Question

Subtract the sum of -5/6 and -1whole 1/35 from the sum of 2whole 2/3 and -6whole 2/5.
plz, answer fast!!
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Answer 1

★ How to do :-

Here, we are given with four fractions to solve with. So, first we should add both of the fractions each, there are two such pairs add subtract their answers. So, they are given some of the fractions as whole numbers which should be converted to improper fractions and the unlike fractions should be converted into like fractions before calculation. So, let's do!

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➤ Solution :-

${\tt \leadsto \bigg(2 \dfrac{2}{3} + - 6 \dfrac{2}{5} \bigg) - \bigg(\dfrac{( - 5)}{6} + - 1 \dfrac{1}{35} \bigg)}$

So, let's solve the brackets one by one.

${\tt \leadsto 2 \dfrac{2}{3} + - 6 \dfrac{2}{5}}$

${\tt \leadsto \dfrac{8}{3} + \dfrac{( - 32)}{5}}$

LCM of 3 and 5 is 15.

${\tt \leadsto \dfrac{8 \times 5}{3 \times 5} + \dfrac{( - 32) \times 3}{5 \times 3}}$

${\tt \leadsto \dfrac{40}{15} + \dfrac{( - 96)}{15}}$

${\tt \leadsto \dfrac{40 + ( - 96)}{15} = \dfrac{( - 56)}{15}}$

Now, let's solve the second bracket.

${\tt \leadsto \dfrac{( - 5)}{6} + - 1 \dfrac{1}{35}}$

${\tt \leadsto \dfrac{( - 5)}{6} + \dfrac{( - 36)}{35}}$

LCM of 6 and 35 is 210.

${\tt \leadsto \dfrac{( - 5) \times 35}{6 \times 35} + \dfrac{( - 36) \times 6}{35 \times 6}}$

${\tt \leadsto \dfrac{( - 175)}{210} + \dfrac{( - 216)}{210}}$

${\tt \leadsto \dfrac{( - 175) + ( - 216)}{210} = \dfrac{( - 391)}{210}}$

Subtraction of both answers :-

${\tt \leadsto \dfrac{( - 56)}{15} - \dfrac{( - 391)}{210}}$

${\tt \leadsto \dfrac{( - 56) \times 14}{15 \times 14} - \dfrac{( - 391)}{210}}$

${\tt \leadsto \dfrac{( - 784)}{210} - \dfrac{( - 391)}{210}}$

${\tt \leadsto \dfrac{( - 784) - ( - 391)}{210}}$

${\tt \leadsto \dfrac{( - 784) + 391}{210}}$

${\tt \leadsto \cancel \dfrac{( - 465)}{210} = \dfrac{( - 31)}{14}}$

${\tt \leadsto \dfrac{( - 31)}{14} = \boxed{\tt - 2 \dfrac{3}{14}}}$

$\Huge\therefore$ The final answer of the sum is ${\tt - 2 \dfrac{3}{14}}$.