Concept 4

Use estimation and bounds to check reasonableness of answers.

Core Idea

A fast estimate can tell you whether an answer is even plausible before you finish exact arithmetic. On ACT Math, that saves time and catches avoidable mistakes.

Understanding

Estimate first, then calculate. A quick bound can tell you whether the answer is even plausible.

Round or bound the numbers enough to predict the size of the result. If the answer should decrease first and then rise slightly, or if multiplying by a fraction should shrink the quantity, the direction matters as much as the arithmetic.

  • Round key values to see the expected size.
  • Track whether each operation should increase or decrease the quantity.
  • Use the estimate to eliminate impossible choices.
  • Compare the exact answer to the estimate before finalizing it.

Step by Step

  1. Round or bound the key numbers enough to see the expected size of the result.
  2. Track whether each operation should increase or decrease the quantity.
  3. Use the estimate to eliminate impossible answer choices quickly.
  4. Compare your exact answer to the estimate before finalizing it.

Misconceptions

  • Treating a percent decrease and a percent increase as one net operation on the original value.
  • Ignoring whether the result should be larger or smaller than the starting amount.
  • Accepting a precise-looking answer without asking whether its size makes sense.
Question

Worked Example

A jacket marked $59.50 is discounted by 15% and then taxed at 8%. Which total price is most reasonable?

Select an answer to see the explanation