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Question
Which is greater in the following?
`-3 5/7, 3 1/9`
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Solution
Given rational numbers are `-3 5/7` and `3 1/9`
Here, `-3 5/7 = - ([(3) xx 7 + 5])/7 = (-[(21) + 5])/7 = (-26)/7`
Also, `3 1/9 = ([3 xx 9 + 1])/9 = (27 + 1)/9 = 28/9`
So, the rational numbers can be written as `(-26)/7` and `28/9`
`(-26)/7 = (-26 xx 9)/(7 xx 9) = - 234/63` and `28/9 = (28 xx 7)/(9 xx 7) = 196/63` ...[∵ LCM of 7 and 9 = 63]
∴ 196 > –234 ...[Since, the denominators of both rational numbers are same]
So, `3 1/9 > - 3 5/7`
Hence, the greater number is `3 1/9`.
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