Question

Which of the following rational numbers 4/9 _5/6 _7/12 11/_24

Answer 1

SOLUTION

TO DETERMINE

Which is smallest of the below rational numbers

$\displaystyle \sf{ \frac{4}{9} \: , \: - \frac{5}{6} \: ,\: - \frac{7}{12} \: ,\: \frac{11}{ - 24} }$

EVALUATION

Here the given rational numbers are

$\displaystyle \sf{ \frac{4}{9} \: , \: - \frac{5}{6} \: ,\: - \frac{7}{12} \: ,\: \frac{11}{ - 24} }$

Which can be rewritten as

$\displaystyle \sf{ \frac{4}{9} \: , \: - \frac{5}{6} \: ,\: - \frac{7}{12} \: ,\: - \frac{11}{ 24} }$

Now the denominators are 9 , 6 , 12 , 24

LCM of the denominators = 72

So the given numbers are reduced to

$\displaystyle \sf{ \frac{4}{9} = \frac{4 \times 8}{9 \times 8} = \frac{32}{72} }$

$\displaystyle \sf{ - \frac{5}{6} = - \frac{5 \times 12}{6 \times 12} = - \frac{60}{72} }$

$\displaystyle \sf{ - \frac{7}{12} = - \frac{7 \times 6}{12 \times 6} = - \frac{42}{72} }$

$\displaystyle \sf{ - \frac{11}{ 24} = - \frac{11 \times 3}{24 \times 3} = - \frac{33}{72} }$

Now

- 60 < - 42 < - 33 < 32

So we get

$\displaystyle \sf{ - \frac{5}{6} < - \frac{7}{12} < \frac{11}{ - 24} < \frac{4}{9} }$

Hence the required smallest rational number

$\displaystyle \sf{ - \frac{5}{6}}$

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