The rule for subtraction from Section 2.3 can be extended to subtraction
involving signed fractions:

To subtract two fractions, add the first to the opposite of the fraction to be

subtracted.

3.4 Adding and Subtracting Fractions 243

Self Check 2

Subtract: 

Now TryProblem 25

a

3

11

b

9

11

Self Check 1

Perform each operation and

simplify the result, if possible.

a.Add: 

b.Subtract: 

Now TryProblems 17 and 21

1

9

8

9

1

12

5

12

EXAMPLE 1

Perform each operation and simplify the result, if possible.

a.Add:  b. Subtract: 

Strategy We will use the rule for adding and subtracting fractions that have the
samedenominator.

WHY In part a, the fractions have the same denominator, 8. In part b, the fractions
have the same denominator, 15.

Solution

a.

This fraction can be simplified.

b.

Since 7 and 15 have no common factors other than 1, the result is in simplest form.



7

15

Subtract the numerators and write the difference

over the common denominator 15.

11

15



4

15



11  4

15

Multiply the remaining factors in the numerator: 1  3 3.

 (^) Multiply the remaining factors in the denominator: 1 4 4.

3

4

To simplify, factor 6 as 2 3 and 8 as 2 4. Then remove the

 (^) common factor of 2 from the numerator and denominator.

2

1

# 3

2

1

4



6

8

Add the numerators and write the sum

(^) over the common denominator 8.

1

8



5

8



1  5

8

4

15

11

15

5

8

1

8

EXAMPLE 2

Subtract: 

Strategy To find the difference, we will apply the rule for subtraction.

WHY It is easy to make an error when subtracting signed fractions. We will
probably be more accurate if we write the subtraction as addition of the opposite.

Solution

We read as “negative seven-thirds minusnegative two-thirds.” Thus, the
number to be subtracted is Subtracting is the same as adding its opposite,
Add

Add the opposite of , which is

the opposite

Write as

Rewrite the result with the  sign in front:

This fraction is in simplest form.

 5

3 ^

5

  5 3.

3

Use the rule for adding two integers

 (^) with different signs:  7  2 5.

 5

3

Add the numerators and write the sum

 (^) over the common denominator 3.

 7  2

3

 7

 3.

7

 (^3)

 7

3



2

3



2

 3.

2

 7 3

3

 a

2

3

b

7

3



2

3



2

 3.

2

 (^3)
2
3.

 73  1  232

a

2

3

 b

7

3