Associativity Math Example 4

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

Example 4

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

Solution

  1. 1
    Regroup: \((2 \times 5) \times 7 = 10 \times 7 = 70\).
  2. 2
    Answer: 70.

Answer

70
Regroup \(2 \times 5 = 10\) first, then \(10 \times 7 = 70\) is easy. Associativity lets us choose the order.

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 3 easy

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

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