Question

find four rational number between 3/4 and 2/3 plz explain this ​

Answer 1

For finding the rational numbers between any two numbers just make the denominators of both the fractions same.

 

For your ease of calculation, just multiply 10, 100, 1000 and so on numbers with the denominator so that, you wouldn't have to think or calculate much.

If the denominator is one - digit number so, multiply it with 10. If it's a two - digit number, then multiply it with 2, and so on.

Here, the denominator is a one - digit number, multiply it with 10. Not only just multiply 10 with denominator, also multiply 10 with the numerator for getting equivalent fraction.

So, multiplying 10 with both the numerator as well as denominators of both the fractions.

(i) $\frac{3}{4} = \frac{3 \times 10}{4 \times 10} = \frac{30}{40}$

(ii) $\frac{2}{3} = \frac{2 \times 10}{3 \times 3} = \frac{20}{30}$

But still here the denominator aren't same. So, try to make them same.

For making them same, multiply them with their LCM.

Here, the LCM of 40 and 30 is 120.

How to find LCM?

Just write all the factors of 40 and 30. Observe that, which digit comes first in both the numbers.

So, by multiplying 4 with $\frac{20}{30}$ and multiplying 3 with $\frac{30}{4}$, we get,

(i) $\frac{30}{40} = \frac{30 \times 3}{40 \times 3} = \frac{90}{120}$

(ii) $\frac{20}{30} = \frac{20 \times 4}{30 \times 4} = \frac{80}{120}$

Now, as their denominators are same, we can easily find out any four rational numbers between $\frac{90}{120} \:\&\: \frac{80}{120}$

As we know, there lie infinite numbers between any two numbers.

So, write any four numbers between $\frac{90}{120} \:\&\: \frac{80}{120}$.

So, the four rational numbers lying between $\frac{90}{120} \:\&\: \frac{80}{120}$ are,

$\frac{81}{120}, \frac{82}{120}, \frac{83}{120} \:\&\: \frac{84}{120}$.