Properties of Addition
Order property of addition
If we
change the order of the addends, the sum remains the same.
Example: 8146 + 3564
= 11710 and 3564 + 8146 = 11710
Thus, 8146
+ 3564 = 3564 + 8146 = 11710
Grouping of addends
When three
or more numbers are added, the sum remains the same regardless of the way
addends are grouped.
Example: (6489 +
2734) + 4698 = 9223 + 4698 = 13921
6489 + (2734
+ 4698) = 6489 + 7432 = 13921
Thus, (6489
+ 2734) + 4698 = 6489 + (2734 + 4698) = 13921
Property of zero
The sum
of any number and 0 is the number itself.
Example: 9754 +
0 = 9754 and 0 + 9754 = 9754
Thus, 9754
+ 0 = 0 + 9754 = 9754
Property of one
The sum
of any number and 1 is always the successor of the number.
Example: 4867 +
1 = 1 + 4867 = 4868
Properties of Subtraction
Property of zero
If 0 is
subtracted from a number, the difference is the number itself.
Example: 95,633
– 0 = 95,633
Property of one
If 1 is subtracted
from a number, the difference is the predecessor of the given number.
Example: 32,577
– 1 = 32,576
Subtraction of a number from itself
If a
number is subtracted from itself, the difference is zero.
Example: 96,762
– 96,762 = 0
Properties of Multiplication
Order property of multiplication
Even if
the order of multiplicand and multiplier is changed, the product remains the
same.
Examples: 52 × 43
= 43 × 52; 524 × 62 = 62 × 524; 345 × 52 = 52 × 345
Property of one
Any
number multiplied by 1 gives the number itself as the product.
Examples:
7413 × 1 = 7413; 2735 × 1 = 2735; 5230 × 1 = 5230
Property of zero
Any
number multiplied by 0 gives 0 as the product.
Examples: 6231 ×
0 = 0; 3745 × 0 = 0; 2837 × 0 = 0
·
The product of a number
(either odd or even) with an even number is always an even number.
Examples: 325 × 2 = 650; 562 × 4 = 2248; 2252 × 8 = 18016
·
The product of
two odd numbers is always an odd number.
Examples: 323 × 3 = 969; 561 × 7 =
3927; 727 × 9 = 6543
Properties of Division
·
When a non-zero
number is divided by 1, the quotient is the number itself and the remainder is
zero.
Examples: 45 ÷ 1 = 45; 328 ÷ 1= 328; 4629 ÷ 1= 4629
·
When a number is
divided by itself, the quotient is 1 and the remainder is zero.
Examples: 210 ÷ 310 = 1; 4762 ÷ 4762 = 1; 23612 ÷ 23612 = 1
·
Division by zero
has no meaning.
·
When 0 is
divided by any number, the quotient is always 0.
Examples: 0 ÷ 26 = 0; 0 ÷ 7540 = 0; 0 ÷ 76241 = 0
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