We Distribute, Yet Things Multiply
Break big multiplications into friendly parts, then put the answers back together.
Fact Sheet: Distributivity
Distributivity connects multiplication with addition and subtraction. It helps us split a difficult multiplication into easier pieces.
5 × (8 + 4)= 5 × 8 + 5 × 4= 60
Formula Hub
Over Addition
a × (b + c) = a × b + a × c
Split the second factor into a sum.
Over Subtraction
a × (b − c) = a × b − a × c
Useful for numbers like 19, 29, 99.
Reverse Distributivity
a × b + a × c = a × (b + c)
Common factor can be taken out.
Area Connection
height × total width = area part 1 + area part 2
This makes distributivity visible.
Friendly Splits
27 = 20 + 7
48 = 50 − 2
99 = 100 − 1
Check Method
Both sides must give the same value.
Example: 6 × 13 = 6 × 10 + 6 × 3 = 78.
Interactive Lab: Distribute & Multiply
Activity Zone
🎛️ Split Builder
Choose a multiplication and split one factor into friendly parts.
🧱 Area Model Builder
The rectangle shows a × (b + c). Aqua cells are a × b, pink cells are a × c.
⚡ Mental Math Shortcut
Use nearby round numbers.
🔁 Match Equivalent Expressions
Which expression is equivalent?
🧮 Distributive Table
Generate examples of a × (b + c).
Worksheet Generator
Create printable worksheets with distributive property, mental math, reverse distributivity, and area-model questions.
Real-World Use
🌍 Real-Life Case Generator
Teacher Tools
Learning Outcomes
- Explain the distributive property using numbers and area models.
- Use a × (b + c) and a × (b − c) to simplify multiplication.
- Identify equivalent expressions.
- Apply distributivity in real-life calculations.
- Use reverse distributivity to combine terms with a common factor.
Exit Ticket Prompts
- Show two ways to calculate 6 × 14.
- Explain why 8 × (10 + 3) equals 8 × 10 + 8 × 3.
- Use distributivity to solve 99 × 7 mentally.