Question

________ are rational numbers between $-\frac{3}{4}$ and $\frac{1}{2}.$

• A. $\frac{-7}{16},\frac{-1}{8},\frac{9}{16}$
• B. $\frac{-15}{16},\frac{-1}{8},\frac{3}{16}$
• C. $\frac{-7}{16},\frac{-1}{8},\frac{3}{16}$
• D. none of the above

Answer 1

The correct option is C $\frac{-7}{16},\frac{-1}{8},\frac{3}{16}$

A rational number between two numbers $a$ and $b=\frac{(a+b)}{2}$

So,

a rational number between $-\frac{3}{4}$ and $\frac{1}{2}$

$=\frac{-\frac{3}{4}+\frac{1}{2}}{2}=-\frac{1}{8}$

Now,

another rational number between $-\frac{3}{4}$ and $-\frac{1}{8}$

$=\frac{-\frac{3}{4}-\frac{1}{8}}{2}=-\frac{7}{16}$

Another rational number between $-\frac{1}{8}$ and $\frac{1}{2}=$

$\frac{-\frac{1}{8}+\frac{1}{2}}{2}=\frac{3}{16}$

Hence, required three rational numbers between $-\frac{3}{4}$ and $\frac{1}{2}$ are $-\frac{3}{4},-\frac{7}{16},-\frac{1}{8},\frac{3}{16},\frac{1}{2}$