Question

find the rational numbers that should be added to,-3/8 to get 5/16​

Answer 1

★ How to do :-

Here, we are given with one of the rational number that should be added to the other number. We are also given with the answer obtained while solving those two rational numbers. But, we are not given with the second number that the first number should be added with. We are asked to find the same. Here, we use the concept of shifting the numbers from one hand side to the other which changes it's sign. We can find the value of other fraction. So, let's solve!!

➤ Solution :-

${\tt \leadsto \dfrac{(-3)}{8} + x = \dfrac{5}{16}}$

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

${\tt \leadsto x = \dfrac{5}{16} - \dfrac{(-3)}{8}}$

LCM of 16 and 8 is 16.

${\tt \leadsto x = \dfrac{5}{16} - \dfrac{(-3) \times 2}{8 \times 2}}$

Multiply the numerator and denominator of second fraction.

${\tt \leadsto x = \dfrac{5}{16} - \dfrac{(-6)}{16}}$

Write the second number with one sign which has two signs.

${\tt \leadsto x = \dfrac{5 - (-6)}{16} = \dfrac{5 + 6}{16}}$

Add the numbers on the numerator to get the answer.

${\tt x = \dfrac{11}{16}}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{11}{16}}}}}$

━━━━━━━━━━━━━━━━━━━━━━

Verification :-

${\tt \leadsto \dfrac{(-3)}{8} + x = \dfrac{5}{16}}$

Substitute the value of x.

${\tt \leadsto \dfrac{(-3)}{8} + \dfrac{11}{16} = \dfrac{5}{16}}$

LCM of 8 and 16 is 16.

${\tt \leadsto \dfrac{(-3 \times 2)}{8 \times 2} + \dfrac{11}{16} = \dfrac{5}{16}}$

Multiply the numerator and denominator of first fraction.

${\tt \leadsto \dfrac{(-6)}{16} + \dfrac{11}{16} = \dfrac{5}{16}}$

Write both numerators in a common denominator.

${\tt \leadsto \dfrac{(-6) + 11}{16} = \dfrac{5}{16}}$

Add the numerators now.

${\tt \leadsto \dfrac{5}{16} = \dfrac{5}{16}}$

So,

${\sf \leadsto LHS = RHS}$

$\:$

Hence verified !!