Question

The sum of two number is -4/3. If one of the number is -5, what is the other? *​

Answer 1

Answer:

x + y = -4/3

x + ( - 5 ) = -4/3

x = -4/3 + 5

x - 4 + 15

__________

3

x = 11/3

Answer 2

★ How to do :-

Here, we are given with a rational number that should be added to the other number. We are also given with the answer obtained while adding those two fractions. But, we aren't given with the second number that the first number should be added with. We are asked to find the same. To find the answer, we make use of some other concepts. The variables are used as the second number and then find the value of that. We shift the numbers from one hand side to the other, this concept is called as transition method in which the sign of the particular number changes. So, let's solve!!

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➤ Solution :-

${\tt \leadsto (-5) + x = \dfrac{(-4)}{3}}$

Shift the number on LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{(-4)}{3} - (-5)}$

Write the second number on RHS in fractional form.

${\tt \leadsto x = \dfrac{(-4)}{3} - \dfrac{(-5)}{1}}$

LCM of 3 and 1 is 3.

${\tt \leadsto x = \dfrac{(-4)}{3} - \dfrac{(-5) \times 3}{1 \times 3}}$

Multiply the numerator and denominator of second fraction.

${\tt \leadsto x = \dfrac{(-4)}{3} - \dfrac{(-15)}{31}}$

Write both numerators with a common denominator.

${\tt \leadsto x = \dfrac{(-4) - (-15)}{3}}$

Write the second number in numerator with one sign.

${\tt \leadsto x = \dfrac{(-4) + 15}{3} = \dfrac{11}{3}}$

Write the obtained answer in the form of mixed fraction.

${\tt \leadsto x = \dfrac{11}{3} = 3 \dfrac{2}{3}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: 3 \dfrac{2}{3}.}}}}$

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Verification :-

${\tt \leadsto (-5) + \dfrac{11}{3} = \dfrac{(-4)}{3}}$

Write the first number in the form of fraction.

${\tt \leadsto \dfrac{(-5)}{1} + \dfrac{11}{3} = \dfrac{(-4)}{3}}$

LCM of 1 and 3 is 3.

${\tt \leadsto \dfrac{(-5) \times 3}{1 \times 3} + \dfrac{11}{3} = \dfrac{(-4)}{3}}$

Multiply the numerator and denominator of first fraction.

${\tt \leadsto \dfrac{(-15)}{3} + \dfrac{11}{3} = \dfrac{(-4)}{3}}$

Write both numerators with a common denominator.

${\tt \leadsto \dfrac{(-15) + 11}{3} = \dfrac{(-4)}{3}}$

Add those fractions now.

${\tt \leadsto \dfrac{(-4)}{3} = \dfrac{(-4)}{3}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!