Question

The sum of two rational numbers is -5/11. If one of the number is -3/22, find the other.​

Answer 1

Answer:

Given :-

• The sum of two rational number is - 5/11.
• One of the number is - 3/22.

To Find :-

• What is the other rational number.

Solution :-

Let,

➲ Other rational number = x

Given :

• The sum of two numbers = - 5/11
• One of the number = - 3/22

According to the question,

$\implies \sf x + \bigg\{\dfrac{- 3}{22}\bigg\} =\: \dfrac{- 5}{11}$

$\implies \sf x - \dfrac{3}{22} =\: \dfrac{- 5}{11}$

$\implies \sf x =\: \dfrac{- 5}{11} + \dfrac{3}{22}$

$\implies \sf x =\: \dfrac{- 10 + 3}{22}$

$\implies \sf x =\: \dfrac{- 7}{22}$

$\sf\bold{\underline{\therefore\: The\: other\: rational\: number\: is\: \dfrac{- 7}{22}\: .}}$

__________________________________

VERIFICATION :-

$\leadsto \sf x + \bigg\{\dfrac{- 3}{22}\bigg\} =\: \dfrac{- 5}{11}$

By putting x = - 7/22 we get,

$\leadsto \sf \dfrac{- 7}{22} + \bigg\{\dfrac{- 3}{22}\bigg\} =\: \dfrac{- 5}{11}$

$\leadsto \sf \dfrac{- 7}{22} - \dfrac{3}{22} =\: \dfrac{- 5}{11}$

$\leadsto \sf \dfrac{- 7 - 3}{22} =\: \dfrac{- 10}{22}$

$\leadsto \sf \dfrac{- \cancel{10}}{\cancel{22}} =\: \dfrac{- 5}{11}$

$\leadsto \sf\bold{\purple{\dfrac{- 5}{11} =\: \dfrac{- 5}{11}}}$

Hence Verified !

Answer 2

Question :-

The sum of two rational numbers is $\frac{ - 5}{11}$. If one of the number is $\frac{ - 3}{22}$, find the other.

Answer :-

• The other rational number is -7/22

Step by step explanation :-

The sum of two rational number is -5/11, let's assume that the other rational number be x.

$\rm:\longmapsto{x + \bigg( \frac{ - 3}{22} \bigg) = \frac{ - 5}{11} }$

On opening bracket,

$\rm:\longmapsto{x - \frac{3}{22} = \frac{ - 5}{22} }$

Taking $- \frac{3}{22}$ on RHS,

$\rm:\longmapsto{x = \frac{ - 5}{11} + \frac{3}{22} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{ x = \frac{( - 5 \times 22) + (11 \times 3)}{11 \times 22} } \\ \\ \rm:\longmapsto{ x = \frac{ - 110 + 33 }{242} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm: \longmapsto{x = \frac{ - 77}{242} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{x = \frac{ - 7}{22} } \: \: \: \: (by \: dividing \: 11)$

Verification :-

$\rm:\longmapsto{x + \bigg( \frac{ - 3}{22} \bigg) = \frac{ - 5}{11} } \\ \\ \rm:\longmapsto{ \frac{ - 7}{22} - \frac{ 3 }{22} = \frac{ - 5}{11} } \: \: \\ \\ \rm:\longmapsto{ \frac{ - 7 - 3}{22} = \frac{ - 5}{11} } \: \: \: \: \: \\ \\ \rm:\longmapsto{ \frac{ - 10}{22} } = \frac{ - 5}{11} \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{ \frac{ - 5}{11} = \frac{ - 5}{11} } \: \: \: \: \: \: \: \: \:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬