Page 116 - ArithBook5thEd ~ BCC

Solution. The order of operations is multiplication, division, addition. We first convert mixed numbers
into improper fractions, and change the division into multiplication by the reciprocal.

5 2 7 " 3 # 10 7 " 2 #
· + ÷ − = + · −
4 3 6 2 12 6 3
10 " 14 #
= + −
12 18
5 " 7 #
= + − (lowest terms)
6 9
15 " 14 #
= + − (LCD = 18)
18 18
15 14
= −
18 18
1
= .
18

1 2 1
" #
& ' 1 ()
Example 140. Calculate 1+ 2+ 1 · − 1 ÷ 1 .
4 3 6 2
Solution. In this example we have so-called nested grouping symbols, that is, grouping symbols inside
other grouping symbols. In this case, we must work “from the inside out.” This means we work within
the innermost grouping symbols first. From the previous example we know that
1 2 1 1 1
1 · − 1 ÷ 1 = ,
4 3 6 2 18
thus we get
" #
1 2 1
& ' 1 ()
1+ 2+ 1 · − 1 ÷ 1
4 3 6 2
1 () ' 37 ( 55 1
" #
= 1+ 2+ = {1+ } = =3 .
'
&
18 18 18 18
3.13.1 Exercises

Calculate, using the correct order of operations. Express improper fractions as mixed numbers.
3 2 4
1. + ÷
4 3 9
" #
3 1
2. 2 − − 3
4 2
3 " 1 #
3. − 3 − 2
4 2

1 2 1
" #
4. 8 − 1 ÷
4 3 3

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