Associative Property

The associative property is a fundamental property of addition and multiplication. It states that the way in which numbers are grouped when adding or multiplying does not change the sum or product. In other words, changing the grouping of numbers does not change the result.

Addition

For addition, the associative property can be written as:

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

This means that when adding three or more numbers, the sum will remain the same regardless of how the numbers are grouped.

Example:

Let's consider the numbers 2, 3, and 4:

(2 + 3) + 4 = 2 + (3 + 4) = 9

Multiplication

For multiplication, the associative property can be written as:

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

This means that when multiplying three or more numbers, the product will remain the same regardless of how the numbers are grouped.

Example:

Let's consider the numbers 2, 3, and 4:

(2 * 3) * 4 = 2 * (3 * 4) = 24

Study Guide

To understand and apply the associative property, follow these steps:

Identify the numbers involved in the addition or multiplication operation.
Group the numbers in different ways to test the property. For addition, group the numbers using parentheses in different orders. For multiplication, rearrange the order of multiplication using parentheses.
Perform the operations following different groupings and compare the results.
Observe that the sum or product remains the same regardless of the grouping, which demonstrates the associative property.
Practice applying the property with various sets of numbers to reinforce understanding.

Remember that the associative property only applies to addition and multiplication, and it does not apply to subtraction or division.

By understanding and practicing the associative property, you can efficiently manipulate numbers and simplify calculations in mathematics.

Good luck with your studies!

◂Math Worksheets and Study Guides Fourth Grade. More 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.

Grade 4 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication

Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multi-digit whole numbers. They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.