The Distributive Law
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the distributive law (distributive property of multiplication over addition). Students learn that a(b + c) = ab + ac, and apply this property to expand algebraic expressions, multiply polynomials, and simplify equations.
Key Concepts
Property If $a$, $b$, and $c$ are any numbers, then $$a(b + c) = ab + ac$$ Steps for Solving Linear Equations. 1. Use the distributive law to remove any parentheses. 2. Combine like terms on each side of the equation. 3. By adding or subtracting the same quantity on both sides of the equation, get all the variable terms on one side and all the constant terms on the other. 4. Divide both sides by the coefficient of the variable to obtain an equation of the form $x = a$.
Examples To simplify $5(x+3)$, you distribute the 5 to both $x$ and 3. This gives $5 \cdot x + 5 \cdot 3$, which simplifies to $5x+15$. To simplify $6(2a 4) + 7$, first distribute the 6 to get $12a 24 + 7$. Then, combine the constant terms to get the final expression $12a 17$. To solve the equation $3(y 2) = 9$, first distribute the 3 to get $3y 6 = 9$. Add 6 to both sides to get $3y = 15$, then divide by 3 to find $y=5$.
Explanation Think of this law as 'distributing' the term outside the parentheses to every term inside. It helps break down multiplication with a group of terms, turning one complex multiplication into several simpler ones.
Common Questions
What is the distributive law?
The distributive law states a(b + c) = ab + ac. It allows you to multiply a factor by each term inside parentheses separately.
How do you use the distributive law to expand an expression?
Multiply the factor outside the parentheses by each term inside. For example, 3(x + 5) = 3x + 15.
Does the distributive law work for subtraction?
Yes. a(b - c) = ab - ac. The factor distributes to both terms, and the subtraction sign is preserved.
How does the distributive law help solve equations?
It allows you to remove parentheses so you can combine like terms and apply inverse operations to solve for the variable.
Where is the distributive law taught in Grade 6?
The distributive law is a foundational topic in the Yoshiwara Elementary Algebra textbook for Grade 6.