Question

Find the sum of suitable rearrangement-$837 + 208 + 363$

Answer 1

We can use suitable rearrangement to simplify the question to solve it quickly. In this method, we put together the unit digit of those numbers together which will give us the sum of $10$. So first we separate the unit’s digits from the numbers by writing them in expanded form. Now, add the unit digits that give the sum of $10$ and then add the rest numbers to this.

Complete step-by-step answer:
First, we will write the numbers in the expanded form-
$\Rightarrow 837 = 830 + 7$
$\Rightarrow 208 = 200 + 8$
$\Rightarrow 363 = 360 + 3$
So now adding all the expanded forms of the given numbers, we get-
$\Rightarrow 830 + 7 + 200 + 8 + 360 + 3$
Here we see that on adding $7$ and$3$, we will get the sum of ten so we can write-
$\Rightarrow 830 + 200 + 360 + \left( {7 + 3} \right) + 8$
On adding them we get,
$\Rightarrow 830 + 200 + 360 + 10 + 8$
Now we will add those terms together whose sum of unit digits will be equal to $10$
So adding the first and second terms, we get-
$\Rightarrow 1030 + 360 + 10 + 8$
Again adding the first and second term we get-
$\Rightarrow 1390 + 10 + 8$
We will add the first and second term again as the sum of their unit digits is $10$
$\Rightarrow 1400 + 8$
Now we will add the last two terms as there are no such terms left whose sum of unit digits will be equal to$10$. So adding the last two digits, we get-
$\Rightarrow 1400 + 8 = 1408$
The sum of the given numbers is $1408$.

Note: Here we write the digits in the expanded form so it will be easy for us to know whose unit digits will add to give the number$10$. The unit’s digits that will give the sum as$10$ are- $\left( {1 + 9} \right)$,$\left( {2 + 8} \right)$, $\left( {3 + 7} \right)$, $\left( {4 + 6} \right)$ and $\left( {5 + 5} \right)$. When the question has to be solved using suitable rearrangement, the numbers having these unit digit numbers should be added first then the other numbers should be added.