In this publication, we will consider 6 basic properties of the subtraction of natural numbers, accompanying them with examples for a better understanding of the theoretical material.
Number subtraction properties
Property 1
The difference of two equal natural numbers is equal to zero.
a – a = 0
examples:
- 6 – 6 = 0
- 35 – 35 = 0
- 170 – 170 = 0
Note: If zero is subtracted from a number, the result is the same number.
a – 0 = a
Property 2
The commutative law, which works for , does not apply when subtracting them.
a – b ≠ b – a
In other words, the reduced (a) and subtrahend (b) cannot be interchanged, because this will lead to different results.
examples:
- 66 – 37 ≠ 37 – 66
- 182 – 16 ≠ 16 – 182
Property 3
If it is required to subtract the sum of other numbers from a natural number, this means that we subtract the first term of this sum from it, then the second from the resulting difference, and so on. (or vice versa, from last to first).
In this case, the brackets can be removed:
examples:
75 – (20 + 13) =(75 – 20) – 13 110 – (16 + 24 + 9) =110 – 16 – 24 – 9
Property 4
If it is required to subtract a natural number from the sum of other numbers, then we can subtract it from any summand.
Or you can omit the parentheses:
examples:
(42 + 51) – 25 =(42 – 25) + 51 =(51 – 25) + 42 (337 + 602 + 409) – 116 =337 – 116 + 602 + 409
Property 5
When subtracting a natural number from the difference of other numbers, it can be subtracted from the minuend or added to the subtrahend.
Parentheses can be removed by strictly observing the original order of numbers in the expression:
(a – b) – c = a – b – c
examples:
(75 – 29) – 15 =(75 – 15) – 29 =75 – (29 + 15) (216 – 50 – 81) – 36 =216 – 50 – 81 – 36
Property 6
If it is required to subtract the difference of other numbers from a natural number, then, according to the rules for opening brackets, this is done as follows:
a – (b – c) = a – b + c
Those. we subtract the numbers in brackets with the plus sign from the original, and add the numbers with the minus sign.
examples:
88 – (53 – 16) =88 – 53 + 16 140 – (91 – 42 – 11) =140 – 91 + 42 + 11