Estimating Percentages

As a check on percentage calculations, students need to know some standard simple fractions and their percentages equivalents. This will help estimating percentages as a check on calculation.

Preliminary

First check that the students know these simple fractions and percentage equivalents. These must be known off by heart.

10% = 1/10
12.5% = 1/8
20% = 1/5
25% = 1/4
50% = 1/2

Using Number Properties

Problem: “Melissa works out 4.9% of $456 on a calculator and gets $22.34. Check Melissa’s calculation by estimation.”

Discuss why although 4.9% ≈ 5% = 1/20, this is not useful in estimating.
(Answer: Finding 1/20 of a number mentally is not easy.)

Discuss why starting at 10% is useful and then this amount is halved.
(Answer: 10% of 460 = 1/10 of 460 = 46. Halving this to 5% is easy: ½ of 46 = 23.)

Write 4.9% of $456 ≈ $23 on the board. Discuss whether Melissa’s calculator answer is acceptable.
(Answer: Yes. 22.34 is near enough to 23.)

Problem: “16% of 3 961 TVs are found to be faulty at the factory and need repairs before they are sent for sale. About how many sets is this?”

(Possible answer: Discuss why 10% of 4 000 = 400, 5% of 4 000 = half of 400 = 200, so 16% of 3 961 ≈ 400 + 200 = 600.)

Examples: Worksheet (Material Master 8–19).

Understanding Number Properties:

Explain how you would estimate 61% of a number. (Answer: 50% + 10%.)