# GRE Math : How to multiply fractions

## Example Questions

### Example Question #1 : How To Multiply Fractions

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?

122

306

The answer cannot be determined from the given information.

103

136

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.

### Example Question #41 : Fractions

If  of a number is , what is  of that number?

Explanation:

The least common multiple of 4 and 6 is 12.

So we know if  of the number is  then

of the number is

.

So then it follows that

of the number is

.

### Example Question #1 : How To Multiply Fractions

If  and , what is the value of ?

Explanation:

### Example Question #1 : Operations

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?

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:

Drive:

Remaining:

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.

### Example Question #11 : Operations

Simplify:

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:

Now, cancel the  from the :

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

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

### Example Question #12 : Operations

Simplify:

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:

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

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

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

### Example Question #13 : Operations

Solve for :

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,

is the same as:

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

Now, subtract  from both sides:

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

Now, multiply both sides by :

Simplify:

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