12. The sum of two numbers $a$ and $b$ is 7 and the difference between them is 2 .
What is the value of $a \times b$ ?
A $8 \frac{1}{4}$
B $9 \frac{1}{4}$
C $10 \frac{1}{4}$
D $11 \frac{1}{4}$
E $12 \frac{1}{4}$
12. D Assume that $a>b$. Then $a+b=7$ and $a-b=2$. Adding these two equations together gives $2 a=9$. So $a=\frac{9}{2}$ and hence $b=7-\frac{9}{2}=\frac{14-9}{2}=\frac{5}{2}$. Therefore $a \times b=\frac{9}{2} \times \frac{5}{2}=\frac{45}{4}=11 \frac{1}{4}$.