}{20}+\frac{1}{20}\right)\right)$

$2\frac{9}{10}-\left(1\frac{3}{7}\cdot \left(\frac{6}{20}\right)\right)$

Simplify $\frac{6}{20}$ to $\frac{3}{10}$ and convert $1\frac{3}{7}$ to not a mixed fraction:

$1\frac{3}{7}=\frac{10}{7}$

$2\frac{9}{10}-\left(\frac{10}{7}\cdot \frac{3}{10}\right)$

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).

$2\frac{9}{10}-\left(\frac{30}{70}\right)$

$2\frac{9}{10}-\left(\frac{3}{7}\right)$

Now convert $2\frac{9}{10}$ to a non-mixed fraction. It will become $\frac{29}{10}$ .

$\frac{29}{10}-\frac{3}{7}$

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

$\frac{203}{70}-\frac{30}{70}$

Now subtract, and find the answer!

$\frac{173}{70}$ is the answer

← Didn't Know|Knew It →

Question

Solve:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Tap to reveal answer

Answer

To simplify a complex fraction, simply invert the denomenator and multiply by the numerator:

$\frac{\frac{2}{3}}{\frac{1}{5}} + \frac{9}{\frac{3}{2}} =$

Multiplying the numerator by the reciprocal of the denominator for each term we get:

$\frac{2}{3} \cdot\frac{5}{1} + \frac{9}{1}\cdot \frac{2}{3} =$

$\frac{10}{3} + \frac{18}{3} =$

Since we have a common denominator we can now add these two terms.

$\frac{28}{3}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{1}{2}}{8}+\frac{\frac{x}{4}}{4}$

Tap to reveal answer

Answer

Although you could look for the common denominator of the fraction as it has been written, it is probably easiest to rewrite the fraction in slightly simpler terms. Thus, recall that you can rewrite your fraction as:

$\frac{\frac{1}{2}}{\frac{8}{1}}+\frac{\frac{x}{4}}{\frac{4}{1}}$

Using the rule for dividing fractions, you can rewrite your expression as:

$\frac{1}{2} \cdot \frac{1}{8} + \frac{x}{4} \cdot \frac{1}{4}$

Then, you can multiply each set of fractions, getting:

$\frac{1}{16} + \frac{x}{16}$

This makes things very easy, for then your value is:

$\frac{1+x}{16}$

← Didn't Know|Knew It →

Question

Simplify:

$\frac{\frac{3}{5}}{\frac{3}{10}}+\frac{12}{5}$

Tap to reveal answer

Answer

For this problem, begin by rewriting the complex fraction, using the rule for dividing fractions:

$\frac{\frac{3}{5}}{\frac{3}{10}} = \frac{3}{5} \cdot \frac{10}{3}$

This is much easier to work on. Cancel out the s and the and the , this gives you:

$\frac{1}{1} * \frac{2}{1}$ , which is merely . Thus, your problem is:

$2+\frac{12}{5}$

The common denominator is , so you can rewrite this as:

$\frac{10}{5}+\frac{12}{5} = \frac{22}{5}$

← Didn't Know|Knew It →

Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Tap to reveal answer

Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

← Didn't Know|Knew It →

Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Tap to reveal answer

Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

← Didn't Know|Knew It →

Question

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

Tap to reveal answer

Answer

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}\frac{y}{y}+\frac{12}{y}\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

← Didn't Know|Knew It →

Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Tap to reveal answer

Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

← Didn't Know|Knew It →

Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Tap to reveal answer

Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

← Didn't Know|Knew It →

Question

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

Tap to reveal answer

Answer

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}\frac{y}{y}+\frac{12}{y}\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

← Didn't Know|Knew It →

Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Tap to reveal answer

Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

← Didn't Know|Knew It →

Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Tap to reveal answer

Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

← Didn't Know|Knew It →

0

Knew It