Question

Write the following rational numbers in descending order :
(i) 7/9, -3/5, -2/4
(ii) 3/5, 5/7, -2/5
(iii) 3/-5, -13/15, 2/-5
​

Answer 1

(i).,-3/5,-2/4,7/9

(ii).-2/5,3/5,5/7

(iii).-13/15,3/-5,2/-5

Answer 2

➤ Answer :-

$\tt\longrightarrow \dfrac{7}{9} \: ; \: \dfrac{( - 3)}{5} \: ; \: \dfrac{( - 2)}{4}$

Convert them into like fractions by taking the LCM of the denominators i.e, 9,5 and 4.

LCM of 9,5 and 4 is 180.

$\tt \longrightarrow \dfrac{7 \times 20}{9 \times 20} \: ; \: \dfrac{( - 3) \times 36}{5 \times 36} \: ; \: \dfrac{( - 2) \times 45}{4 \times 45}$

$\tt \longrightarrow \dfrac{140}{180} \: ; \: \dfrac{( - 108)}{180} \: ; \: \dfrac{( - 90)}{180}$

$\tt \longrightarrow \dfrac{140}{180} \: \boxed{ > } \: \dfrac{( - 90)}{180} \: \boxed{ > } \: \dfrac{( - 108)}{180}$

$\tt \longrightarrow \boxed{ \tt\dfrac{7}{9} \: \boxed{ > } \: \dfrac{( - 2)}{4} \: \boxed{ > } \: \dfrac{( - 3)}{5} }$

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$\tt\longrightarrow\dfrac{3}{5} \: ; \: \dfrac{5}{7} \: ; \: \dfrac{( - 2)}{5}$

Convert them into like fractions by taking the LCM of the denominators i.e, 5 and 7.

LCM of 5 and 7 is 35.

$\tt \longrightarrow \dfrac{3 \times 7}{5 \times 7} \: ; \: \dfrac{5 \times 5}{7 \times 5} \: ; \: \dfrac{( - 2) \times 7}{5 \times 7}$

$\tt \longrightarrow \dfrac{21}{35} \: ; \: \dfrac{25}{35} \: ; \: \dfrac{( - 14)}{35}$

$\tt \longrightarrow \dfrac{25}{35} \: \boxed{ > } \: \dfrac{21}{35} \: \boxed{ > } \: \dfrac{( - 14)}{35}$

$\tt \longrightarrow \boxed{ \tt\dfrac{5}{7} \: \boxed{ > } \: \dfrac{3}{5} \: \boxed{ > } \: \dfrac{( - 2)}{5} }$

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$\tt\longrightarrow \dfrac{3}{( - 5)} \: ; \: \dfrac{( - 13)}{15} \: ; \: \dfrac{2}{( - 5)}$

Convert them into like fractions by taking the LCM of the denominators i.e, (-5) and 15.

LCM of (-5) and 15 is 15.

$\tt\longrightarrow \dfrac{3 \times ( - 3)}{( - 5) \times ( - 3)} \: ; \: \dfrac{( - 13)}{15} \: ; \: \dfrac{2 \times ( - 3)}{( - 5) \times ( - 3)}$

$\tt\longrightarrow \dfrac{( - 9)}{15} \: ; \: \dfrac{( - 13)}{15} \: ; \: \dfrac{( - 10)}{15}$

$\tt\longrightarrow \dfrac{( - 9)}{15} \: \boxed{ > } \: \dfrac{( - 10)}{15} \: \boxed{ > } \: \dfrac{( - 13)}{15}$

$\tt\longrightarrow \boxed{ \tt \dfrac{3}{( - 5)} \: \: \dfrac{2}{( - 5)} \: \: \dfrac{( - 13)}{15} }$

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$\dashrightarrow$Remember…………

• While comparing or arranging the fractions in ascending and descending order, if the denominators are different i.e, if they are unlike fraction, we should convert them to like fractions by taking the LCM of the denominators. Then we can compare or arrange them in ascending and descending order.
• If the given rational numbers are having the same denominators i.e, if they are like fractions, we can compare or arrange them in ascending and descending order easily by looking to the numerators.