Question

2. Write the following rational numbers in ascending order.
(i) -4/5, -2/5, -3/5
(ii) 2/3, -2/9, -5/3
(iii) -4/7, -4/3, -4/2​

Answer 1

Answer:

(i) -4/5, -3/5, -2/5

(ii) -5/3, -2/9, 2/3

(iii) -4/2, -4/3, -4/7

Answer 2

➤ Answer :-

$\tt\longrightarrow \dfrac{( - 4)}{5} \: ; \: \dfrac{( - 2)}{5} \: ; \: \dfrac{( - 3)}{5}$

We can compare the given fractions easily by looking to the numerators, because they are like fractions.

$\tt\longrightarrow \boxed{ \tt \frac{( - 4)}{5} \: \boxed{<} \: \frac{( - 3)}{5} \: \boxed{<} \: \frac{( - 2)}{5} }$

━━━━━━━━━━━━━━━━━━

$\tt\longrightarrow \dfrac{2}{3} \: ; \: \dfrac{( - 2)}{9} \: ; \: \dfrac{( - 5)}{3}$

Convert them into like fractions by taking the LCM of the denominators i.e, 9 and 3.

LCM of 9 and 3 is 9.

$\tt\longrightarrow \dfrac{2 \times 3}{3 \times 3} \: ; \: \dfrac{( - 2)}{9} \: ; \: \dfrac{( - 5) \times 3}{3 \times 3}$

$\tt\longrightarrow \dfrac{6}{9} \: ; \: \dfrac{( - 2)}{9} \: ; \: \dfrac{( - 15)}{9}$

$\tt\longrightarrow \tt \dfrac{( - 15)}{9} \: \boxed{ < } \: \dfrac{( - 2)}{9} \: \boxed { < } \: \dfrac{6}{9}$

$\tt\longrightarrow \boxed{ \tt\dfrac{( - 5)}{3} \: \boxed {< }\: \dfrac{( - 2)}{9} \: \boxed {< } \: \dfrac{2}{3} }$

━━━━━━━━━━━━━━━━━━

$\tt\longrightarrow \dfrac{( - 4)}{7} \: ; \: \dfrac{( - 4)}{3} \: ; \: \dfrac{( - 4)}{2}$

Convert them into like fractions by taking the LCM of the denominators i.e, 7,3 and 2.

LCM of 7,3 and 2 is 42.

$\tt\longrightarrow \dfrac{( - 4) \times 6}{7 \times 6} \: ;\: \dfrac{( - 4) \times 14}{3 \times 14} \: ; \: \dfrac{( - 4) \times 24}{2 \times 24}$

$\tt\longrightarrow \dfrac{( - 24)}{48} \: ; \: \dfrac{( - 56)}{48} \: ; \: \dfrac{( - 96)}{48}$

$\tt\longrightarrow \dfrac{( - 96)}{48} \: \boxed{ < } \: \dfrac{( - 56)}{48} \: \boxed{ < } \: \dfrac{( - 24)}{48}$

$\tt\longrightarrow \boxed{ \tt\dfrac{( - 4)}{2} \: \boxed{ < } \: \dfrac{( - 4)}{3} \: \boxed{ < } \: \dfrac{( - 4)}{7} }$

━━━━━━━━━━━━━━━━━━

Remember…………

• While comparing the fractions or arranging the fractions in ascending and descending order, if the rational numbers are not having the same denominators i.e, if they are not unlike fractions, we should convert them to like fractions by taking the LCM of the denominators, and then compare and arrange them in ascending or descending order.
• If the rational numbers are having the same denominators i.e, if they are like fractions, we can compare and arrange them in ascending or descending order easily by looking into the numerators.