Question

Insert two rational numbers between
and
and arrange in ascending order
.​

Answer 1

SOLUTION

TO DETERMINE

• Insert two rational numbers between $\displaystyle \sf{ \frac{1}{3} \: \: and \: \: \frac{1}{4} }$

• Arrange in ascending order

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 rational numbers are

$\displaystyle \sf{ \frac{1}{3} \: \: and \: \: \frac{1}{4} }$

Denominators of the given numbers are 3 & 4

LCM of the denominators = 12

Now

$\displaystyle \sf{ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} }$

$\displaystyle \sf{ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} }$

Now the given numbers can be rewritten as

$\displaystyle \sf{ \frac{1}{3} = \frac{4}{12} = \frac{20}{60} }$

$\displaystyle \sf{ \frac{1}{4} = \frac{3}{12} = \frac{15}{60} }$

Hence the required two rational numbers are

$\displaystyle \sf{ \frac{17}{60} \: \: and \: \frac{19}{60} }$

Now clearly we see that

$\displaystyle \sf{ \frac{1}{4} < \frac{17}{60} \: < \: \frac{19}{60} < \frac{1}{3} }$

So rearranging in ascending order we get

$\displaystyle \sf{ \frac{1}{4} \: , \: \frac{17}{60} \: , \: \frac{19}{60} \: , \: \frac{1}{3} }$

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