Commutativity Math Example 2

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

Example 2

medium
Verify that \(4 \times 7 = 7 \times 4\) using a rectangular array. Explain what changes and what stays the same.

Solution

  1. 1
    \(4 \times 7\): 4 rows, 7 columns → 28 items.
  2. 2
    \(7 \times 4\): 7 rows, 4 columns → 28 items.
  3. 3
    The array is rotated, but the total count is the same.
  4. 4
    \(4 \times 7 = 7 \times 4 = 28\). ✓

Answer

Both equal 28; commutativity holds for multiplication
Commutativity for multiplication: \(a \times b = b \times a\). Rotating an array changes its orientation but not its total.

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 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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