Contents
In this publication, we will consider 3 main properties of the addition of natural numbers, accompanying them with examples for a better understanding of the theoretical material.
Number addition properties
Property 1: commutative law
From the rearrangement of the places of the terms, the sum does not change.
a + b = b + a
examples:
- 7 + 4 = 4 + 7
- 12 + 46 = 46 + 12
- 371 + 52 = 52 + 371
Note: the number of terms can be any. For example, here is the sum of three natural numbers:
Property 2: associative law
The result of adding one number to the sum of others (for example, the second and third) is equal to the result of adding the sum of the first and second numbers to the third.
(a + b) + с = a + (b + c)
In other words, neighboring (and not only) terms can be replaced by their sum.
Recall that, according to the rules of arithmetic, brackets determine the order in which actions are performed – they indicate expressions that are considered first.
examples:
- 11 + (27 + 60) = (11 + 27) + 60
- 20 + 81 + 48 + 55 =
(20 + 81) + (48 + 55)
Note: similarly to the first property, there can be more terms (both in brackets and outside them).
Property 3: adding to zero
If zero is added to a number (several terms), then the result will be the same number (their sum).
to + 0 = to
a + b + c + 0 = a + b + c
Those. we just discard zero.
examples:
- 5 + 0 = 5
- 12 + 0 + 18 + 6 = 12 + 18 + 6
- 0 + 0 = 0