Multiply using the distributive property

key notes :

What is the Distributive Property?

  • The distributive property lets you multiply a number by a group of numbers added or subtracted together.
  • It breaks down complex multiplication into simpler parts.

Formula:

a×(b+c)=a×b+a×c

Distribute Over Addition

Example:

3×(4+5)=(3×4)+(3×5)=12+15=27

Distribute Over Subtraction

Example:

6×(10−2)=(6×10)−(6×2)=60−12=48

Using the Property to Simplify Mental Math

Example:

7×13=7×(10+3)=(7×10)+(7×3)=70+21=91

Distributive Property with Variables

Example:

x × (5+2) = x × 5 + x ×

Visualizing with Area Models

  • Break rectangles into smaller parts.
  • Multiply the area of each part.
  • Add them together to find the total.

Example: To find 12×4, split 12 into 10 and 2:

(10+2)×4=(10×4)+(2×4)=40+8=48

Why Use It?

  • Makes large numbers easier to handle.
  • Helps with mental math and algebra.
  • Prepares students for algebraic expressions.

Learn with an example

⛱️ Simplify the expression: 4(2 + 3w) =_____

  • Simplify.
  • 4(2 + 3w) = 4(2) + 4(3w) Apply the distributive property
  • = 8 + 12w Simplify

⛱️ Simplify the expression: 2(y + 1) =_______

  • Simplify.
  • 2(y + 1) = 2(y) + 2(1) Apply the distributive property
  • = 2y + 2 Simplify

⛱️ Simplify the expression: (3u + 3)(3) =____

  • Simplify.
  • (3u + 3)(3) = 3u(3) + 3(3) Apply the distributive property
  • = 9u + 9 Simplify

Let’s practice!🖊️