Question

insert 2 rational numbers between -⅔ and -1

Wrong answers will be reported and correct one's will be marked as brainlist​

Answer 1

Given:-

$\frac{ - 2}{3} \: and \: - 1$

To Find:-

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

Solution:-

$\frac{ - 2}{3} \: and \: - 1 \\ \\ \frac{ - 2}{3} \: and \: \frac{ - 1}{1} \\ \frac{ - 2}{3} \times 1 \: \: and \: \: \frac{ - 1}{1} \times 3 \\ \frac{ - 2}{3} \: and \: \frac{ - 3}{3} \\ not \: appropriate \\ \\ \frac{ - 2}{3} \times 4 \: \: and \: \: \frac{ - 3}{ 3} \times 4 \\ \frac{ - 8}{12} \: \: and \: \: \frac{ - 12}{12}$

∴Hence,Answer will be$\frac{ - 9}{12} \: \: and \: \: \frac{ - 10}{12} \: or \: \\ \frac{ - 10}{12} \: \: and \: \: \frac{ - 11}{12}$

Answer 2

Answer:

The two rational numbers are: $\frac{-25}{30} and \frac{-27}{30}$.

Step-by-step explanation:

1. Find the LCM

The LCM of the numbers $\frac{-2}{3}$ and -1 is 3.

Therefore,

⇒ $\frac{-2}{3}$ =

⇒ -1 = ($\frac{-1}{1}$ )× 3 = $\frac{-3}{3}$

2. Find two rational numbers between the numbers found in the previous step.

The two numbers we found in the previous step are $\frac{-2}{3}$ and $\frac{-3}{3}$.

As we can see the difference between the two numerators is very less, so we can multiply each number by 10 to obtain the 2 rational numbers.

⇒ ($\frac{-2}{3}$) × 10 = $\frac{-20}{30}$

⇒ $\frac{-3}{3}$ × 10 = $\frac{-30}{30}$

Now, the rational numbers become $\frac{-20}{30}$ and $\frac{-30}{30}$.

Hence ,

⇒ the two rational numbers between $\frac{-20}{30} and \frac{-30}{30}$ is $\frac{-25}{30} and \frac{-27}{30}$.

therefore, the two rational numbers between $\frac{-2}{3} and -1$ is $\frac{-25}{30} and \frac{-27}{30}$.