Page 111 - ArithBook5thEd ~ BCC

7 5
Solution. Adding the opposite of 2 to 1 ,we get
8 6

5 " 7 # " 7 5 #
1 + −2 = − 2 − 1
6 8 8 6
" #
21 20
= − 2 − 1 (LCD = 24)
24 24
1
= −1 .
24

Recall that the product or quotient of two numbers with oppositesigns is always negative, and that
the product or quotient of two numbers with the same sign is always positive.
3 " 6 #
Example 130. Find the product · − .
4 5

Solution. The numbers have opposite signs, so the product is negative.

3 ✚ 6 9
" ✚❃ 3 #
− 2 · = − (pre-cancelling 2).
✚ 4 ✚❃ 5 10

1 1
" #" #
Example 131. Find the product − 2 −3 .
2 4
Solution. The numbers have the same sign so the product is positive, and we compute with the absolute
values. Converting the mixed numbers to improper fractions for multiplication,

5 13 65 1
· = =8 .
2 4 8 8

33
Example 132. Express the fraction − as a mixed number.
5
Solution. The fraction represents division of numbers with opposite signs, so the result is negative. For
the division 33 ÷ 5, the quotient is 6 and the remainder is 3, so

33 3
− = −6 .
5 5

5 1
" # " #
Example 133. Find −2 ÷ − .
9 6

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