# GRE Math : Operations

## Example Questions

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### Example Question #1 : Operations

What is the result of adding  of  to ?

Explanation:

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.

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

Reduce to simplest form:

Explanation:

Simplify expressions inside parentheses first:   and

Now we have:

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:

### Example Question #2 : How To Add Fractions

Quantity A:

Quantity B:

Which of the following is true?

Quantity A is larger.

The two quantities are equal.

Quantity B is larger.

The relationship between the two quantities cannot be determined.

The two quantities are equal.

Explanation:

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

This is the same as:

, or

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

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

Solve for :

Explanation:

Begin by isolating the  factors:

Now, the common denominator of these two fractions is .  Therefore, multiply  by :

Now, you can subtract the left values:

Now, multiply both sides by :

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

Simplify:

Explanation:

Just like adding fractions, when you subtract fractions, you need to find a common denominator. For  and , the least common denominator is . In order to do your subtraction, you need to multiply appropriately to give your fractions this denominator:

Which is the same as...

Now, you can subtract the numerators and retain the denominator:

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

Which of the following is true?

Quantity A:

Quantity B:

The relationship between the quantities cannot be determined.

Quantity B is larger.

The two quantities are equal.

Quantity A is larger.

Quantity A is larger.

Explanation:

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.

### Example Question #1 : 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?

103

122

136

The answer cannot be determined from the given information.

306

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 #2 : How To Multiply 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 #3 : How To Multiply Fractions

If  and , what is the value of ?

Explanation:

### Example Question #1 : 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?

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.

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