GRE Math : How to add complex fractions

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Example Question #1 :Complex Fractions

Solve:

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

Possible Answers:

$\frac{26}{3}$

$\frac{28}{3}$

$\frac{28}{2}$

Correct answer:

$\frac{28}{3}$

Explanation:

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.

$\frac{28}{3}$

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Example Question #2 :Complex Fractions

Simplify:

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

Possible Answers:

$\frac{3x + 4}{8}$

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

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

$\frac{x+12}{3}$

$\frac{x+6}{32}$

Correct answer:

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

Explanation:

虽然你可以找公分母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:

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

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Example Question #3 :Complex Fractions

Simplify:

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

Possible Answers:

$\frac{21}{50}$

$\frac{25}{3}$

$\frac{129}{50}$

$\frac{22}{5}$

$\frac{11}{15}$

Correct answer:

$\frac{22}{5}$

Explanation:

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 thes and theand 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:

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

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Example Question #4 :Complex Fractions

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

Possible Answers:

$-\frac{18}{25}$

$\frac{71}{70}$

$\frac{173}{70}$

$\frac{23}{10}$

Correct answer:

$\frac{173}{70}$

Explanation:

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

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GRE Math : How to add complex fractions

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