GRE Math : How to multiply fractions

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Example Questions

Example Question #5 : Operations

There are 340 students at Saint Louis High School in the graduating senior class. Of these students, 9/10 are going to college. Of those going to college, 2/5 are going to Saint Louis University. How many students are going to Saint Louis University?

Possible Answers:

103

The answer cannot be determined from the given information.

306

122

136

Correct answer:

122

Explanation:

122 students are going to Saint Louis University. To answer this question, the following equation can be used: 340*(9/10)*(2/5) . This is then rounded down to 122 students attending Saint Louis University.

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Example Question #1 : How To Multiply Fractions

If $\frac{4}{7}$ of a number is , what is $\frac{6}{7}$ of that number?

Possible Answers:

Correct answer:

Explanation:

The least common multiple of 4 and 6 is 12.

So we know if $\frac{4}{7}$ of the number is then

$3\cdot \frac{4}{7}=\frac{12}{7}$ of the number is

$3\cdot 22=66$ .

So then it follows that

$\frac{1}{2}\cdot \frac{12}{7}=\frac{12}{14}=\frac{6}{7}$ of the number is

$\frac{1}{2}\cdot 66=33$ .

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Example Question #2 : How To Multiply Fractions

If 11x=3 and 3y=11 , what is the value of $\frac{x}{y}$ ?

Possible Answers:

$\frac{11}{3}$

$\frac{9}{121}$

$\frac{121}{9}$

$\frac{3}{121}$

Correct answer:

$\frac{9}{121}$

Explanation:

$11x=3\Rightarrow x=\frac{3}{11}$

$3y=11\Rightarrow y=\frac{11}{3}$

$\frac{x}{y}= \frac{\frac{3}{11}}{\frac{11}{3}}=\frac{3}{11}\cdot \frac{3}{11}=\frac{9}{121}$

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Example Question #3 : How To Multiply Fractions

At a certain company, one quarter of the employees take the bus to work and one third drive. Of the remaining employees, half walk, one third ride a bike, and the rest take the subway.

Out of the total number of employees, what fraction ride a bike to work?

Possible Answers:

$\small \frac{6}{15}$

$\small \frac{2}{21}$

$\small \frac{5}{36}$

$\small \frac{8}{15}$

$\small \frac{1}{12}$

Correct answer:

$\small \frac{5}{36}$

Explanation:

First we want to find the fraction of employees that neither take the bus nor drive, so we’ll add the fractions that do take the bus or drive and subtract that result from the total.

Bus: $\frac{1}{4}$

Drive: $\frac{1}{3}$

Remaining: $1-(\frac{1}{4}+\frac{1}{3})=1-(\frac{7}{12})=\frac{5}{12}$

Now we need the fraction representing one third of these remaining employees (the fraction that ride a bike). Since "of " means multiply, we'll multiply.

$\frac{1}{3}*\frac{5}{12}=\frac{5}{36}$

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Example Question #11 : Operations

Simplify:

$\frac{44}{18}*\frac{3}{11}*\frac{5}{8}$

Possible Answers:

$\frac{41}{20}$

$\frac{88}{15}$

$\frac{132}{65}$

$\frac{5}{12}$

$\frac{125}{22}$

Correct answer:

$\frac{5}{12}$

Explanation:

Multiplying fractions is very easy. All you do is multiply all the numerators by each other and all the denominators by each other. You do not have to do anything that has to do with fancy common denominators like you do for adding and subtracting. For a question like this, it is often easiest just to cancel factors before you start your final multiplication. First, note:

$\frac{44}{18}*\frac{3}{11}*\frac{5}{8}=\frac{44*3*5}{18*11*8}$

Now, cancel the from the :

$\frac{4*3*5}{18*8}$

Next, the in the numerator cancels with the in the denominator:

$\frac{3*5}{18*2}$

Finally, the in the numerator cancels with the in the denominator:

$\frac{5}{6*2}=\frac{5}{12}$

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Example Question #12 : Operations

Simplify:

$\frac{15}{2}*\frac{12}{45}*\frac{3}{4}$

Possible Answers:

$\frac{5}{2}$

$\frac{3}{5}$

$\frac{3}{2}$

$\frac{3}{15}$

$\frac{100}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

$\frac{15}{2}*\frac{12}{45}*\frac{3}{4}=\frac{15*12*3}{2*45*4}$

Now, cancel the in the denominator with the in the numerator:

$\frac{15*3*3}{2*45}$

Next, the 3*3 in the numerator cancels with the in the denominator:

$\frac{15}{2*5}$

Finally, cancel the in the denominator with the in the numerator:

$\frac{3}{2}$

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Example Question #1 : How To Multiply Fractions

Solve for :

$\frac{1}{3}(4x+\frac{12}{5})=2$

Possible Answers:

$\frac{122}{9}$

$\frac{15}{2}$

$\frac{9}{10}$

Correct answer:

$\frac{9}{10}$

Explanation:

Begin by distributing the group on the left side of the equation. Remember that it is easy to multiply fractions. You only need to multiply the denominators and numerators. There are no "fancy" steps in between.

Therefore,

$\frac{1}{3}(4x+\frac{12}{5})=2$

is the same as:

$(\frac{1}{3}*4x+\frac{1}{3}*\frac{12}{5})=2$

You can cancel part of the second fraction out, so you get:

$\frac{4x}{3}+\frac{4}{5}=2$

Now, subtract $\frac{4}{5}$ from both sides:

$\frac{4x}{3}=2-\frac{4}{5}$

Simplifying the right side of the equation, you get...

$\frac{4x}{3}=\frac{10}{5}-\frac{4}{5}$

$\frac{4x}{3}=\frac{6}{5}$

Now, multiply both sides by $\frac{3}{4}$ :

$\frac{3}{4}*\frac{4x}{3}=\frac{6}{5}*\frac{3}{4}$

Simplify:

$x=\frac{18}{20} = \frac{9}{10}$

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GRE Math : How to multiply fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #5 : Operations

Example Question #1 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #11 : Operations

Example Question #12 : Operations

Example Question #1 : How To Multiply Fractions

All GRE Math Resources

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