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Maths-

General

Easy

Question

Which of the two rational numbers is greater in the given pair $fraction numerator 9 over denominator negative 13 end fraction$ and $fraction numerator 7 over denominator negative 12 end fraction$

hint Hint:

Find the least common multiple of denominators.

The correct answer is: 9/-13

Given rational numbers are $fraction numerator 9 over denominator negative 13 end fraction$ and $fraction numerator 7 over denominator negative 12 end fraction$ .
Here, $fraction numerator 9 over denominator negative 13 end fraction equals fraction numerator 9 x minus 1 over denominator negative 13 x minus 1 end fraction equals fraction numerator negative 9 over denominator 13 end fraction$ and $fraction numerator 7 over denominator negative 12 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 12 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 12 end fraction$
So we have $fraction numerator negative 9 over denominator 13 end fraction$ and $fraction numerator negative 7 over denominator 12 end fraction$
By taking LCM of denominators 13 and 12, we get LCM as 156
On multiplying $fraction numerator negative 9 over denominator 13 end fraction$ with 12, we get $fraction numerator negative 9 cross times 12 over denominator 13 cross times 12 end fraction equals fraction numerator negative 108 over denominator 156 end fraction$
On multiplying $fraction numerator negative 7 over denominator 12 end fraction$ with 13, we get $fraction numerator negative 7 cross times 13 over denominator 12 cross times 13 end fraction equals fraction numerator negative 91 over denominator 156 end fraction$
On comparing the above fractions with same denominator,
we have -91 > -108
Hence $fraction numerator negative 91 over denominator 156 end fraction greater than fraction numerator negative 108 over denominator 156 end fraction equals fraction numerator 7 over denominator negative 12 end fraction greater than fraction numerator 9 over denominator negative 13 end fraction$

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