Question

find three rational number between -1&1 with photo &process​

Answer 1

Answer:

• if a/b and c/d are two rational numbers, such that a/b<c/d, then 1/2(a/b+c/d) is a rational number lying between a/b and c/d

Answer 2

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Question :-

Find three rational numbers between -1 & 1 .

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Answer :-

Given :-

- 1 & 1

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Required to find :-

• Three rational numbers between them .

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Solution :-

In the question it is given and asked that ,

Find three rational numbers between - 1 & 1 .

We can solve this question in 2 methods .

So, let's start with the first method .

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First Method :-

As it given that find three rational numbers between - 1 & 1 .

( Just refer to the number line in the attachment )

However,

From the Number line we now that ;

Between -1 % 1 there is a number 0 (zero).

So,

The first rational number is 0 .

Similarly,

Observe the number line and consider -1 & 0 .

Here, the decimal numbers play a major role .

So, as we know there is a decimal number - 0.5 between -1 & 0 .

Hence, 2nd Rational number is - 0.5

(here why I took - 0.5 is because 0.5 is exactly a middle number )

Similarly,

Now consider 0 & 1 .

So,

However we know that ,

0.5 is the number which exactly lies between 0& 1

Hence, third rational number is 0.5 .

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2. Second Method :

The method which we are using now is popularly know as the mean method for finding rational numbers between any given numbers .

So, In this mean method we have to use an formula to find the rational numbers between any two rational numbers "a" and "b" is ;

$\mathrm{\dfrac{a + b}{2}}{\longleftarrow}$

Here, a & b refers to the given rational numbers .

Here, is the solution .

We know that,

First , rational number lies between - 1 and 1 .

So,

$\longrightarrow{\mathrm{ \dfrac{-1 + 1}{2}}}$

$\Rightarrow{\mathrm{ \dfrac{0}{2}}}$

Any number which divides zero will become zero .

$\red{\implies{\tt{0}}}$

So, first rational number is 0 .

similarly, 2nd rational number lies between -1 and 0 .

So,

$\longrightarrow{\mathrm{ \dfrac{-1 + 0 }{2}}}$

$\longrightarrow{\mathrm{ \dfrac{-1}{2}}}$

For a bit simplicity we don't change the fraction into decimal .

(But actually -1/2 = -0.5)

Hence,

$\red{\implies{\tt{ \dfrac{-1}{2}}}}$

So, second rational number is -1/2 .

Similarly,

3rd rational number lies between 0 & 1 .

So,

$\longrightarrow{\mathrm{ \dfrac{0 + 1}{2}}}$

$\longrightarrow{\mathrm{\dfrac{ 1 }{2}}}$

(Actually 1/2 is 0.5)

$\red{\implies{\tt{ \dfrac{1}{2}}}}$

So, third rational number is 1/2 .

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Points to remember :-

1. These are 2 methods in which we can use solve these questions .

2. But mostly widely accepted method is the 2nd method that is mean method .

3. so always try using mean method .

4. Remember, don't convert the fraction into decimal untill or unless it is mentioned .

This actually simplifies our work .

5. Don't forgot to refer to the attachment .

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