McGraw-Hill Education GRE 2019

Dividing Fractions

When dividing by a fraction, multiply the numerator by the reciprocal of the

fraction in the denominator. To find the reciprocal of a fraction, simply switch the

terms in the numerator and denominator.

7

3

14

9

=?

SOLUTION: Multiply^73 by the reciprocal of (^149 ):

(^73 )( 149 ) =^73 × 3 × 37 × 2 =^32

Fractions in Word Problems

Many word problems will test your understanding of fractions in real-world

contexts. In many of these questions, you will be given a value for the part and

will be asked to solve for the whole or vice versa. In these questions, it is essential

to remember the following relationship: part = fraction × whole. As you are

given information, track how that information fits into that formula. Look at the

following example:

Of the 120 boys in a school,^34 are taking chemistry. If^35 of the students in the

school are boys, the number of boys taking chemistry is what fraction of all

the students at the school?

SOLUTION: You are being asked to solve for the number of boys taking

chemistry as a fraction of all students at the school, so the numerator should

be “number of boys taking chemistry” and the denominator should be

“the number of students in the school.” Now use the information from the

question to solve for these values.

boys taking chemistry

students in the school

SOLUTION: In the first sentence, you are told that^34 of all the boys are taking

chemistry. Since there are 120 students in the school, the number of boys

taking chemistry =^34 × 120 = 90. Now figure out the number of students

in the school. The whole is the number of students, the part is the number

of boys, and^35 is the fraction. Thus 120 =^35 × n, where n is the number of

students in the school. Multiply both sides of the equation by^53 to solve for n:

120 × 53 = n

n = 200

SOLUTION: So the fraction you arrive at is 20090 , which reduces to 209.

214 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 214 12/05/17 11:51 am