Question

Find five rational number between 3/5 and 5/6

Answer 1

SOLUTION

TO DETERMINE

The five rational number between $\displaystyle \sf{ \frac{3}{5} \: \: \: and \: \: \frac{5}{6} }$

CONCEPT TO BE IMPLEMENTED

Rational Number

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

EVALUATION

Here the given numbers are

$\displaystyle \sf{ \frac{3}{5} \: \: \: and \: \: \frac{5}{6} }$

So the denominators are 5 and 6

LCM of the denominators = 30

Now

$\displaystyle \sf{ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} }$

$\displaystyle \sf{ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} }$

Hence the required five rational numbers are

$\displaystyle \sf{ \frac{19}{30} \: , \: \frac{20}{30} \:, \: \frac{21}{30} \: , \: \frac{22}{30} \: , \: \frac{23}{30} }$

Which can be rewritten as

$\displaystyle \sf{ \frac{19}{30} \: , \: \frac{2}{3} \:, \: \frac{7}{10} \: , \: \frac{11}{15} \: , \: \frac{23}{30} }$

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Answer 2

Step-by-step explanation:

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