Introduction

Changing the order of the numbers does not change the result.
- $a + b = b + a$‬‭‬‭‬‭‬ and ‭$a \cdot b = b \cdot a$‬‭‬‭‬‭‬
- ‭$4 + 2 = 2 + 4$‬‭‬‭‬‭‬ or ‭$3 \cdot 5 = 5 \cdot 3$‬‭‬‭‬‭‬

Changing how numbers are grouped with parentheses does not change the result. It is all about who the numbers associate with first.
- ‭$(a + b) + c = a + (b + c)$‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬ and ‭$(a \cdot b) \cdot c = a \cdot (b \cdot c)$‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬
- ‭$(1 + 2) + 4 = 1 + (2 + 4)$‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬

• Multiplying a single number by a sum inside parentheses is equivalent to multiplying that number by each item inside individually.
• $a \cdot (b + c) = a \cdot b + a \cdot c$‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬
• ‭$3 \cdot (10 + 2) = (3 \cdot 10) + (3 \cdot 2) = 36$‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬