Commutative property facts for kids

The commutative property is a cool math rule! It tells us that you can change the order of numbers when you add or multiply them, and your answer will still be the same. It's like saying it doesn't matter if you put on your left sock then your right, or your right sock then your left – you still end up with both socks on!

What is the Commutative Property?

This property is super handy in math. For example, if you add 2 and 8, you get 10. If you switch them around and add 8 and 2, you still get 10!

• equals 10
• also equals 10

It works the same way for multiplication. If you multiply 5 by 7, you get 35. If you multiply 7 by 5, you also get 35.

• equals 35
• also equals 35

You can use this rule with any numbers, and even with more than two numbers!

Commutative Property in Action

In math, we often use letters to stand for any number. These letters are called variables. The definition of the commutative property for addition looks like this: Here, a and b can be any number you choose. This simple rule helps us understand how numbers work together.

When Does it NOT Work?

Not all math operations follow the commutative property. For example, dividing numbers is not commutative.

• If you divide 6 by 3, you get 2. (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 6\div3 = 2 )
• But if you switch the numbers and divide 3 by 6, you get a fraction: one-half. (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 3\div6 = \frac{1}{2} )

Since 2 is not the same as one-half, division is not commutative.

Subtraction also does not follow this rule.

• If you subtract 2 from 6, you get 4. (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 6-2 = 4 )
• But if you subtract 6 from 2, you get negative 4. (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 2-6 = -4 )

Since 4 is not the same as negative 4, subtraction is not commutative.

Beyond Basic Math

As you learn more advanced math, like calculus, you'll discover other operations that are also commutative, not just adding and multiplying. This property is a basic idea that helps mathematicians understand how different math systems work.

Images for kids

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  The first known use of the term was in a French Journal published in 1814

See also

In Spanish: Conmutatividad para niños