The distributive property is a fundamental property in mathematics that allows us to simplify expressions and solve equations. It states that for any numbers a, b, and c, the following holds true:

a * (b + c) = a * b + a * c

This means that when we have a number outside of a set of parentheses, we can distribute that number to each term inside the parentheses by multiplying. This property is extremely useful in simplifying algebraic expressions and solving equations.

Example 1: 3 * (2 + 4) = 3 * 2 + 3 * 4

Example 2: 5 * (x + 2) = 5x + 10

Example 3: -2 * (3x - 7) = -6x + 14

- Understand the concept of the distributive property: The distributive property allows us to distribute a number to each term inside a set of parentheses.
- Practice using the distributive property with both numbers and variables: Work through examples where you distribute numbers and variables to expressions inside parentheses.
- Apply the distributive property to simplify expressions: Use the distributive property to simplify and combine like terms in algebraic expressions.
- Solve equations using the distributive property: Apply the distributive property to solve equations by distributing a number to terms on both sides of the equation.
- Challenge yourself with word problems: Practice solving word problems that involve the distributive property to apply the concept in real-life scenarios.

Mastering the distributive property is essential for success in algebra and higher level mathematics. By understanding and applying this property, you'll be able to simplify expressions and solve equations with confidence.

.Study GuideDistributive Property Worksheet/Answer key

Distributive Property Worksheet/Answer key

Distributive Property Worksheet/Answer key

Distributive Property

Number and Operations (NCTM)

Understand meanings of operations and how they relate to one another.

Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Connections to the Grade 6 Focal Points (NCTM)

Algebra: Students use the commutative, associative, and distributive properties to show that two expressions are equivalent. They also illustrate properties of operations by showing that two expressions are equivalent in a given context (e.g., determining the area in two different ways for a rectangle whose dimensions are x + 3 by 5). Sequences, including those that arise in the context of finding possible rules for patterns of figures or stacks of objects, provide opportunities for students to develop formulas.