# Online Pre-Algebra Tutoring: Properties of Multiplication

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## Learn Â about Properties of Multiplication from Certified Online Pre-Algebra Tutor

There are five properties involving multiplication that will help make problems easier to solve. They are the commutative, associative, multiplicative identity, distributive properties and multiplicative Inverse Property.

**Commutative Property of Multiplication:Â ** The Commutative Property of Multiplication of Whole Numbers states that changing the order of the numbers being multiplied does not change the product.

**General Property:Â aÃ—b = bÃ—a**

**Associative Property of Multiplication:Â ** The Associative Property of Multiplication of Whole Numbers states that how the numbers being multiplied are grouped does not change the product.

**General Property:Â (aÃ—b) c = a (bÃ—c)**

**Identity Property for Multiplication:Â ** The Identity Property for Multiplication of Whole Numbers states that when a number is multiplied by one the result is the number itself; i.e., multiplication by one does not change the value of a number. One is called the multiplicative identity.

**General Property:Â 1 âˆ™ a = a âˆ™ 1 = a**

**Distributive Property of Multiplication:Â ** The Distributive Property of Multiplication states that multiplying a sum or difference, we may multiply each term of the sum or difference, and then add or subtract the partial products.

**General Property:Â Â a (b + c) = ab + acÂ Â or a (b â€“ c) = ab â€“ ac**

**Multiplicative Inverse Property: **A multiplicative inverse is a reciprocal. The multiplicative inverse of a is 1/a;

a/b is b/a and vice versa

a/b Ã— b/a = 1 (where a and b are non zero)

### Letâ€™s understand with an example:

Which property of multiplication is shown?

6 Ã— 8 = 8 Ã— 6

This equation shows the commutative property. The order of the factors is changed.

6 Ã— 8 = 8 Ã— 6

### Check Point

**a) **Which property of multiplication is shown?

7 Ã— (3 + 8) = 7 Ã—3 + 7 Ã— 8

**b)** Which property of multiplication is shown?

(12 Ã— 3) Ã—4 = 12 Ã— (3 Ã— 4)

**c)** Which property of multiplication is shown?

1Ã—986 = 986

**d)** Which property of multiplication is shown?

14/3 Ã— 3/14 =1

**e)** Which property of multiplication is shown?

453 Ã—89= 89Ã—453

### Answer key

**a)** Distributive Property of Multiplication

**b)** Associative Property of Multiplication

**c)** Identity Property for Multiplication

**d)** Multiplicative Inverse Property

**e)** Commutative Property of Multiplication

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