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Maths-

General

Easy

Question

Which of the numbers $fraction numerator 3 over denominator negative 4 end fraction$ and $fraction numerator negative 5 over denominator 6 end fraction$ is greater

hint Hint:

Find the least common multiple of denominators.

The correct answer is: -5/6

Complete step by step solution:
Given rational numbers are $fraction numerator 3 over denominator negative 4 end fraction$ and $fraction numerator negative 5 over denominator 6 end fraction$ .
Here, $fraction numerator 3 over denominator negative 4 end fraction equals fraction numerator 3 cross times negative 1 over denominator negative 4 cross times negative 1 end fraction equals fraction numerator negative 3 over denominator 4 end fraction$
So we have $fraction numerator 3 over denominator negative 4 end fraction$ and $fraction numerator negative 5 over denominator 6 end fraction$
By taking LCM of denominators 4 and 6, we get LCM as 12
On multiplying $fraction numerator 3 over denominator negative 4 end fraction$ with 3, we get $fraction numerator negative 3 cross times 3 over denominator 4 cross times 3 end fraction equals fraction numerator negative 9 over denominator 12 end fraction$
On multiplying $fraction numerator negative 5 over denominator 6 end fraction$ with 2, we get $fraction numerator negative 5 cross times 2 over denominator 6 cross times 2 end fraction equals fraction numerator negative 10 over denominator 12 end fraction$
On comparing the above fractions with same denominator,
we have -9 > -10
Hence $fraction numerator negative 9 over denominator 12 end fraction greater than fraction numerator negative 10 over denominator 12 end fraction equals fraction numerator 3 over denominator negative 4 end fraction greater than fraction numerator negative 5 over denominator 6 end fraction$

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