Basic Mathematics for College Students

242 Chapter 3 Fractions and Mixed Numbers

SECTION 3.4

Adding and Subtracting Fractions

Objectives

1 Add and subtract fractions that

have the same denominator.

2 Add and subtract fractions that

have different denominators.

3 Find the LCD to add and

subtract fractions.

4 Identify the greater of two

fractions.

5 Solve application problems

by adding and subtracting

fractions.

In mathematics and everyday life, we can only add (or subtract) objects that are

similar. For example, we can add dollars to dollars, but we cannot add dollars to

oranges. This concept is important when adding or subtracting fractions.

Add and subtract fractions that have the same denominator.

Consider the problem  When we write it in words, it is apparent that we are

adding similar objects.

Similar objects

Because the denominators of and are the same, we say that they have a common

denominator.Since the fractions have a common denominator, we can add them.

The following figure explains the addition process.

three-fifths one-fifth four-fifths

We can make some observations about the addition shown in the figure.

The sumof the numerators is the numerator of the answer.

The answer is a fraction that has the samedenominator

as the two fractions that were added.

These observations illustrate the following rule.

Adding and Subtracting Fractions That Have the Same Denominator

To add (or subtract) fractions that have the same denominator, add (or

subtract) their numerators and write the sum (or difference) over the common

denominator. Simplify the result, if possible.

Caution!We do notadd fractions by adding the numerators and adding the

denominators!

The same caution applies when subtracting fractions.

3

5



1

5



3  1

5  5



4

10

  

3

5



1

5



4

5

  

(^3) –
5
(^1) –
5
(^4) –
5
+=
1
5
3
5
three-fifths  one-fifth
1
5.
3
5
1