- Prime Numbers Factors and Multiples
- Home
- Even and Odd Numbers
- Divisibility Rules for 2, 5, and 10
- Divisibility Rules for 3 and 9
- Factors
- Prime Numbers
- Prime Factorization
- Greatest Common Factor of 2 Numbers
- Greatest Common Factor of 3 Numbers
- Introduction to Distributive Property
- Understanding the Distributive Property
- Introduction to Factoring With Numbers
- Factoring a Sum or Difference of Whole Numbers
- Least Common Multiple of 2 Numbers
- Least Common Multiple of 3 Numbers
- Word Problem Involving the Least Common Multiple of 2 Numbers

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# Introduction to Distributive Property

The **distributive property** states that when we multiply a factor and a sum or difference, we multiply the factor by each term of the sum or difference.

### Formula

The distributive property of multiplication for any three real numbers 'a', 'b' and 'c' isa × (b + c) = (a × b) + (a × c)

a × (b − c) = (a × b) − (a × c)

**Example**

Rewrite 8 × (7 + 4) using distributive property in order to simplify

**Solution**

**Step 1:**

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b + c) = (a × b) + (a × c)

**Step 2:**

8 × (7 + 4) = (8 × 7) + (8 × 4) = 56 + 32 = 88

Rewrite given expression using distributive property in order to simplify

8 × (7 + 4)

### Solution

**Step 1:**

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b + c) = (a × b) + (a × c)

**Step 2:**

8 × (7 + 4) = (8 × 7) + (8 × 4) = 56 + 32 = 88

Rewrite given expression using distributive property in order to simplify

9 × (6 − 2)

### Solution

**Step 1:**

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b − c) = (a × b) − (a × c)

**Step 2:**

9 × (6 − 2) = (9 × 6) − (9 × 2) = 54 − 18 = 36