Question

FIND TWO RATIONAL NUMBERS BETWEEN :
2/5 AND 3/10

Answer 1

Step-by-step explanation:

2/5=2×10/5×10=20/50

3/10=3×5/10×5=15/50

the rational numbers between 20/50&15/50 are

18/50&17/50

Answer 2

Two rational numbers between $\frac {2}{5}$ and $\frac {3}{10}$ are $\frac {7}{20}$ and $\frac {15}{40}$.

Concept used:

Mid-value method:

If p and q are two rational numbers then $\frac {p + q}{2}$ is between p and q such that $p < \frac {p + q}{2} < q$.

By the repeated use of the above property, we can say that there are infinitely many rational numbers between two rational numbers.

Given: Two rational numbers $\frac {2}{5}$ and $\frac {3}{10}$

To find: 2 rational numbers between  $\frac {2}{5}$ and $\frac {3}{10}$

Solution:

Step1: First rational number between $\frac {2}{5}$ and $\frac {3}{10}$:

$\frac {1}{2}(\frac {2}{5} + \frac {3}{10}) = \frac {1}{2}(\frac {2 \times 2}{5 \times 2} + \frac {3}{10}) \\\\= \frac {1}{2}(\frac {4}{10} + \frac {3}{10}) \\\\= \frac {1}{2}(\frac {4 \ + \ 3}{10}) \\\\= \frac {1}{2}(\frac {7}{10}) \\\\= \frac {7}{20}$

Step 2: Second rational number between $\frac {2}{5} \ and \ \frac {7}{20}$ :

$\frac {1}{2}(\frac {2}{5} + \frac {7}{20}) = \frac {1}{2}(\frac {2 \times 4}{5 \times 4} + \frac {7}{20}) \\\\= \frac {1}{2}(\frac {8}{20} + \frac {7}{20}) \\\\= \frac {1}{2}(\frac {8 \ + \ 7}{20}) \\\\= \frac {1}{2}(\frac {15}{20} )\\\\= \frac {15}{40}$

Hence two rational numbers between $\frac {2}{5} \ and \ \frac {3}{10}$ are $\frac {7}{20} \ and \ \frac {15}{40}.$

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