Multiplication Is Fast Addition
Multiplication is a shortcut for adding the same number over and over.
- 3 + 3 + 3 + 3 = 12 → 4 groups of 3 → 4 × 3 = 12
- 5 + 5 + 5 = 15 → 3 groups of 5 → 3 × 5 = 15
The two numbers being multiplied are called factors. The answer is called the product.
The Commutative Property
3 × 4 = 12 and 4 × 3 = 12 — the order of the factors does not change the product. This is the commutative property of multiplication.
It means you only have to memorize half of the times table, because every fact has a mirror: knowing 7 × 8 = 56 automatically tells you 8 × 7 = 56.
Arrays Show Multiplication
An array is a grid of objects arranged in equal rows and columns. A 3-row, 4-column array has 3 × 4 = 12 objects. Rotating the array — 4 rows, 3 columns — still gives 12 objects. This is the commutative property you can see.