PRACTICE PROBLEMS INVOLVING RATIONAL EXPRESSIONS

Courtesy of Kelly Kaiser

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1) If the same number is added to the numerator and denominator of 3/5, the result is 1/3. Find the number.

2)
If
the same number is added to the numerator and denominator of –4/7, the result
is –9/2. Find the number.

3)
If
a number is added to the numerator of 2/7, and twice the number is subtracted
from the denominator, the result is 5.
Find the number.

4)
In
a certain fraction, the numerator is 3 less than the denominator. If 5 is added to both the numerator and
denominator, the result is 4/5. Find
the original fraction.

5)
In
a certain fraction, the denominator is 5 more than the numerator. If 4 is added to both the numerator and
denominator, the result is 2/7. Find
the original fraction.

6)
The
sum of a number and its reciprocal is 17/4.
Find the number.

7)
The
difference between a number and its reciprocal is 3/2. Find the number.

8)
If
three times a number is subtracted from twice its reciprocal, the result is
–1. Find the number.

9)
If
a number is added to twice its reciprocal, the result is 9/2. Find the number.

10)
If
two times a number is added to one-half its reciprocal, the answer is
13/6. Find the number.

11)
If
one-eighth of a number is added to one-third of the number, the result is 13
less than the number. Find the number.

12)
If
the same number is added to both the numerator and denominator of the fraction
4/19, the value of the resulting fraction is 3/8. Find the number.

13)
The
denominator of a certain fraction is 4 times the numerator. If 6 is added to the numerator and
subtracted from the denominator, the resulting fraction is equal to 11/14. Find the original fraction.

14)
In
a certain fraction, the numerator is 5 less than the denominator. If 4 is added to both the numerator and denominator,
the resulting fraction is equal to 2/3.
Find the original fraction.

15)
Twice
a number is subtracted from the numerator of the fraction 9/8, while 3 times
the number is added to the denominator.
If the result is 5/14, find the number.

Answers:

1)
–2

2)
–5

3)
3

4)
7/10

5)
–2/3

6)
4
or ¼

7)
2
or –1/2

8)
–2/3
or 1

9)
½
or 4

10)
¾ or 1/3

11)
24

12)
5

13)
5/20

14)
6/11

15)
2