Question

five rational numbers between 1/5 and 1/3 step by step explanation​

Answer 1

Answer Rational number between 1/5 and 1/3 =====:::

∆∆∆ 1/5x3/3=3/15

∆∆∆ 1/3x5/5= 5/15

l15x6/6 = 18/90

5/15x6/6= 30/90

Then -:

Rational Number Between 18/90 and 30/90

Are -:

19/90, 20/90, 21/90,22/90,23/90 etc is Rational number between 1/5 And 1/3

Answer 2

Given: Two rational numbers $\frac{1}{5}$ and $\frac{1}{3}$

To find: Five rational numbers between the given numbers

Solution:

The given rational numbers have different denominators.

Step 1: First we need to make their denominators same.

LCM of their denominators 3 and 5 = 15

Step 2: To convert the rational numbers with same denominators, we have

$\frac{1}{5} = \frac{1}{5}$ × $\frac{3}{3} = \frac{3}{15}$ and $\frac{1}{3} = \frac{1}{3}$ × $\frac{5}{5} = \frac{5}{15}$

Step 3: To insert five rational numbers, we need to multiply both numerator and denominator of each rational number by 5 + 1 i.e., 6.

$\frac{3}{15} = \frac{3}{15}$ × $\frac{6}{6} = \frac{18}{90}$ and $\frac{5}{15} = \frac{5}{15}$ ×  $\frac{6}{6} = \frac{30}{90}$

We see that 19, 20, 21...28 and 29 are the integers between 18 and 30.

i.e., $\frac{18}{90} < \frac{19}{90} < \frac{20}{90} < \frac{21}{90} < \frac{22}{90} < \frac{23}{90} < \frac{24}{90} < \frac{25}{90} < \frac{26}{90} < \frac{27}{90} < \frac{28}{90} < \frac{29}{90} < \frac{30}{90}$

We can choose any five rational numbers.

Hence, five rational numbers between the given numbers are:

$\frac{20}{90}, \frac{21}{90}, \frac{22}{90}, \frac{23}{90} \ and \ \frac{24}{90}$