Question

Subtract the sum of $ \dfrac{{ - 4}}{7} $ and $ \dfrac{{ - 5}}{3} $ from the sum of $ \dfrac{1}{2} $ and $ \dfrac{{ - 21}}{{22}} $ .

Answer 1

Hint: First add the terms $ \dfrac{{ - 4}}{7} $ and $ \dfrac{{ - 5}}{3} $ . Now add the terms $ \dfrac{1}{2} $ and $ \dfrac{{ - 21}}{{22}} $ . Then subtract the sum of terms $ \dfrac{1}{2} $ and $ \dfrac{{ - 21}}{{22}} $ from the sum of terms $ \dfrac{{ - 4}}{7} $ and $ \dfrac{{ - 5}}{3} $ .

Complete step-by-step answer:
Let's add the given two fractions first,
$ \Rightarrow \dfrac{{ - 4}}{7} + \dfrac{{ - 5}}{3} = \dfrac{{ - 4}}{7} - \dfrac{5}{3} = \dfrac{{ - 12 - 35}}{{21}} = \dfrac{{ - 47}}{{21}}\;\;\; \ldots \left( 1 \right) $
We took the LCM of $ 7 $ and $ 3 $ and then apply simple addition and subtraction
Now we will add the next two terms
$ \Rightarrow \dfrac{1}{2} + \dfrac{{ - 21}}{{22}} = \dfrac{1}{2} - \dfrac{{21}}{{22}} = \dfrac{{11 - 21}}{{22}} = \dfrac{{ - 10}}{{22}} = \dfrac{{ - 5}}{{11}}\;\;\; \ldots \left( 2 \right) $
Similary here as well we took the LCM of 2 and 22 and then apply simple addition and subtraction operation.
Now we will subtract equation $ \left( 1 \right) $ from equation $ \left( 2 \right) $
 $ \Rightarrow \dfrac{{ - 5}}{{11}} + \dfrac{{47}}{{21}} = \dfrac{{ - 5(21) + 47(11)}}{{11\times 21}} = \dfrac{{ - 105 + 517}}{{11.21}} = \dfrac{{412}}{{231}} $
So this is the final answer.

Note: Avoid the calculation mistakes during the L.C.M. of two numbers while adding the two rational numbers and also take care of it while subtracting both the sums from each other.