Question

-4/9 + -2/7 + -15/14 + -3/18​

Answer 1

★ How to do :-

Here, we are given with four fractions in which we are asked to add all the fractions together. We can see that all the fractions have different denominators, so first we should take the same equivalent fractions to each of them and make all their denominators same. For this method, the concept of LCM can be used, in which we take LCM of the denominators and convert them into LCM value. We should multiply some numbers to numerator and denominator of each fraction and then add them together. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{(-4)}{9} + \dfrac{(-2)}{7} + \dfrac{(-15)}{14} + \dfrac{(-3)}{18}}$

LCM of 9, 7, 14 and 18 is 126.

${\tt \leadsto \dfrac{(-4) \times 14}{9 \times 14} + \dfrac{(-2) \times 18}{7 \times 18} + \dfrac{(-15) \times 9}{14 \times 9} + \dfrac{(-3) \times 7}{18 \times 7}}$

Multiply the numerators and denominators of all the four fractions.

${\tt \leadsto \dfrac{(-56)}{126} + \dfrac{(-36)}{126} + \dfrac{(-135)}{126} + \dfrac{(-21)}{126}}$

Now, write all the numerators in a single fraction with common denominator.

${\tt \leadsto \dfrac{(-56) + (-36) + (-135) + (-21)}{126}}$

Write all the numbers in numerator with only single sign.

${\tt \leadsto \dfrac{(-56) - 36 - 135 - 21}{126}}$

Simplify two integers together in numerator.

${\tt \leadsto \dfrac{(-92) - 156}{126}}$

Subtract the fractions in the numerator to get the answer.

${\tt \leadsto \cancel \dfrac{(-248)}{126} = \pink{\underline{\boxed{\tt \dfrac{(-124)}{63}}}}}$

$\Huge\therefore$ The final answer when simplified is ${\tt \dfrac{(-124)}{63}}$

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$\dashrightarrow$ Some important laws :-

${\tt \to (+) \times (+) = (+)}$

${\tt \to (-) \times (-) = (+)}$

${\tt \to (+) \times (-) = (-)}$

${\tt \to (-) \times (+) = (-)}$

Answer 2

Answer:

$\frac{( - 124)}{63}$

Step-by-step explanation:

It is the correct answer.