Question

Insert 3 rational numbers between `3/7` and `7/9`.

Answer 1

To insert 3 rational numbers between `3/7` and `7/9`, let’s follow these steps:

Step 1: Convert both fractions to have a common denominator.

The denominators of `3/7` and `7/9` are 7 and 9.

The LCM (least common multiple) of 7 and 9 is 63. 

Let’s convert both fractions to have a denominator of 63.

Convert `3/7` to a denominator of 63:

`3/7 = (3 xx 9)/(7 xx 9) = 27/63`

Convert `7/9` to a denominator of 63:

`7/9 = (7 xx 7)/(9 xx 7) = 49/63`

Now we have:

`27/63` and `49/63`

Step 2: Identify three rational numbers between `27/63` and `49/63`.

These rational numbers will have numerators between 27 and 49.

Three examples are:

1. `29/63`

2. `31/63`

3. `32/63`

The three rational numbers between `3/7` and `7/9` are `29/63, 31/63, 32/63`.