Fundamentals of Mathematics, 2008a

319
5·4
36 − 1·9
36 = 20
3
5 + ( 9 11
44 36
36 − 9 36 = 20−9
Now we have )
(b) Perform the multiplication.
36
= 11
36
1 1
3
5 + )9 )11
· = 3 )44 )36 5 + 1·1
4·4 = 3 5 + 1
16
4 4
(c) Now perform the addition. The LCD=80.
3
5 + 1
16 = 3·16
80 + 1·5
80 = 48
80 + 5
80 = 48+5
80
= 53
80
Thus, 3 5 + 9
44
( 5
9 − 1 4
Example ( 5.28 ) (
8 − 15
426 2 − 1
4
15 3
1
5 + 2 )
1
8
)
=
53
80
(a) Work within each set of parentheses individually.
2 − 1 4
15
= 2 1·15+4
15
= 2 − 19
15
= 30
15 − 19
15 = 30−19
15
= 11
15
3 1 5 + 2 1 3·5+1
8
=
5
+ 2·8+1
8
16
=
5 + 17 8
LCD = 40
Now we have
(
8 − 15 11
) ( 213
)
426 15 40
(b) Now multiply.
1
)15
)426
2
8 − · 11 ·
)15
1
(c) Now subtract.
8 − 11
Thus, 8 − 15
426
Example 5.29
( 3
) 2
4 · 8
9 − 5 12
16·8
=
40 + 17·5
40
128
=
40 + 85
40
128+85
=
40
=
213
40
1
)213
40 = 8 − 1·11·1
2·1·40 = 8 − 11
80
(
2 − 1
4
15
) (
3
1
5 + 2 1 8
)
= 7
69
80
80 = 80·8
80 − 11
80 = 640
80 − 11
80 = 640−11
80
= 629
(a) Square 3
(
4 .
3
) 2
4 =
3
4 · 3
4 = 3·3
4·4 = 9
16
Now we have
9
16 · 8
9 − 5 12
(b) Perform the multiplication.
1 1
)9 )8
· − 5 )16 )9 12 = 1·1
2·1 − 5 12 = 1 2 − 5
12
2 1
(c) Now perform the subtraction.
1
2 − 5
12 = 6
12 − 5
12 = 6−5
12 = 1 12
Thus, ( )
4 2
3 · 8
9 − 5 12 = 1 12
80
or 7 69
80
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