Question

What number should be added to-5/8 so as to get -3/2?​

Answer 1

★ How to do :-

Here, we are given with a number to add with an other number. The sum of both the numbers is also given. But, we are not given with the second fraction to add with. Ww are asked to find the value of the second fraction that the first fraction needs to be added with. Here, we use some other concepts such as shifting the numbers from one hand side to the other, which change it's sign. We can also verify our answer with applying the value of second fraction. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{(-5)}{8} + x = \dfrac{(-3)}{2}}$

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

${\tt \leadsto x = \dfrac{(-3)}{2} - \dfrac{(-5)}{8}}$

LCM of 2 and 8 is 8.

${\tt \leadsto x = \dfrac{(-3) \times 4}{2 \times 4} - \dfrac{(-5)}{8}}$

Multiply the numbers on numerator and denominator of first fraction.

${\tt \leadsto x = \dfrac{(-12)}{8} - \dfrac{(-5)}{8}}$

Subtract the fractions to get the answer.

${\tt \leadsto x = \dfrac{(-12) - (-5)}{8} = \dfrac{(-12) + 5}{8}}$

Add the fractions now.

${\tt \leadsto x = \dfrac{(-12) + 5}{8} = \pink{\underline{\boxed{\tt \dfrac{(-7)}{8}}}}}$

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Verification :-

${\tt \leadsto \dfrac{(-5)}{8} + \dfrac{(-7)}{8} = \dfrac{(-3)}{2}}$

Add the fractions directly as they are like fractions.

${\tt \leadsto \dfrac{(-5) + (-7)}{8} = \dfrac{(-3)}{2}}$

Write the second number in numerator with one sign.

${\tt \leadsto \dfrac{(-5) - 7}{8} = \dfrac{(-3)}{2}}$

Subtract the numbers on numerator.

${\tt \leadsto \dfrac{(-12)}{8} = \dfrac{(-3)}{2}}$

Write the fraction on LHS in lowest form by cancellation method.

${\tt \leadsto \dfrac{(-3)}{2} = \dfrac{(-3)}{2}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!