Question

Find the sum by suitable rearrangement: 837 + 208 + 363.

Answer 1

Hint: The given problem is related to summation of more than two numbers by rearrangement. Rearrange the given three numbers in such a way that the sum of the first two will result in a number with 0 in its unit place. Then, add the third number to find the sum.

Complete step-by-step answer:
Before proceeding with the solution, let’s understand some properties of addition of integers. There are four main properties related to addition of integers.
(i) Closure property: The sum, product, or difference of two integers will always be an integer.
(ii) Associative property: The sum or product of two or more integers does not depend on the order in which the operation is done, i.e. a + (b + c) = (a + b) + c = (a + c) + b
(iii) Distributive property: The multiplication is distributive over addition or subtraction, i.e. a(b + c) = ab + ac ; a(b – c) = ab – ac
(iv) Commutative property: The sum or product of two integers does not depend upon the order of the integers, i.e. a + b = b + a ; ab = ba
Now, coming to the question, we are asked to rearrange and find the value of the sum: 837 + 208 + 363 .
By observation, we can see that if we add the first and the third terms first, then the resultant sum will have 0 in its unit place. So, by associative property, we can write:
837 + 208 + 363 = (837 + 363) + 208
$\Rightarrow $ 837 + 208 + 363 = 1200 + 208
$\Rightarrow $ 837 + 208 + 363 = 1408
Hence, we can say that the value of the sum 837 + 208 + 363 is equal to 1408.

Note: The properties should be properly understood and the operations in which certain property does not hold should be properly understood. For example: Commutative property does not hold for subtraction. If a student does not know this, he can write a – b = b – a , which is wrong. So, such details should be properly understood and remembered.