DISTRIBUTIVE PROPERTY

Distributive Property

Definition Of Distributive Property

Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number.
That is, a(b + c) = ab + ac
a(b + c) = ab + ac is known as left distributive
(b + c)a = ba + ca is known as right distributive

More About Distributive Property

The property is true for any number of addends.
That is, a(b + c + d + . . . .) = ab + ac + ad + . . . . .
Also,
a(b - c) = ab - ac and a (b - c - d - . . . ) = ab - ac - ad - . . .

Example of Distributive Property

5(3 + 1) = 5 x 3 + 5 x 1
Consider LHS: 5(3 + 1) = 5(4) = 20
Consider RHS: 5 x 3 + 5 x 1 = 15 + 5 = 20
LHS = RHS

Quick Summary

Distributive Property involves multiplying a term by multiple terms inside parentheses.
It simplifies expressions by removing parentheses.
It applies to both addition and subtraction within the parentheses.
Left and right distribution are possible: a(b+c) = ab + ac and (b+c)a = ba + ca

\[ a(b + c) = ab + ac \]

🍎 Teacher Insights

Use visual aids like arrays or area models to demonstrate the distributive property. Start with simple numerical examples before introducing variables.

🎓 Prerequisites

Basic Arithmetic
Addition
Multiplication

Check Your Knowledge

Q1: What is 3(x + 2)?

3x + 2 3x + 6 x + 6 5x

Q2: What is 5(y - 1)?

5y - 1 5y + 5 5y - 5 y - 5

Frequently Asked Questions

Q: What is the distributive property?
A: The distributive property lets you multiply a sum by multiplying each addend separately and then adding the products.

Q: Does the distributive property work with subtraction?
A: Yes, it works with subtraction as well. a(b - c) = ab - ac

Q: Can I use the distributive property with more than two terms in the parentheses?
A: Yes, for example a(b + c + d) = ab + ac + ad