Practice Reasoning vs Computation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The distinction between understanding why something works and mechanically calculating.

Computation is following a recipe; reasoning is deciding which recipe to use and why. Most math mistakes come from computing when you should be reasoning first.

Example 1

easy
Without computing, determine whether 997 \times 1003 is greater than, less than, or equal to 1000^2. Then verify by computation.

Example 2

medium
Use reasoning (not direct computation) to find the units digit of 7^{100}.

Example 3

easy
Without long division, determine whether 2^{10} is greater or less than 10^3. Explain your reasoning.

Example 4

medium
By reasoning (not expanding), determine the degree of the polynomial (x^3+2)^4(x^2-1)^5.
← Back to Reasoning vs Computation Worked Examples