← Back to Math Adventures

The Distributive Property

Overview

Sharing the multiplier.

What is it?

a(b + c) = ab + ac.

History

This is the foundational rule for Algebra.

Key Idea

Multiply the outside number by EVERY inside number.

Practice This Topic

Concept Guide

Plain English: If you buy 3 combo meals, that means you bought 3 burgers AND 3 fries. You distribute the '3' to everything inside the bag.

Real-world example: Mental math. 5 x 104 is hard. 5 x (100 + 4) is easy. 500 + 20 = 520.

Common Pitfall

Only multiplying the first number. 3(x+2) is 3x+6, NOT 3x+2.

Word Problem
"You need to paint 4 walls. Each wall needs 10 gallons of blue and 2 gallons of white."
Reasoning: 4 x (10 + 2). That's 40 blue and 8 white. Total 48 gallons.

Practice Examples

Algebraic
2(x + 4) = 2x + 8
2 times x, 2 times 4.
Numeric
3(10 + 2) 30 + 6 36
Easier than 3x12?