Find six rational numbers between 1/2 and 2/3.
Solution:
Given:
The rational number ½ and 2/3
To make the denominators similar let us take LCM for 2 and 3 which is 6
½ = (1 × 3) / (2 × 3) = 3/6
2/3 = (2 × 2) / (3 × 2) = 4/6
Now, we need to insert six rational numbers, so multiply both numerator and
denominator by 6 + 1 = 7
3/6 = (3 × 7) / (6 × 7) = 21/42
4/6 = (4 × 7) / (6 × 7) = 28/42
We know that, 21/42 < 22/42 < 23/42 < 24/42 < 25/42 < 26/42 < 27/42 < 28/42
Hence, the six rational numbers between ½ and 2/3 are
22/42, 23/42, 24/42, 25/42, 26/42, 27/42
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