Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Commutative Property of Addition

## What is the Commutative Property of Addition?

**The commutative property of addition tells us that we can add things in any order and still get the same sum.** The commutative property is one of the building blocks for the rules of algebra. Here’s an example of the property in use:

2 + 4 = 4 + 2

The commutative property of addition also applies to variables in the same way it applies to numbers. Here’s an example:

a + b = b + a

### When to use it: The Commutative Property is Everywhere

This math property is simple and still very useful. When we are re-arranging equations and performing algebraic maneuvers, the commutative property of addition allows us to write summed numbers and variables in any order. You may not even notice when you use it, but any time you rearrange summed terms on one side of an equation, you are using the commutative property of addition!

In math, **something is commutative if changing the order of numbers does not affect the result**. The commutative property also applies to multiplication. Called the commutative property of multiplication, it tells us that numbers and variables can be multiplied in any order while having the same result.

### Example Problems

**Problem 1:**

Prove the commutative property of addition by calculating the sum of 5 and 8.

Solution:

Let’s write out the equation for summing 5 and 8 with the numbers in both possible orders.

5 + 8 = 13

8 + 5 = 13**Therefore, 5 + 8 = 8 + 5.**

**Problem 2:**

Following the rules of algebra, rewrite the equation 3b + 4c + a = 9 so the variables are in alphabetical order.

Solution:

The commutative property of addition tells us that we can add things in any order and still get the same sum. So, let’s change the order of terms on the left-hand side of this equation.**a + 3b + 4c = 9**

Result :

Worksheet 1

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Cheat sheet

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