State true or false: Four rational numbers between $57$ and $78$ and are $4156, 4256, 4356, 4456$ are .

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Detailed Solution

Here, we are given two rational numbers as

57

and

78

, and we have to list four rational numbers between these two numbers.
We know that rational numbers are always in the form of ration of two integers, i.e.,

p q

, where p and q are integers and q is non-zero.
So, in order to get numbers of this form, we will first make the denominators of the two given rational numbers same, and then list four rational numbers which lie between them. So,

5 × 8 7 × 8 = 4056 7 × 7 8 × 7 = 4956

Now, we can observe that the denominators of the given rational numbers are now the same and there is a difference of (49 – 40 =) 9 in between the numerators.
This means that there are 9 rational numbers lying between