Distributive Property
Learn how to multiply a number or variable by a sum or difference inside parentheses.
Definition
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Worked Examples
Simplify:
Identify the factor outside
The number is outside the parentheses → Factor:
Distribute to each term
and →
Add the products
→
Answer:
Common Mistakes
Only distributing to the first term:
Why it's wrong: The factor must multiply EVERY term inside the parentheses, not just the first one.
Correct: (multiply by both AND )
Forgetting to change signs when distributing a negative:
Why it's wrong: A negative factor changes the sign of EACH product.
Correct: (negative times positive equals negative)
Double negative error:
Why it's wrong: Negative times negative equals positive, not negative.
Correct: (because )
Interactive Visual
Click on the circle to change the fraction
Balance Scale
Solution: x = 4
Interactive Sandbox
Expression Calculator
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Practice Problems
18 problemsWhich expression is equivalent to ?
Why It Matters
- Simplifying expressions: Turn into
- Mental math: Calculate as
- Factoring: Reverse the process to factor expressions
- Real-world applications: Calculate totals when buying multiple items at different prices
Real World Applications
Shopping Calculations
The distributive property helps calculate totals when buying multiples of items with different components.
Example:
You buy 3 meal deals that each include a burger for 5 euros and fries for 2 euros. Total: euros.
You are buying 4 gift bags. Each bag contains a toy for 8 euros and candy for 3 euros.
What is the total cost?
Step 1: Write the mathematical expression
Write the expression using distributive property:
Mental Math Tricks
Use the distributive property to make difficult calculations easier in your head.
Example:
To calculate , think of it as .
You need to calculate in your head.
How can you break this down?
Step 1: Write the mathematical expression
Rewrite as :
Key Takeaways
- 1The distributive property:
- 2Multiply the outside factor by EACH term inside the parentheses
- 3Works with both addition and subtraction
- 4When distributing a negative, all signs change
- 5Useful for simplifying expressions and mental math
Frequently Asked Questions
Glossary
- Distributive property
- A rule that states
- Factor
- A number or expression that multiplies another (the number outside the parentheses)
- Term
- A part of an expression separated by + or - signs
- Expand
- To remove parentheses by applying the distributive property
- Distribute
- To multiply the outside factor by each term inside the parentheses
Formula Card
Distributive Property (Addition)
Multiply the factor by each term inside, then add
Distributive Property (Subtraction)
Multiply the factor by each term inside, keep the minus
Right-side Distribution
The factor can also be on the right side