Question

Substract-2/9 from the sum of 13/42 and-5/6

Answer 1

★ How to do :-

Here, we are given with a fraction that should be subtracted from the sum of other two numbers. We are asked to find the difference of those two numbers. So, first we should find the sum of the two numbers given to us to find the other number that the second number should be subtracted with. We'll obtain with the second number by adding those two fractions. Then, we can find the final answer of our question by subtracting the first fraction by the obtained answer while adding those two fractions. We use the concept called as LCM, least common multiple to convert the unlike fractions to like fractions by taking the LCM of the denominators and then we can subtract the numerators only. Then, we'll obtain with the final answer. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \dfrac{(-2)}{9} - \bigg( \dfrac{13}{42} + \dfrac{(-5)}{6} \bigg)}$

LCM of 42 and 6 is 42.

${\sf \leadsto \dfrac{(-2)}{9} - \bigg( \dfrac{13}{42} + \dfrac{(-5) \times 7}{6 \times 7} \bigg)}$

Multiply the second fraction's numerator and denominator in the bracket.

${\sf \leadsto \dfrac{(-2)}{9} - \bigg( \dfrac{13}{42} + \dfrac{(-35)}{42} \bigg)}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{(-2)}{9} - \bigg( \dfrac{13 + (-35)}{42} \bigg)}$

Write the second numerator in the bracket with one sign.

${\sf \leadsto \dfrac{(-2)}{9} - \bigg( \dfrac{13 - 35}{42} \bigg)}$

Subtract the numerators in the bracket given.

${\sf \leadsto \dfrac{(-2)}{9} - \dfrac{22}{42}}$

LCM of 9 and 42 is 126.

${\sf \leadsto \dfrac{(-2) \times 14}{9 \times 14} - \dfrac{22 \times 3}{42 \times 3}}$

Multiply the numerators and denominators of both fractions.

${\sf \leadsto \dfrac{(-28)}{126} - \dfrac{66}{126}}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{(-28) - 66}{126}}$

Subtract the fractions to get the answer.

${\sf \leadsto \dfrac{(-94)}{126}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \dfrac{(-94)}{126}.}}}}$