Question

Write ten rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$

Accepted Answer

Given: $\frac{1}{3}$ and $\frac{1}{2}$ .

Converting the given fractions with equivalent fractions with the denominator as $66,$ [LCM of $3$ and $2$ is $6,$ which is not sufficient to choose $10$ rational numbers between the given numbers. So, we shall choose denominator $= 6 \times 11 = 66$ ] we get,

$\frac{1}{3} = \frac{1 \times 22}{3 \times 22} = \frac{22}{66}$ and $\frac{1}{2} = \frac{1 \times 33}{2 \times 33} = \frac{33}{66}$ .

Now, we shall choose $23, 24, 25, 26, 27, 28, 29, 30, 31$ and $32$ as the numerators of the required ten rational numbers and $66$ will be the denominators for all of them.

Hence, the required ten rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ are $\frac{23}{66}, \frac{24}{66}, \frac{25}{66}, \frac{26}{66}, \frac{27}{66}, \frac{28}{66}, \frac{29}{66}, \frac{30}{66}, \frac{31}{66}, \frac{32}{66}$ or $\frac{23}{66}, \frac{4}{11}, \frac{25}{66}, \frac{13}{33}, \frac{9}{22}, \frac{14}{33}, \frac{29}{66}, \frac{5}{11}, \frac{31}{66}, \frac{16}{33} .$

Subject Experts Solutions for Chapter: Rational Numbers, Exercise 5: Worksheet 5

Subject Experts Mathematics Solutions for Exercise - Subject Experts Solutions for Chapter: Rational Numbers, Exercise 5: Worksheet 5

Questions from Subject Experts Solutions for Chapter: Rational Numbers, Exercise 5: Worksheet 5 with Hints & Solutions

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