Multiplication & Division
Multiplication is fast adding. Division is splitting into equal groups. Together they power every math class from here on.
Multiplication Basics
Multiplication is repeated addition. 4 × 3 means "four groups of three" or 3 + 3 + 3 + 3 = 12.
Key Vocabulary
Factor × Factor = Product
4 × 6 = 24 (4 and 6 are factors; 24 is the product)
Properties:
- Commutative: 4 × 6 = 6 × 4 (order doesn't matter)
- Associative: (2 × 3) × 4 = 2 × (3 × 4) (grouping doesn't matter)
- Identity: any number × 1 = that number
- Zero: any number × 0 = 0
Times Tables (1–12)
Memorizing multiplication facts up to 12 × 12 saves enormous time. Here are the trickier ones students often miss:
| × | 6 | 7 | 8 | 9 | 12 |
|---|---|---|---|---|---|
| 6 | 36 | 42 | 48 | 54 | 72 |
| 7 | 42 | 49 | 56 | 63 | 84 |
| 8 | 48 | 56 | 64 | 72 | 96 |
| 9 | 54 | 63 | 72 | 81 | 108 |
Division Basics
Division splits a total into equal groups. 20 ÷ 4 = 5 means "20 split into 4 equal groups gives 5 in each group."
Vocabulary
Dividend ÷ Divisor = Quotient
28 ÷ 7 = 4 (28 is the dividend, 7 is divisor, 4 is quotient)
Remainders
When a number doesn't divide evenly: 17 ÷ 5 = 3 remainder 2 (written 3 R2)
Division and multiplication are inverses: if 6 × 8 = 48, then 48 ÷ 8 = 6 and 48 ÷ 6 = 8.
Long Division
Long division handles larger numbers step by step: Divide, Multiply, Subtract, Bring down (DMSB).
Example: 156 ÷ 4
39
4)156
12 ← 4×3
--
36
36 ← 4×9
--
0
156 ÷ 4 = 39
Quick Quiz
Test what you just learned. Choose the best answer for each question.