Associativity Math Example 3

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

Example 3

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

Solution

  1. 1
    \((8+3)+7 = 11+7 = 18\).
  2. 2
    \(8+(3+7) = 8+10 = 18\).
  3. 3
    The second grouping is easier because \(3+7=10\) is a nice round number.

Answer

18 (second grouping is easier)
Associativity lets us pick the most convenient grouping. Here \(8 + (3 + 7) = 8 + 10\) is simpler than \(11 + 7\).

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 1 easy

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

Example 2 medium

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

Example 4 medium

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

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