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

  1. Which property of multiplication is shown?
    7 × (3 + 8) = 7 ×3 + 7 × 8
  2. Which property of multiplication is shown?
    (12 × 3) ×4 = 12 × (3 × 4)
  3. Which property of multiplication is shown?
    1×986 = 986
  4.  Which property of multiplication is shown?
    14/3 × 3/14 =1
  5. Which property of multiplication is shown?
    453 ×89= 89×453
Answer Key
  1.  Distributive Property of Multiplication
  2. Associative Property of Multiplication
  3. Identity Property for Multiplication
  4. Multiplicative Inverse Property
  5. Commutative Property of Multiplication

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