Question

find 4/7+(-6/11)+(-7/21) ​

Answer 1

Answer :-

• The answer is (-71/231)

What to do?

• Find 4/7 + (-6/11) + (-7/21)

Solution :-

$\sf \dfrac{4}{7} + \left(\dfrac{-6}{\:\:11}\right) + \left(\dfrac{-7}{\:21}\right)$

The LCM of 7, 11 and 21 is 462, so adding the fractions using their denominators,

$\sf \dfrac{4\times66 + (-6) \times 42 + (-7) \times 22}{462}$

On simplifying,

$\sf \dfrac{264 + (-252) + (-154)}{462}$

Adding the numbers,

$\left(\sf \dfrac{-142}{\:\:\:462}\right)$

Reducing the fraction to it's simplest form,

$\left(\sf \dfrac{-71}{\:\:\:231} \right)$

$//$

Hence :-

• The required number is (-71/231)

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Know more :-

What is LCM?

• LCM can be defined as the smallest multiple which is common in two or more numbers. That is why the full form of LCM is Lowest Common Multiple.

How to find the LCM?

• We can find the LCM of two or more numbers using prime factorisation method. First we find all the prime factors of the given numbers and then multiply them to find the LCM of the numbers.

An example :-

• Find the LCM of 4 and 8.

Prime factorisation of 4 and 8 :-

$\begin{array}{c | c} \underline{2 }& \underline{4 \: , 8} \\ \underline2& \underline{2 \: ,4} \\ \underline2 & \underline{1 \: ,2} \\ & 1, \: 1\end{array}$

Now :-

• We multiply all the prime factors to find the LCM.

Hence :-

• The LCM of 4 and 8 = 2 × 2 × 2 = 8.