Commutativity Math Example 4

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

Example 4

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

Solution

  1. 1
    \(10 - 3 = 7\).
  2. 2
    \(3 - 10 = -7\).
  3. 3
    \(7 \neq -7\), so \(10 - 3 \neq 3 - 10\).
  4. 4
    Subtraction is NOT commutative.

Answer

No — subtraction is not commutative
Commutativity holds for addition and multiplication but NOT subtraction or division. Order matters when subtracting.

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 1 easy

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

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.

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