Question

Find any ten rational number between
- 1/3 and 1/3

Plzzzz solve it
Who solve this he was genius.....

Answer 1

we want 10 number between them

so we will multiply it with 11

-1/3×11/11=-11/33

1/3×11/11=11/33

now we can write any 10 no. between them

-10/33, -9/33,-8/33,-7/33,-6/33,-5/33,-4/33,-3/33,-2/33,-1/33

Answer 2

For finding the rational numbers between $\frac{-1}{3} \:\&\: \frac{1}{3}$ just increase the denominator but they should be equal.

For your simplicity, always multiply the denominators which number 10, 100, 1000 and so on. Why this only?

You can use not only for our simplicity, but also they are quite easy to use and understand.

Here the doubt arises that, both the fractions have the same denominator but why should we have to multiply?

Because, we (for our simplicity) always like to write whole numbers.

But if we won't get 10 whole numbers. We would get decimal numbers.

So, multiplying 10 to both the numerator as well as denominator in both the fractions.

(i) $\frac{-1}{3} = \frac{-1 \times 10}{3 \times 10} = \frac{-10}{30}$

(ii) $\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}$

Now there are infinite numbers between this two new numbers i.e., $\frac{-10}{30} \:\&\: \frac{10}{30}$

Therefore, the ten rational numbers between $\frac{-10}{30} \:\&\: \frac{10}{30}$ are,

$\frac{-9}{30}, \frac{-8}{30}, \frac{-7}{30}, \frac{-6}{30}, \frac{1}{30}, \frac{3}{30}, \frac{4}{30}, \frac{5}{30}, \frac{6}{30}, \frac{7}{30}$