Question

Which of the following rational number is the greatest?(a)-17/24 (b) -13/16 (c)7/-8 (d) -31/32

Answer 1

Answer:

a) -17/24

Step-by-step explanation:

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Answer 2

Given: Four rational numbers-  $\frac{-17}{24}, \frac{-13}{16}, \frac{7}{-8} \ and \ \frac{-31}{32}$

To find: Which of the given rational numbers is the greatest

Solution:

The given rational numbers have different denominators. First we need to make their denominators same so that we can compare them based on their numerators.

LCM of their denominator 24, 16, 8 and 32 = 96

To convert the rational numbers with same denominator, we have

$\frac{-17}{24} = \frac{-17}{24}$ × $\frac{4}{4} = \frac{-68}{96}$

$\frac{-13}{16} = \frac{-13}{16}$ × $\frac{6}{6} = \frac{-78}{96}$

$\frac{7}{-8} = \frac{7}{-8}$ × $\frac{-12}{-12} = \frac{-84}{96}$

$\frac{-31}{32} = \frac{-31}{32}$ × $\frac{3}{3} = \frac{-93}{96}$

We observe that, -68 > -78 > -84 > -93

i.e., $\frac{-68}{96}$ is the greatest

Hence, the greatest rational number is $\frac{-17}{24}$