Associativity Math Example 1

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

Example 1

easy
Show that \((2 + 5) + 4 = 2 + (5 + 4)\) by calculating both sides.

Solution

  1. 1
    Left side: \((2 + 5) + 4 = 7 + 4 = 11\).
  2. 2
    Right side: \(2 + (5 + 4) = 2 + 9 = 11\).
  3. 3
    Both sides equal 11.
  4. 4
    The grouping does not change the sum.

Answer

Both equal 11
The associative property: \((a + b) + c = a + (b + c)\). You can change the grouping without changing the result.

About Associativity

A property where changing the grouping of operands does not change the result: (a⋆b)⋆c=a⋆(b⋆c)(a \star b) \star c = a \star (b \star c).

Learn more about Associativity →

More Associativity Examples

Example 2 medium

Use associativity to make this multiplication easier: (5 times 4 times 6).

Example 3 easy

Calculate ((8 + 3) + 7) and (8 + (3 + 7)). Which is easier? Why?

Example 4 medium

Use associativity to simplify: (2 times 7 times 5).

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