Question

यदि परिमेय संख्या a/36, परिमेय संख्या1/9 और 1/4 के बीच में स्थित है ,तो a का सबसे बड़ा संभावित मान क्या होगा

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{a}{36} }$ is a rational number lies between $\displaystyle \sf{ \frac{1}{9} }$ & $\displaystyle \sf{ \frac{1}{4} }$

TO DETERMINE

The greatest value of a

EVALUATION

Here the given rational numbers are

$\displaystyle \sf{ \frac{1}{9} }$ & $\displaystyle \sf{ \frac{1}{4} }$

So the denominators are 4 and 9

LCM of the denominators = 36

$\displaystyle \sf{ \frac{1}{9} = \frac{1 \times 4}{9 \times 4} = \frac{4}{36} }$

$\displaystyle \sf{ \frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36} }$

Now by the given condition

$\displaystyle \sf{ \frac{1}{9} < \frac{a}{36} < \frac{1}{4} }$

$\displaystyle \sf{ \implies \: \frac{4}{36} < \frac{a}{36} < \frac{9}{36} }$

$\displaystyle \sf{ \implies \: 4 < a < 9}$

Thus a = 5 , 6 , 7 , 8

Hence the required greatest value of a = 8

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