PROBLEM SOLVING

Estimation And Checking

Learn the reliable method for estimation and checking, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Estimation gives a quick, sensible range for checking an exact calculation.

Picture itPlan, solve, then check
2 · THE METHOD

Follow these steps

  1. Round each value to an appropriate place.
  2. Calculate with the rounded values.
  3. Compare the estimate with the exact answer and use an inverse where possible.
3 · WORKED EXAMPLES

See the method in action

Example 1

Round each factor to the nearest hundred. What estimate does this give for 410 × 215?

  1. Round 410 to 400 and 215 to 200, so the best estimate is 400 × 200 = 80000.
Answer: 80000
Example 2

A calculation gives 84436 for 404 × 209. Use 400 × 200 as an estimate, then find the difference between the estimate and the calculation.

  1. First estimate 400 × 200 = 80,000.
  2. Then compare it with 84436: the difference is 4436, so the stated result has a reasonable magnitude.
Answer: 4436
4 · ELEVENSPRINT TIP

A useful shortcut

Compare the estimate with the exact answer and use an inverse where possible.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.