Question

$\text{Integers that lie between}\frac{-1}{3}\text{and}\frac{-5}{2}\text{are}$ .

• A. 0, -1
• B. -1, -2
• C. -2, -3

Answer 1

The correct option is B -1, -2

To find rational numers between any two rational numbers, the denominators must be same.
So, LCM of the denominators 2 and 3 is 6.

$\frac{-1}{3}=\frac{-1\times 2}{3\times 2}=\frac{-2}{6}$

$\frac{-5}{2}=\frac{-5\times 3}{2\times 3}=\frac{-15}{6}$

So, to find the integers between $\frac{-1}{3}and\frac{-5}{2}$ is same as finding integers between $\frac{-2}{6}and\frac{-15}{6}.$
For that, the numerator must be a multiple of 6.
The multiples of 6 between the numerators -2 and -15 are -6 and -12.
So, the integers between $\frac{-2}{6}and\frac{-15}{6}$ are $\frac{-6}{6}=-1and\frac{-12}{6}=-2$