Distributive Property and Order of Operations
Grade 8 math lesson on the distributive property and order of operations (PEMDAS/BODMAS). Students learn to apply the distributive property to expand expressions, and use the correct order of operations to evaluate multi-step arithmetic and algebraic expressions.
Key Concepts
New Concept This property lets you multiply a sum by multiplying each addend separately before adding. It is essential for expanding and factoring algebraic expressions. $$a(b+c) = a \cdot b + a \cdot c$$ What’s next You’ll start by using this property to expand and factor expressions. Then, you’ll see how it fits within the order of operations to solve multi step problems.
Common Questions
What is the distributive property?
The distributive property states that a(b + c) = ab + ac. You multiply the factor outside the parentheses by each term inside. For example, 3(4 + 5) = 3 x 4 + 3 x 5 = 12 + 15 = 27.
What is the order of operations?
The order of operations (PEMDAS) requires you to evaluate: Parentheses first, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. This ensures everyone gets the same answer.
How do the distributive property and order of operations work together?
The distributive property allows you to rewrite expressions with parentheses in an equivalent form without parentheses. The order of operations then tells you the sequence for evaluating the resulting expression.
Why must we follow the order of operations?
Without a universal agreement on order of operations, the same expression could produce different answers. PEMDAS ensures that 2 + 3 x 4 always equals 14 (not 20) because multiplication comes before addition.