Question

Solve using suitable property
-2/3 + 5/7 + -8/9 + 3/14

Answer 1

Answer :-

$\frac{ - 2}{3} + \frac{5}{7} + \frac{ - 8}{9} + \frac{3}{14}$

$\frac{( - 2 \times 7) + (3 \times 5)}{3 \times 7} + \frac{( - 8 \times 14) + (9 \times 3)}{9 \times 14}$

$\frac{ - 14 + 15}{21} + \frac{ - 112 + 27}{126}$

$\frac{1}{21} + \frac{ - 85}{126}$

$\frac{(1 \times 126) + ( 21 \times ( - 85)}{21 \times 126}$

$\frac{21 - 1785}{2646}$

$\frac{ - 1764}{2646}$

$\frac{ - 882}{1323 }$

Answer is -882/1323

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Answer 2

★ How to do :-

Here, we are given with four fractions in which we are asked to find the sum of those all fractions. We are also said that we should use the suitable property here. We can use the associative property in which we rearrange the fractions suitably and then we can add the fractions step by step. The concept of LCM, least common multiple is used here in which we take LCM of the denominators and convert them into like fractions. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{(-2)}{3} + \dfrac{5}{7} + \dfrac{(-8)}{9} + \dfrac{3}{14}}$

Rearrange them.

${\tt \leadsto \dfrac{(-2)}{3} + \dfrac{(-8)}{9} + \dfrac{5}{7} + \dfrac{3}{14}}$

LCM of 3 and 9 is 9.

${\tt \leadsto \dfrac{(-2) \times 3}{3 \times 3} + \dfrac{(-8) \times 1}{9 \times 1} + \dfrac{5}{7} + \dfrac{3}{14}}$

LCM of 7 and 14 is 14.

${\tt \leadsto \dfrac{(-6)}{9} + \dfrac{(-8)}{9} + \dfrac{5 \times 2}{7 \times 2} + \dfrac{3 \times 1}{14 \times 1}}$

Multiply the numerator and denominator of third and fourth fractions.

${\tt \leadsto \bigg( \dfrac{(-6)}{9} + \dfrac{(-8)}{9} \bigg) + \bigg( \dfrac{10}{14} + \dfrac{3}{14} \bigg)}$

Add two fractions each in brackets.

${\tt \leadsto \dfrac{(-14)}{9} + \dfrac{13}{14}}$

LCM of 9 and 14 is 126.

${\tt \leadsto \dfrac{(-14) \times 14}{9 \times 14} + \dfrac{13 \times 9}{14 \times 9}}$

Multiply the numerator and denominator of both fractions.

${\tt \leadsto \dfrac{(-196)}{126} + \dfrac{117}{126}}$

Add both fractions to get the answer.

${\tt \leadsto \dfrac{(-196) + 117}{126} = \pink{\underline{\boxed{\tt \dfrac{(-79)}{126}}}}}$