Structure vs Computation Math Example 4

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

Example 4

medium
Is 37×4337 \times 43 closer to 15001500 or 16001600? Use structure.

Solution

  1. 1
    37×43=(40−3)(40+3)=402−9=1600−9=159137 \times 43 = (40-3)(40+3) = 40^2 - 9 = 1600 - 9 = 1591.
  2. 2
    Closer to 16001600.

Answer

15911591 — closer to 16001600.
Recognizing 37×4337 \times 43 as (40−3)(40+3)(40-3)(40+3), a difference of squares, makes the mental computation trivial. This is structure vs computation in action.

About Structure vs Computation

The distinction between recognizing mathematical structure and patterns versus performing step-by-step arithmetic computations.

Learn more about Structure vs Computation →

More Structure vs Computation Examples

Example 1 easy

Without computing, which is larger: [formula] or [formula]?

Example 2 medium

Compute [formula] using structure, not brute force.

Example 3 easy

Simplify [formula] structurally (don't substitute values).

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