Commutativity Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Show that \(6 + 9 = 9 + 6\). Does the order of adding matter?

Solution

  1. 1
    Calculate \(6 + 9\): count on from 9 to 15. \(6 + 9 = 15\).
  2. 2
    Calculate \(9 + 6\): count on from 9 to 15. \(9 + 6 = 15\).
  3. 3
    Both equal 15, so \(6 + 9 = 9 + 6\).
  4. 4
    The order does NOT matter for addition.

Answer

Both equal 15; order does not matter
The commutative property of addition states \(a + b = b + a\). You get the same sum no matter which number you start with.

About Commutativity

A property where swapping the order of two operands does not change the result: a ⋆ b=b ⋆ aa \ \star\ b = b\ \star\ a.

Learn more about Commutativity →

More Commutativity Examples

Example 2 medium

Verify that (4 times 7 = 7 times 4) using a rectangular array. Explain what changes and what stays t

Example 3 easy

If (13 + 27 = 40), what is (27 + 13)? Explain without calculating.

Example 4 medium

Does commutativity work for subtraction? Check with (10 - 3) and (3 - 10).

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