Question

what should be added to -4 to get 2/5

Answer 1

Step-by-step explanation:

hope this helps you and look the answer once

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 transposition method in which the sign of the particular number changes. So, let's solve!!

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➤ Solution :-

Let the other number be y.

${\sf \leadsto (-4) + y = \dfrac{2}{5}}$

Write the first number on LHS in the form of fraction.

${\sf \leadsto \dfrac{(-4)}{1} + y = \dfrac{2}{5}}$

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

${\sf \leadsto y = \dfrac{2}{5} - \dfrac{(-4)}{1}}$

LCM of 5 and 1 is 5.

${\sf \leadsto y = \dfrac{2}{5} - \dfrac{(-4) \times 5}{1 \times 5}}$

Multiply the numerators and denominators of second fraction.

${\sf \leadsto y = \dfrac{2}{5} - \dfrac{(-20)}{5}}$

Write the second number with one sign.

${\sf \leadsto y = \dfrac{2 - (-20)}{5} = \dfrac{2 + 20}{5}}$

Add the numbers.

${\sf \leadsto y = \dfrac{22}{5} = 4 \dfrac{2}{5}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: 4 \dfrac{2}{5}.}}}}$

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Verification :-

${\sf \leadsto (-4) + y = \dfrac{2}{5}}$

Write the first number as fraction and substitute the value of y.

${\sf \leadsto \dfrac{(-4)}{1} + 4 \dfrac{2}{5} = \dfrac{2}{5}}$

Write the second fraction as a improper fraction.

${\sf \leadsto \dfrac{(-4)}{1} + \dfrac{22}{5} = \dfrac{2}{5}}$

LCM of 1 and 5 is 5.

${\sf \leadsto \dfrac{(-4) \times 5}{1 \times 5} + \dfrac{22}{5} = \dfrac{2}{5}}$

Multiply the numerators and denominators of first fraction.

${\sf \leadsto \dfrac{(-20)}{20} + \dfrac{22}{5} = \dfrac{2}{5}}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{(-20) + 22}{5} = \dfrac{2}{5}}$

Add the numbers.

${\sf \leadsto \dfrac{2}{5} = \dfrac{2}{5}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!