Associative Property of Addition

The Associative Property of Addition states that the way numbers are grouped in an addition problem does not change the sum. In other words, for any real numbers \( a \), \( b \), and \( c \):

\[ (a + b) + c = a + (b + c) \]

Where:

\(a,b,c\) = real numbers

Example:

\[ (3 + 5) + 2 = 3 + (5 + 2) \]\[ 8 + 2 = 3 + 7 \]\[ 10 = 10 \]

This property shows that you can regroup the numbers without affecting the result, making calculations more flexible and efficient.

The Associative Property does not work with subtraction. This is because changing the grouping of numbers in subtraction can lead to different results.

Example:

\[ (10 - 5) - 2 \neq 10 - (5 - 2) \]

Calculating both sides:

\[ (10 - 5) - 2 = 5 - 2 = 3 \]\[ 10 - (5 - 2) = 10 - 3 = 7 \]

Since \( 3 \neq 7 \), subtraction is not associative.

Latex

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