Fractions in Disguise
NoteWhat This Chapter Covers
A percentage is nothing more than a fraction in a costume, it always whispers “out of one hundred.” This chapter teaches you to see through the costume and to move smoothly between fractions, decimals and percentages (the FDP trio). We use percentages to pull out a part of a quantity, to compare proportions on a level playing field, and to capture how things swell or shrink, prices climbing, audiences thinning, profit and loss, discounts, taxes, and the slow snowball of compound growth. Along the way we collect a handful of trap percentages that catch nearly everyone the first time, and we trace the “per hundred” idea back through Roman tax ledgers and ancient Indian treatises.
Learning Outcomes
By the end of this chapter, you will be able to:
- say what per cent really means and convert without effort between fractions, decimals and percentages;
- compute a given percentage of a quantity, and run the process in reverse to recover the whole;
- rewrite a ratio as a percentage, and lean on percentages to compare proportions fairly;
- find a percentage increase or decrease, including profit, loss, discount and tax;
- describe compound growth and decline, and write down the formulas for simple and compound change;
- recognise and unpick trap percentages, why “30% then 25%” is not 55%, and why a percentage of one whole says nothing on its own about another.