Contents
In this publication, we will consider 8 basic properties of the division of natural numbers, accompanying them with examples for a better understanding of the theoretical material.
Number division properties
Property 1
The quotient of dividing a natural number by itself is equal to one.
a : a = 1
examples:
- 9: 9 = 1
- 26: 26 = 1
- 293: 293 = 1
Property 2
If a natural number is divided by one, the result is the same number.
a : 1 = a
examples:
- 17: 1 = 17
- 62: 1 = 62
- 315: 1 = 315
Property 3
When dividing natural numbers, the commutative law cannot be applied, which is valid for .
a : b ≠ b : a
examples:
- 84 : 21 ≠ 21 : 84
- 440 : 4 ≠ 4 : 440
Property 4
If you want to divide the sum of numbers by a given number, then you need to add the quotient of dividing each summand by a given number.
Reverse property:
examples:
(45 + 18) : 3 =45 : 3 + 18 : 3 (28 + 77 + 140) : 7 =28 : 7 + 77 : 7 + 140 : 7 120 : (6 + 20) =120 : 6 + 120 : 20
Property 5
When dividing the difference of numbers by a given number, you need to subtract the quotient from dividing the subtrahend by the given number from the quotient from dividing the minuend by this number.
Reverse property:
examples:
(60 – 30) : 2 =60: 2-30: 2 (150 – 50 – 15) : 5 =150 : 5 – 50 : 5 – 15 : 5 360 : (90 – 15) =360: 90-360: 15
Property 6
Dividing the product of numbers by a given one is the same as dividing one of the factors by this number, then multiplying the result by another.
If the number being divided by is equal to one of the factors:
- (a ⋅ b) : a = b
- (a ⋅ b) : b = a
Reverse property:
examples:
(90 ⋅ 36) : 9 =(90 : 9) ⋅ 36 =(36 : 9) ⋅ 90 180 : (90 ⋅ 2) =180: 90: 2 =180: 2: 90
Property 7
If you need the quotient of division of numbers a и b divide by number c, it means that a can be divided into b и c.
Reverse property:
examples:
(16 : 4) : 2 =16 : (4 ⋅ 2) 96 : (80 : 10) =(96 : 80) ⋅ 10
Property 8
When zero is divided by a natural number, the result is zero.
0 : a = 0
examples:
- 0: 17 = 0
- 0: 56 = 56
Note: You can’t divide a number by zero.