Question

write five rational numbers between 2/3 and 3/4

Answer 1

to find these

1st u need to take L.C.M

LCM of the denominator u need to take
it means LCM of 3,4
u will get 12 as LCM

2/3=2/3×4/4=8/12
3/4=3/4×3/3=9/12

so multiply 8/12 and 9/12 by 11/11

u will get as:
8/12×11/11=88/132
9/12×11/11=99/132

So,the five rational numbers are 89/132,90/132,91/132,92/132,93/132

Answer 2

Concept:

A rational number is a number that can be represented in the form of p/q of two integers, where q ≠ 0.

Given:

2/3 and 3/4

Find:

We are asked to find five rational numbers between 2/3 and 3/4.

Solution:

We have,

2/3 and 3/4

Now,

The denominator of the given fractions are different,

So,

Multiply the numerator and denominator of 2/3 by 4,

We get,

= 8/12

Now,

Multiply the numerator and denominator of 3/4 by 3,

We get,

= 9/12

Now,

Multiply the numerator and denominator of the new fractions by 8,

We get,

i.e. (8/12) × 8 = 64/96

And,

(9/12) × 8 = 72/96

Now,

The rational number between 64/96 and 72/96,

i.e.

65/96, 66/96, 67/96, 68/96, 69/96, ...

So, these are the rational numbers between 2/3 and 3/4.

Hence, the rational numbers between 2/3 and 3/4 are 65/96, 66/96, 67/96, 68/96, and 69/96.

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