Basic Mathematics for College Students

Success Tip We can use rounding to check the results when adding (or

subtracting) mixed numbers. To check the answer from Example 1, we

proceed as follows:

Since is less than , round down to 4.

Since is greater than , round up to 3.

Since 61112 is close to 7, it is a reasonable answer.

(^3421 234)
61 21 461
4

1

6

 2

3

4

 4  3  7

(^61112)
272 Chapter 3 Fractions and Mixed Numbers
EXAMPLE 2
Add:
Strategy We 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.
Negative three and one-eighth One and one-half
Solution
Write and as improper fractions.
Since the smallest number the denominators 8 and 2 divide exactly is 8, the LCD is 8.
We will only need to build an equivalent fraction for.
To build so that its denominator is 8,
multiply it by a form of 1.
 1 Write  8 13 as a negative mixed number by dividing 13 by 8.

5

8

Use the rule for adding integers that have

 different signs:  25  12 13.

 13

8

Add the numerators and write the sum

 over the common denominator 8.

 25  12

8

Multiply the numerators.

 (^) Multiply the denominators.

25

8



12

8

3

 25 2

8



3

2



4

4

3

2

 3  381 1 21

1

8

 1

1

2



25

8



3

2

T T

 3

1

8

 1

1

2

 3

1

8

 1

1

2

Self Check 2

Add:

Now TryProblem 17

 4

1

12

 2

1

4

We can also add mixed numbers by adding their whole-number parts and their

fractional parts. To do so, we follow these steps.

Adding Mixed Numbers: Method 2

1. Write each mixed number as the sum of a whole number and a fraction.


2. Use the commutative property of addition to write the whole numbers
   together and the fractions together.


3. Add the whole numbers and the fractions separately.


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

Method 2 works well when the whole number parts of the mixed numbers are

large.