The properties of multiplying integers are explained using examples.
For any integers ‘a’, ‘b’ and ‘c’, etc.
1. Closure property:
a × b is an integer i.e., product (multiplication) of two integers is always an integer
For example: 2 and 3 are two integers, now 2 × 3 = 6, which is an integer.
2. Commutative property:
a × b = b × a.
For example: 2 × 5 = 5 × 2 and so on.
3. Associative property:
a × (b × c) = (a × b) × c.
For example: 2 × (3 × 4) = (2 × 3) × 4 and so on.
4. Multiplicative Property of Zero:
a × 0 = 0 × a = 0
For example: 5 × 0 = 0 × 5 = 0 and so on.
The result of multiplication of any number with zero (0) is always zero.
i.e., any number × 0 = 0 and 0 × any number = 0
Thus, 7 × 0 = 0, 0 × 7 = 0, (10) × 0 = 0, 0 × (10) = 0
5. Multiplicative identity property:
a × 1 = 1 × a = a
For example: 3 × 1 = 1 × 3 = 3 and so on.
6. Distributive of property multiplication over addition:
(i) a × (b + c) = a × b + a × c,
For example: 2 × (4 + 5) = 2 × 4 + 2 × 5 and so on.
(ii) (b + c) × a = b × a + c × a
For example: (4 + 9) × 3 = 4 × 3 + 9 × 3 and so on.
7. Distributive of property multiplication over subtraction:
(i) a × (b  c) = a × b  a × c
For example: 4 × (7  9) = 4 × 7  4 × 9 and so on.
(ii) (b  c) × a = b × a  c × a
For example: (2  8) × 6 = 2 × 6  8 × 6 and so on.
`Numbers Page
6th Grade Page
From Properties of Multiplying Integers to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.