State true or false: The ascending order of the rational numbers $− 7 10$ , $5 − 8$ , , $2 − 3$ , , $− 1 4$ , and $− 3 5$ and is $− 84 120 < − 80 120 < − 75 120 < − 72 120 < − 30 120$ is

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True

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answer is A.

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Detailed Solution

The given rational numbers are as follows,

− 7 10

5 − 8

2 − 3

− 1 4

and

− 3 5

In order to arrange them in ascending order, we need to make their denominators the same.
For that, we will take the LCM of the denominators of each of the given fractions by prime factorisation as follows,

10 = 2 × 5 × 1 8 = 2 × 2 × 2 × 1 3 = 3 × 1 4 = 2 × 2 × 1 5 = 5 × 1

So, the LCM of the denominators will be,

23 × 5 × 3 = 8 × 15 = 120

Using this LCM, we can rewrite the given fractions as follows,

(− 7 × 12), (− 5 × 15), (− 2 × 40), (− 1 × 30), (− 3 × 24) 120 − 84, − 75, − 80, − 30, − 72 120 − 84 120, − 75 120, − 80 120, − 30 120, − 72 120

Rearranging them in the ascending order, we get,

− 84 120 < − 80 120 < − 75 120 < − 72 120 < − 30 120

So, it can be observed that the order as obtained above is the same as mentioned in the statement.
Hence, the statement is true.
Hence, the correct option is (1).

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