- 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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# Understanding the Distributive Property

When multiplying a number by a sum or difference, we use the distributive property.

The **distributive property** states that for any three numbers 'a', 'b' and 'c'

- a × (b + c) = (a × b) + (a × c)
- a × (b − c) = (a × b) − (a × c)

For **example**, in the math statement 7 × (4 + 9), we are multiplying 7 with a sum of 4 and 9. Here we can use the distributive property as follows.

7 × (4 + 9) = (7 × 4) + (7 × 9) = 28 + 63 = 91

Similarly, in the math statement 5 × (8 − 3), we are multiplying 5 with a difference of 8 and 3. Here we can use the distributive property as follows.

5 × (8 − 3) = (5 × 8) − (5 × 3) = 40 − 15 = 25

In an expression for example, 6 × (3 + 5), we can simplify using the order of operations rule PEMDAS or use distributive property.

If **PEMDAS rule** is followed

6 × (3 + 5) = 6 × (8) = 48

(We simplify the parentheses first and then do multiplication operation next)

If **distributive property** is used

6 × (3 + 5) = (6 × 3) + (6 × 5) = 18 + 30 = 48

Either way, the answer is the **same**.

Sometimes it is easier to use the distributive property to simplify than using the order of operations rule PEMDAS.

Simplify 4 × (3 + 50) using distributive property

### Solution

**Step 1:**

In 4 × (3 + 50), it is easier to simplify using distributive property as follows

4 × (3 + 50) = (4 × 3) + (4 × 50) = 12 + 200 = 212

**Step 2:**

If PEMDAS rule is used

4 × (3 + 50) = 4 × 53 = 212