Question

Arrange the following rational numbers in ascending order-
3/-5,-9/10,-14/15,-17/20

Answer 1

Given Information :

Given rational numbers,

• $\sf{ \dfrac{3}{ - 5} , \dfrac{ - 9}{10} , \dfrac{ - 14}{15} , \dfrac{ - 17}{20} }$

To find :

• Arrange the given rational numbers numbers in ascending order.

Clarification :

Here, we are provided some rational numbers. We are asked to arrange them in ascending order. In order to arrange them in ascending order, we'll make the denominator of the given rational numbers same.

How to make denominators same of different rational numbers?

• To make the denominators same of different rational numbers, we firstly the the L.C.M of the numbers in the denominators of the given rational numbers. After that, we multiply a same number with both the denominator and the numerator of the rational numbers such that their denominators become same.

So, let's commence the steps!

Explication of steps :

We know that,

• $\sf{ \dfrac{a}{ - b} = \dfrac{ - a}{b} }$

So, $\sf{ \dfrac{3}{ - 5} }$ can be written as $\sf{ \dfrac{-3}{ 5} }$.

Now, making the denominators of the rational numbers equal.

LCM of 5,10,15 and 20 is 60. Now, we have to multiply a same number with denominator and the numerator of the given rational numbers such that their denominator becomes 60.

First rational number :

$\longrightarrow \sf{ \dfrac{-3}{ 5} = \dfrac{ - 3 \times 12 }{5 \times 12 } }$

$\longrightarrow \sf{ \dfrac{-3}{ 5} = \dfrac{ - 36 }{60} }$

Second rational number :

$\longrightarrow \sf{ \dfrac{-9}{ 10} = \dfrac{ - 9 \times 6 }{10 \times 6 } }$

$\longrightarrow \sf{ \dfrac{-9}{ 10} = \dfrac{ - 54}{60} }$

Third rational number :

$\longrightarrow \sf{ \dfrac{-14}{ 15} = \dfrac{ - 14 \times 4}{15 \times 4} }$

$\longrightarrow \sf{ \dfrac{-14}{ 15} = \dfrac{ - 56}{60} }$

Fourth rational number :

$\longrightarrow \sf{ \dfrac{-17}{ 20} = \dfrac{ - 17 \times 3}{20 \times 3} }$

$\longrightarrow \sf{ \dfrac{-17}{ 20} = \dfrac{ - 51}{60} }$

❖ Arranging them in ascending order :

• Since, all the numbers are negative rational numbers.

$\longrightarrow \sf{ \dfrac{ - 56}{60} }$ < $\sf{ \dfrac{ - 54}{60} }$ < $\sf{ \dfrac{ - 51}{60} }$ < $\sf{ \dfrac{ - 36 }{60} }$

$\longmapsto \underline{\boxed{\sf{ \dfrac{-14}{ 15} < \dfrac{ - 9}{10} < \dfrac{ - 17}{20} , \dfrac{ 3}{-5} }} } \; \; \bigstar$

Answer 2

Answer:

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