Question

find two rational number between 1/3 and 2/5​

Answer 1

Given :

• 1st rational number = 1/3
• 2nd rational number = 2/5

To Find :

• Two rational number between the given rational number.

Solution :

First we convert given rational numbers to rational number with the same denominator equal to the LCM (Lowest Common Factor) of their denominator. The LCM of denominator 3 and 5 is 15.

⠀⟶⠀1/3 = 1 × 5/3 × 5 = 5/15

⠀⟶⠀2/5 = 2 × 3/5 × 3 = 6/15

Between the numerator 5 and 6 of these equivalent rational numbers there is no Integer. So, we replace these numbers by equivalent rational numbers having a sufficiently large common denominator.

⠀⟶⠀5/15 = 5 × 3/15 × 3 = 15/45

⠀⟶⠀6/15 = 6 × 3/15 × 3 = 18/45

Between 15 and 18 there are two integer 16 and 17.

⛬ Two Rational numbers between 1/3 and 2/5 are 16/45 and 17/45

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Answer 2

Given :

1st rational number = 1/3

2nd rational number = 2/5

To Find :

Two rational number between the given rational number.

Solution :

First we convert given rational numbers to rational number with the same denominator equal to the LCM (Lowest Common Factor) of their denominator. The LCM of denominator 3 and 5 is 15.

⠀⟶⠀1/3 = 1 × 5/3 × 5 = 5/15

⠀⟶⠀2/5 = 2 × 3/5 × 3 = 6/15

Between the numerator 5 and 6 of these equivalent rational numbers there is no Integer. So, we replace these numbers by equivalent rational numbers having a sufficiently large common denominator.

⠀⟶⠀5/15 = 5 × 3/15 × 3 = 15/45

⠀⟶⠀6/15 = 6 × 3/15 × 3 = 18/45

Between 15 and 18 there are two integer 16 and 17.

⛬ Two Rational numbers between 1/3 and 2/5 are 16/45 and 17/45

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Hope it will helps you ❤️