Fundamentals of Mathematics, 2008a

320
CHAPTER 5. ADDITION AND SUBTRACTION OF FRACTIONS,
COMPARING FRACTIONS, AND COMPLEX FRACTIONS
Example √ 5.30
2 7 8 + 25
36 ÷ ( 2 1 2 − 1 )
1
3
(a) Begin by operating inside the parentheses.
2 1 2 − 1 1 3
= 2·2+1
2
− 1·3+1
3
= 5 2 − 4 3
15
=
6 − 8 6 = 15−8
6
= 7 6
(b) Now
√
simplify
(
the square root.
25
36 = 5 6
since ( ) )
5 2
6 =
25
36
Now we have
2 7 8 + 5 6 ÷ 7 6
(c) Perform the division.
1
2 7 8 + 5 )6
·
)6 7 = 2 7 8 + 5·1
1·7 = 2 7 8 + 5 7
1
(d) Now perform the addition.
2 7 8 + 5 7
= 2·8+7
8
+ 5 7 = 23 8 + 5 7
LCD = 56.
23·7
=
56 + 5·8
56 = 161
56 + 40
56
161+40
=
56
= 201
56
√
Thus, 2 7 8 + 25
36 ÷ ( 2 1 2 − 1 ) 1
3 = 3
33
56
or 3
33
56
5.7.2.2 Practice Set A
Find the value of each of the following quantities.
Exercise 5.7.1 (Solution on p. 334.)
5
16 · 1
10 − 1 32
Exercise 5.7.2 (Solution on p. 334.)
6
7 · 21
40 ÷ 9
10 + 5 1 3
Exercise 5.7.3 (Solution on p. 334.)
8 7
10 − 2 ( 4 1 2 − 3 )
2
3
Exercise 5.7.4 (Solution on p. 334.)
17
18 − ( 58 1
30 4 − ) ( )
3
32 1 −
13
29
Exercise ( 5.7.5 (Solution on p. 334.)
1
10 + 1 ) ( 1
2 ÷ 1
4
5 − 1 )
6
25
Exercise 5.7.6 (Solution on p. 334.)
2
3 − 3 8 · 4
9
7
16 ·1 1 3 +1 1 4
Exercise 5.7.7 (Solution on p. 334.)
( 3
) 2
8 +
3
4 · 1
8
Exercise 5.7.8 (Solution on p. 334.)
√
2
3 · 2 1 4 −
4
25
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