Properties of Operations

# Properties of Operations

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

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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