Adding and Taking Off a Percentage - More About

Four key understandings are required for students to realise that adding on (or taking off) a percentage (eg 5.3%) can be undertaken by multiplication by a decimal. Students need to:

(1) Understand that they need 105.3% of the base quantity ie 100% of base quantity plus 5.3% of the base quantity for a mark-up and 100% - 5.3% of the base quantity for a discount. Some students are not confident with percentages over 100%.

(2) Link finding a percentage of a quantity with multiplication by a decimal. (eg to find 80%, multiply by 0.80; to find 120%, multiply by 1.20)

(3) Be able to convert the 5.3% and 105.3% to its decimal representation (0.053 and 1.053).

(4) Students need to appreciate the effect of multiplying a number by 1.053 (or 0.947) so that they are able to estimate and check answers, especially when using technology.

Understanding the link between adding and subtracting a percentage and multiplying by a decimal is the key to appreciating that constant percentage growth or decay is exponential growth or decay. The relevant progression point is in Structure 5.5 "Students identify and represent quadratic and exponential functions by table (from constant difference or constant ratio/percentage difference), rule and graph with consideration of independent and dependent variables, domain and range."

There are many advantages in being able to calculate the result of adding a percentage by multiplying by a decimal. For example if I invest $2000 at 5.3% per year, after one year I have $2000 × 1.053, after two years I have $2000 × 1.053 × 1.053, after 3 years I have $2000 × 1.053 × 1.053 × 1.053 etc. Students who calculated the 5.3% interest and add have more calculations.

Calculating interest method					Multiplying by decimal
Year	Amount	Interest	Total		Year	Amount
1	2000	106	2106		1	2000
2	2106	112	2218		2	2106
3	2218	118	2335		3	2218
4	2335	124	2459		4	2335
5	2459				5	2459