Question

Insert three rational numbers between 3\5 and 2\3.

Answer 1

Rational umber inserting = ( r + s ) / 2
= ( 3/5 + 2/3 ) ÷ 2
= ( 9 + 10 ) / 15 ÷ 2
= 19/15 × 1/2
= 19/30

In 3/5 and 19/30
= ( 3/5 + 19/30 ) ÷ 2
= 37/30 × 1/2
= 37/60

In 19/30 and 2/3

= ( 19/30 + 2/3 ) ÷ 2
= 39/30 × 1/2
= 39/60

3/5 < 37/60 < 38/30 < 39/60 < 2/3
Hence, three rational numbers are $\frac{37}{60},\frac{38}{30},\frac{39}{60}$.