The distributive property is a fundamental concept in mathematics that allows us to simplify and solve expressions involving multiplication and addition. It states that for any real numbers a, b, and c:

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

In other words, when a number is multiplied by the sum of two other numbers, it is the same as the sum of the products of the number and each of the other two numbers individually.

Let's look at a few examples to understand the distributive property better:

**Example 1:**

Simplify the expression 3 * (2 + 4).

Using the distributive property, we have:

3 * (2 + 4) = 3 * 2 + 3 * 4 = 6 + 12 = 18

So, 3 * (2 + 4) simplifies to 18.

**Example 2:**

Simplify the expression 5 * (x + 3).

Using the distributive property, we have:

5 * (x + 3) = 5x + 5 * 3 = 5x + 15

So, 5 * (x + 3) simplifies to 5x + 15.

To master the distributive property, here are some key points to remember and practice:

- Understand the concept: The distributive property shows the relationship between multiplication and addition. It helps in breaking down complex expressions into simpler forms.
- Practice problems: Work on various exercises involving the distributive property to reinforce your understanding. Start with simple numerical expressions and then move on to algebraic expressions.
- Combine like terms: After applying the distributive property, always look for like terms to combine and simplify the expression further.
- Apply to real-life situations: Understand how the distributive property can be applied in real-world scenarios, such as distributing items into groups or calculating costs.

By mastering the distributive property, you'll gain a strong foundation in algebra and problem-solving skills that are essential for higher-level mathematics.

Keep practicing and exploring different types of problems to become proficient in applying the distributive property effectively.

Happy learning!

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.