Question

Write the following rational numbers in ascending and descending order.

$\frac{- 3}{5}, \frac{7}{- 10}, \frac{- 15}{20}, \frac{14}{- 30}, \frac{- 8}{15}$

Accepted Answer

Given,

$\frac{- 3}{5}, \frac{7}{- 10}, \frac{- 15}{20}, \frac{14}{- 30}, \frac{- 8}{15}$

First make the denominators to be positive and write the numbers in standard form as $\frac{- 3}{5}, \frac{- 7}{10}, \frac{- 15}{20}, \frac{- 14}{30}, \frac{- 8}{15}$ .

We have to find the LCM of $5, 10, 15, 20$ and $30$ .

$\begin{matrix} 5 & 5, 10, 15, 20, 30 \\ 2 & 1, 2, 3, 4, 6 \\ 2 & 1, 1, 3, 2, 3 \\ 3 & 1, 1, 3, 1, 3 \\ 1, 1, 1, 1, 1 \end{matrix}$

So, $LCM$ of $5, 10, 15, 20, 30 = 5 \times 2 \times 2 \times 3 = 60$

Change the given rational numbers in equivalent form with common denominator $60$ .

$\begin{aligned} \frac{- 3}{5} \\ = \frac{- 3}{5} \times \frac{12}{12} \\ = \frac{- 36}{60} \end{aligned} \begin{aligned} \frac{- 7}{10} \\ = \frac{- 7}{10} \times \frac{6}{6} \\ = \frac{- 42}{60} \end{aligned} \begin{aligned} \frac{- 15}{20} \\ = \frac{- 15}{20} \times \frac{3}{3} \\ = \frac{- 45}{60} \end{aligned} \begin{aligned} \frac{- 14}{30} \\ = \frac{- 14}{30} \times \frac{2}{2} \\ = \frac{- 28}{60} \end{aligned} \begin{aligned} \frac{- 8}{15} \\ = \frac{- 8}{15} \times \frac{4}{4} \\ = \frac{- 32}{60} \end{aligned}$

Comparing the numerators alone, that is, $- 36, - 42, - 45, - 28$ and $- 32$ , we see that
$- 45 < - 42 < - 36 < - 32 < - 28$

Hence, $\frac{- 45}{60} < \frac{- 42}{60} < \frac{- 36}{60} < \frac{- 32}{60} < \frac{- 28}{60}$ and so, $\frac{- 15}{20} < \frac{7}{- 10} < \frac{- 3}{5} < \frac{- 8}{15} < \frac{14}{- 30}$ .

So, the ascending order is $\frac{- 15}{20}, \frac{7}{- 10}, \frac{- 3}{5}, \frac{- 8}{15}$ and $\frac{14}{- 30}$ .

Also, its reverse order gives the descending order as $\frac{14}{- 30}, \frac{- 8}{15}, \frac{- 3}{5}, \frac{7}{- 10}$ and $\frac{- 15}{20}$ .

Tamil Nadu Board Solutions for Chapter: Numbers, Exercise 7: Example

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Numbers, Exercise 7: Example

Questions from Tamil Nadu Board Solutions for Chapter: Numbers, Exercise 7: Example with Hints & Solutions

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