Page 272 - Basic College Mathematics with Early Integers

S E C T I O N 3.7 I OPERATIONS ON MIXED NUMBERS 249

Solution: 48 inches

1. UNDERSTAND the problem. To do so, read and
reread the problem.Then draw a diagram:
3 …
We want to know how many 1 s there are in 48.
5
1E inches
2. TRANSLATE.

number of divided 3
In words: is 48 1
strips by 5
T T T T T
number of 3
Translate: = 48 , 1
strips 5
3
3. SOLVE: Let’s estimate a reasonable answer. The mixed number 1 rounds to
5
2 and 48 , 2 = 24.

1
# #
#
3 8 48 5 48 5 8 6 5 30
48 , 1 = 48 , = # = = = or 30
#
#
5 5 1 8 1 8 1 8 1
1
4. INTERPRET. Check your work. Since the exact answer of 30 is close to our es-
timate of 24, our answer is reasonable. State your conclusion: Thirty strips can
be cut from the 48-inch piece of stock.
Work Practice 16

Objective Operating on Negative Mixed Numbers

To perform operations on negative mixed numbers, let’s first practice writing these
numbers as negative fractions and negative fractions as negative mixed numbers.
To understand negative mixed numbers, we simply need to know that, for
example,
2 2
-3 means - a3 b
5 5
Thus, to write a negative mixed number as a fraction, we do the following.

#
2 2 5 3 + 2 17 17
-3 = - a3 b = - a b =- a b or -
5 5 5 5 5

Examples Write each as a fraction. PRACTICE 17–18
Write each as a fraction.
#
7 8 1 + 7 15 7 3 10
17. -1 = - = - Write 1 as an improper fraction and keep the 17. -9 18. -5
8 8 8 8 7 11
()* ('')''* negative sign.
Î
#
1 2 23 + 1 47 1
18. -23 = - = - Write 23 as an improper fraction and keep the
2 2 2 2
(')'* ('')''* negative sign.
Answers
Î
66 65
Work Practice 17–18 17. - 7 18. - 11