Distributive Property
Practice Distributive Property in Grade 10 algebra: apply distribution rules to multiply and simplify expressions step by step with Saxon Algebra 2 Saxon Algebra 2.
Key Concepts
The Distributive Property states that $a(b + c) = ab + ac$. It allows you to multiply a sum by multiplying each addend separately and then adding the products.
a. To solve $7(32)$, split it into $7(30 + 2)$, which becomes $7 \cdot 30 + 7 \cdot 2 = 210 + 14 = 224$. b. Buying 4 concert tickets at 49 dollars each is $4(50 1) = 4 \cdot 50 4 \cdot 1 = 200 4 = 196$ dollars.
This property is your ultimate shortcut for tough multiplication! It lets you break apart a intimidating number into friendly pieces. Instead of fighting a big boss, you get to take on two smaller, much easier minions one at a time. It is a secret weapon for mental math.
Common Questions
What is the Distributive Property formula?
The Distributive Property states a(b + c) = ab + ac. Every term inside the parentheses gets multiplied by the term outside. For 8(2x - 5): 8·2x = 16x and 8·(-5) = -40, giving 16x - 40.
How do you use the Distributive Property for mental math?
Break a hard number into friendly parts. To calculate 7 × 32, write it as 7(30 + 2) = 7·30 + 7·2 = 210 + 14 = 224. For 4 tickets at $49 each: 4(50 - 1) = 200 - 4 = $196.
What is the most common Distributive Property mistake?
Only distributing to the first term. For 8(2x - 5), students write 16x - 5 instead of 16x - 40. Always multiply the outside number by every single term inside the parentheses.