4 mistakes learners make with percentage change, each one named and explained.
Repeated change multiplies, it does not add, and working backwards means dividing by the multiplier rather than putting the percentage back on.
Two hours of 20 per cent growth is worked out for one hour.
The first application is the calculation you know how to do, and it produces a complete answer.
Question. 500 growing by 20 per cent for 2 hours
A common answer. 600
The answer. 720
Why. 600 is the figure after one hour, and the question asked for two.
Count how many times the change happens and write that many multiplications down first.
Two rises of 20% are treated as one rise of 40%, or 10% then 5% off is treated as 15% off.
Adding them is quicker and it is very nearly right, which is exactly what makes it stick.
Question. 500, increased by 20% twice
A common answer. 700, from a single 40% rise
The answer. 720
Why. The second rise is 20% of 600, not of 500, so it is worth more than the first.
Each change acts on what is there at the time. Multiply the multipliers, never add the percentages.
A phone costs £240 after 20% off, and the original is given as £288.
Undoing a subtraction with an addition is right for numbers, and percentages look like they should behave the same way.
Question. £240 after 20% off
A common answer. £288, which is £240 plus 20%
The answer. £300
Why. £240 is 80% of the original, so the original is 240 divided by 0.8.
Going backwards means dividing by the multiplier. Check by going forwards again.
Two years of 20 per cent growth is treated as a single 40 per cent.
Adding the percentages is quicker and it is very nearly right for small changes.
Question. 500 growing by 20 per cent for 2 hours
A common answer. 500 x 1.4 = 700
The answer. 500 x 1.2 x 1.2 = 720
Why. The second increase applies to 600, not to the original 500.
Each change applies to whatever the amount is at the time. Work them one at a time.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.