1.
An expression of the form [tex]a \frac{b}{c}[/tex] is called a "compound fraction"
Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:
[tex]a \frac{b}{c}= \frac{c.a+b}{c}[/tex]
for example,
[tex]4\frac{1}{2}[/tex] can be written as:
[tex]4\frac{1}{2}= \frac{2.4+1}{2}=\frac{9}{2}[/tex]
2.
when we subtract or add a fraction [tex] \frac{m}{n} [/tex] from an integer k,
we first write k as a fraction with denominator n. We can do this as follows:
[tex]k=k. \frac{n}{n}= \frac{kn}{n} [/tex]
for example, if we want to subtract [tex] \frac{9}{2} [/tex] from 8,
we first write 8 as a fraction with denominator 2:
[tex]8=8. \frac{2}{2}= \frac{8.2}{2}= \frac{16}{2} [/tex]
3.
Thus,
[tex]8-4 \frac{1}{2}= \frac{16}{2}- \frac{9}{2}= \frac{16-9}{2}= \frac{7}{2} [/tex]
4.
The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:
[tex] \frac{7}{2}= \frac{6+1}{2}= \frac{6}{2}+ \frac{1}{2}=3+ \frac{1}{2}=3\frac{1}{2} [/tex]
(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)
5. Answer: D
