Commutative Property

The commutative property is a fundamental property in mathematics that applies to operations such as addition and multiplication. It states that the order in which two numbers are added or multiplied does not change the result. In other words, the numbers can be rearranged without affecting the outcome.

Addition

For addition, the commutative property can be expressed as:

a + b = b + a

In other words, when adding two numbers, you can change the order of the numbers without changing the sum. For example:

3 + 5 = 5 + 3

Multiplication

For multiplication, the commutative property can be expressed as:

a × b = b × a

This means that the order of the numbers being multiplied can be changed without affecting the product. For example:

2 × 4 = 4 × 2

Study Guide

Here are some key points to remember about the commutative property:

The commutative property applies to addition and multiplication.
It states that the order of the numbers being added or multiplied can be changed without affecting the result.
For addition, the property can be expressed as a + b = b + a.
For multiplication, the property can be expressed as a × b = b × a.
It is important to note that the commutative property does not apply to subtraction or division.

Understanding the commutative property is essential for performing arithmetic operations and simplifying mathematical expressions.

By applying the commutative property, you can rearrange numbers in a way that makes calculations easier and more efficient.

Be sure to practice using the commutative property with different sets of numbers to reinforce your understanding of this important mathematical concept.

◂Math Worksheets and Study Guides Fifth Grade. Multiplication

Vocabulary/Answer key

Multiplication

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

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.

Connections to the Grade 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).