Distributive Property

The distributive property is a fundamental concept in mathematics that helps in simplifying expressions and solving equations. It is used to distribute a value across the terms inside parentheses. The general form of the distributive property is:

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

This means that when a value is multiplied by the sum of two other values inside the parentheses, it can be distributed or split up and multiplied with each term inside the parentheses individually.

Example:

Let's consider the expression 3 * (2 + 4). Using the distributive property, we can simplify it as:

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

It's important to note that the distributive property also works in reverse. That is, we can also use it to factor out a common term from multiple terms in an expression.

Example:

Consider the expression 5x + 10x. We can factor out the common term '5' using the distributive property as:

5x + 10x = 5(x) + 5(2x) = 5(x + 2x) = 5(3x) = 15x

Study Guide:

Understand the concept of multiplication and addition.
Learn to recognize expressions where the distributive property can be applied.
Practice applying the distributive property to simplify expressions and solve equations.
Understand how to factor out common terms using the distributive property.
Practice with various examples to strengthen your understanding of the concept.

By mastering the distributive property, you will be able to simplify expressions and equations more efficiently, which is a crucial skill in algebra and higher-level mathematics.

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills:

Number and Operations (NCTM)

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

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Data Analysis and Probability (NCTM)

Understand and apply basic concepts of probability.

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.

Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

Connections to the Grade 4 Focal Points (NCTM)

Number and Operations: Building on their work in grade 3, students extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances. Students develop understandings of strategies for multi-digit division by using models that represent division as the inverse of multiplication, as partitioning, or as successive subtraction. By working with decimals, students extend their ability to recognize equivalent fractions. Students' earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.