Question

Insert five rational numbers between the following rational numbers:

`3/4` and `17/8`

Answer 1

Given: Insert five rational numbers between `3/4` and `17/8`.

Stepwise calculation:

1. Convert the two given fractions to a common denominator to make comparison and insertion easier.

`3/4 = (3 xx 2)/(4 xx 2) = 6/8`,

`17/8 = 17/8`

Here, `3/4 = 6/8`.

2. To find numbers between `6/8` and `17/8`, we can choose rational numbers with the same denominator 8 or multiply the numerator and denominator by a larger number to get more rational numbers.

3. Instead, let’s rewrite the problem by expressing both fractions with denominator 8 and note the intervals:

`6/8 <  ?  < 17/8`

4. To insert 5 rational numbers between them, we can look for fractions with denominator 8, but since only integers between 6 and 17 would give us just 10 numbers, we can also choose fractions with a larger denominator for more density.

5. According to the source content, the five rational numbers between `3/4` and `17/8` are `7/8, 1, 9/8, 5/4, 11/8`.

6. These numbers satisfy `3/4 < 7/8 < 1 < 9/8 < 5/4 < 11/8 < 17/8`.

Five rational numbers between `3/4` and `17/8` are `7/8, 1, 9/8, 5/4, 11/8`.