(c)
Write 10 as^101.5
8
, 10 =
5
8
,
10
1
=
5
8
#^1
10
=
5 # 1
8 # 10=
5 # 1
8 # 5 # 2=
1
16
6 CHAPTER 1 The Real Number System
NOW TRY ANSWERS
- (a) (b)
5.^12
7
89
28Remember
to write
1 in the
numerator.(d)
Write each mixed number as an
improper fraction.Multiply numerators.= Multiply denominators. NOW TRY
10
27
=
5
3
#^2
9
1
2
3
, 4
1
2
=
5
3
,
9
2
OBJECTIVE 4 Add and subtract fractions.The result of adding two numbers is
called the sumof the numbers. For example, 2 + 3 = 5,so 5 is the sum of 2 and 3.
Adding FractionsIf and are fractions, then
That is, to find the sum of two fractions having the samedenominator, add the
numerators and keep the same denominator.
a
b
c
b
ac
b
.
c
b
a
b
Adding Fractions with the Same DenominatorFind each sum, and write it in lowest terms.
(a)
Add numerators.
Keep the same denominator.(b) Write in lowest terms. NOW TRY
If the fractions to be added do nothave the same denominators, we must first
rewrite them with a common denominator. For example, to rewrite as an equivalent
fraction with denominator 32, think,
We must find the number that can be multiplied by 4 to give 32. Since
we multiply numerator and denominator by 8.
3
4
=
3 # 8
4 # 8=
24
32
4 # 8 =32,
3
4
=
?
32
.
3
42
10
+
3
10
=
2 + 3
10
=
5
10
=
1
2
3
7
+
2
7
=
3 + 2
7
=
5
7
NOW TRY EXAMPLE 5
EXERCISE 5
Find the sum, and write it in
lowest terms.
1
8+
3
8
(^34) and (^2432) are equivalent fractions.
Finding the Least Common Denominator
To add or subtract fractions with different denominators, find the least common
denominator (LCD)as follows.
Step 1 Factor each denominator.
Step 2 For the LCD, use every factor that appears in any factored form. If a
factor is repeated, use the largest number of repeats in the LCD.
NOW TRY
EXERCISE 4
Find each quotient, and write
it in lowest terms.
(a) (b) 3
3
4
, 4
2
7
2
7
,
8
9
Multiply by the reciprocal of the
second fraction.http://www.ebook777.com
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