The Distributive Property

Sharing the multiplier.

a(b + c) = ab + ac.

This is the foundational rule for Algebra.

Multiply the outside number by EVERY inside number.

The Field Guide

In 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.

In The Real World: Mental math. 5 x 104 is hard. 5 x (100 + 4) is easy. 500 + 20 = 520.

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

Real World Challenge

"You need to paint 4 walls. Each wall needs 10 gallons of blue and 2 gallons of white."

The Logic: 4 x (10 + 2). That's 40 blue and 8 white. Total 48 gallons.

Algebraic

2(x + 4) = 2x + 8

2 times x, 2 times 4.

Numeric

3(10 + 2) 30 + 6 36

Easier than 3x12?