Basic Mathematics for College Students

3.6 Adding and Subtracting Mixed Numbers 271

In this section, we discuss several methods for adding and subtracting mixed numbers.

Add mixed numbers.

We can add mixed numbers by writing them as improper fractions. To do so, we
follow these steps.

Adding Mixed Numbers: Method 1

1. Write each mixed number as an improper fraction.


2. Write each improper fraction as an equivalent fraction with a denominator
   that is the LCD.


3. Add the fractions.


4. Write the result as a mixed number, if desired.

Method 1 works well when the whole-number parts of the mixed numbers are small.

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SECTION 3.6

Adding and Subtracting Mixed Numbers

Objectives

1 Add mixed numbers.

2 Add mixed numbers in vertical

form.

3 Subtract mixed numbers.

4 Solve application problems by

adding and subtracting mixed

numbers.

EXAMPLE 1

Add:

StrategyWe will write each mixed number as an improper fraction, and then use
the rule for adding two fractions that have different denominators.

WHY We cannot add the mixed numbers as they are; their fractional parts are not
similar objects.

Four and one-sixth Two and three-fourths

Solution

Write as improper fractions.

By inspection, we see that the lowest common denominator is 12.

To build and so that their denominators

are 12, multiply each by a form of 1.

Write the improper fraction

as a mixed number.

83

 6 11 12

12

Add the numerators and write the

sum over the common denominator 12.

The result is an improper fraction.



83

12

Multiply the numerators.

 (^) Multiply the denominators.

50

12



33

12

11

4

25

 25 6

# 2

6 # 2



11 # 3

4 # 3

4 4 16 and 2 (^34)

1

6

 2

3

4



25

6



11

4

T T

4

1

6

 2

3

4

4

1

6

 2

3

4

Self Check 1

Add:

Now TryProblem 13

3

2

3

 1

1

5

6

12  83

 72

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