Multiplication and Division

These are inverse operations that work with groups.

Multiplication

Multiplication is repeated addition: $4 \times 3 = 3 + 3 + 3 + 3 = 12$

"4 groups of 3"

Multiplication Properties

Commutative Property

$3 \times 5 = 5 \times 3 = 15$

Associative Property

$(2 \times 3) \times 4 = 2 \times (3 \times 4) = 24$

Identity Property

$7 \times 1 = 7$

Zero Property

$7 \times 0 = 0$

Distributive Property

$3 \times (4 + 2) = 3 \times 4 + 3 \times 2 = 12 + 6 = 18$

Division

Division splits a number into equal groups: $12 \div 3 = 4$

"12 split into 3 groups has 4 in each group"

Division Vocabulary

$20 \div 4 = 5$

• 20 is the dividend
• 4 is the divisor
• 5 is the quotient

Division with Remainders

When division doesn't come out even: $17 \div 5 = 3 \text{ R } 2$

Check: $5 \times 3 + 2 = 15 + 2 = 17$ ✓

Long Division Steps

Divide → Multiply → Subtract → Bring down

Example: $156 \div 12$

1. 12 goes into 15 once (1)
2. $12 \times 1 = 12$
3. $15 - 12 = 3$
4. Bring down 6 → 36
5. 12 goes into 36 three times (3)
6. $12 \times 3 = 36$
7. $36 - 36 = 0$

Answer: 13