Question

Find five rational number between 1 and 2

Answer 1

Hint: We first explain the general conditions to find the in between rational numbers. We convert them in fractions and find the equal forms in fraction. We find the in between numbers of the numerators keeping the denominator fixed.

Complete step-by-step answer:
To find in between rational numbers we first transform the given integers into fraction form by taking 1 as their denominator.
Then we add 1 to the numbers in between the rational numbers we needed.
Then we multiply the number with both denominator and numerator of the fractions.
To find five rational numbers between 1 and 2, we first convert them into fraction forms of $ \dfrac{1}{1} $ and $ \dfrac{2}{1} $ respectively.
Now we add 1 to 5 and get 6.
Now we have to multiply 6 to both denominator and numerator of the fractions of $ \dfrac{1}{1} $ and $ \dfrac{2}{1} $ .
Multiplying 6 we get $ \dfrac{1\times 6}{1\times 6}=\dfrac{6}{6} $ and $ \dfrac{2\times 6}{1\times 6}=\dfrac{12}{6} $ .
We can see that $ \dfrac{1\times 6}{1\times 6}=\dfrac{6}{6} $ and $ \dfrac{2\times 6}{1\times 6}=\dfrac{12}{6} $ are basically the extended form of 1 and 2 respectively.
We now take the in between numbers of the numerators keeping the denominator fixed.
So, the in between rational numbers are $ \dfrac{7}{6},\dfrac{8}{6},\dfrac{9}{6},\dfrac{10}{6},\dfrac{11}{6} $
So, the correct answer is “ $ \dfrac{7}{6},\dfrac{8}{6},\dfrac{9}{6},\dfrac{10}{6},\dfrac{11}{6} $ ”.

Note: We need to remember that the requirement of converting into fraction is to keep the denominator the same for all the fractions. So, in case of fractions we just need to care about their denominators.