Question

Insert two rational numbers between -1/3 and -1/2 and arrange in ascending order

Answer 1

Answer:The answer is -7/18 and -8/18

Step-by-step explanation:

The LCM of 3 and 2 = 6

-1/3 becomes -2/6

-1/2 becomes -3/6

So, (2+1) = 3

-2/6 * 3/3 = -6/18

-3/6 * 3/3 = -9/18

The two rational numbers are

-7/18 and -8/18

HOPE THAT IT HELPS

Answer 2

Given: Two rational numbers-  $\frac{-1}{3}$ and $\frac{-1}{2}$

To find: Two rational numbers between the given numbers

Solution:

The given rational numbers have different denominators. First we need to make their denominators same.

LCM of their denominators 3 and 2 = 6

To convert the rational numbers with same denominators, we have

$\frac{-1}{3} = \frac{-1}{3}$ × $\frac{2}{2} = \frac{-2}{6}$ and $\frac{-1}{2} = \frac{-1}{2}$ × $\frac{3}{3} = \frac{-3}{6}$

To insert two rational numbers, we need to multiply both numerator and denominator of each rational number by 2 + 1 i.e., 3.

We get $\frac{-2}{6} = \frac{-2}{6}$ × $\frac{3}{3} = \frac{-6}{18}$ and $\frac{-3}{6} = \frac{-3}{6}$ × $\frac{3}{3} = \frac{-9}{ 18}$

We see that -8 and -7 are two integers between -9 and -6.

(The largest number becomes the smallest number on having -ve sign)

i.e., $\frac{-9}{18} < \frac{-8}{18} < \frac{-7}{18} < \frac{-6}{18}$ (Arranged in ascending order)

Hence, two rational numbers between $\frac{-1}{2} \ and \ \frac{-1}{3}$ are:

$\frac{-8}{18} \ and \ \frac{-7}{18}$