# Online Pre-Algebra Tutoring: Properties of Multiplication

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## Learn 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: ** 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: a×b = b×a**

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

**General Property: (a×b) c = a (b×c)**

**Identity Property for Multiplication: ** 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: 1 ∙ a = a ∙ 1 = a**

**Distributive Property of Multiplication: ** 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: a (b + c) = ab + ac or a (b – c) = ab – 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 × b/a = 1 (where a and b are non zero)

### Let’s understand with an example:

Which property of multiplication is shown?

6 × 8 = 8 × 6

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

6 × 8 = 8 × 6

### Check Point

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

7 × (3 + 8) = 7 ×3 + 7 × 8

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

(12 × 3) ×4 = 12 × (3 × 4)

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

1×986 = 986

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

14/3 × 3/14 =1

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

453 ×89= 89×453

### 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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