Distributing Over Addition
Apply the distributive property over addition in Grade 9 algebra. Expand a(b+c) = ab+ac to remove parentheses, simplify expressions, and set up linear equation solutions.
Key Concepts
Property To simplify expressions like $\frac{A}{B}\left(\frac{C}{D} + \frac{E}{F}\right)$, you distribute the outside term to each term inside the parentheses: $\frac{A \cdot C}{B \cdot D} + \frac{A \cdot E}{B \cdot F}$.
Examples $\frac{a^2}{b^3}\left(\frac{a^3}{b^2} + \frac{2b^4}{c}\right) = \left(\frac{a^2}{b^3} \cdot \frac{a^3}{b^2}\right) + \left(\frac{a^2}{b^3} \cdot \frac{2b^4}{c}\right) = \frac{a^5}{b^5} + \frac{2a^2b}{c}$ $\frac{m}{n}\left(\frac{xy}{mk} 3m^2\right) = \frac{m \cdot xy}{n \cdot mk} \frac{m \cdot 3m^2}{n} = \frac{xy}{nk} \frac{3m^3}{n}$.
Explanation This is like being a delivery person for math! The fraction outside the parentheses has to be delivered, or multiplied, to every single term waiting inside. After you've made all your deliveries, you just need to tidy up by using exponent rules to simplify each of the new fractions you've created. It's all about sharing the multiplication!
Common Questions
How does distributing over addition work?
Multiply the factor outside parentheses by each term inside. For a(b + c), you get ab + ac. Every term inside gets multiplied by the outside factor.
Why is the distributive property fundamental in algebra?
It enables expanding expressions, combining like terms, factoring, and solving equations. It connects multiplication and addition for flexible algebraic manipulation.
How do you distribute when there are multiple terms inside parentheses?
Multiply the outside factor by every single term inside. For 3(2x + 5 - y), distribute to get 6x + 15 - 3y. Never skip terms, especially those with negative signs.