Any Percentage, and Discounts

Any percentage ending in five or zero can be built from ten per cent and five per cent. Fifteen per cent of forty dollars: ten per cent is four, five per cent is half of that, two, and fifteen per cent is six. Thirty-five per cent of sixty: three tens are eighteen, a five is three, twenty-one. The split can be anything that adds to the percentage you want — sixty-five per cent is fifty plus ten plus five if that is easier — so choose the split with the friendliest numbers.

For percentages that ten and five do not build neatly, use one per cent. One per cent is a hundredth: divide by a hundred. One per cent of three hundred is three, so seven per cent is twenty-one. One per cent of six hundred is six, so three per cent is eighteen. You can mix the methods — twelve per cent of eighty is ten per cent plus two per cent, eight plus one point six. One per cent always works; ten and five are simply quicker when they fit. And check the size: seven per cent is a small slice, well under the ten per cent of thirty.

Any discount is the same two steps: find the percentage of the price, then take it off. Thirty per cent off fifty dollars: ten per cent is five, thirty per cent is fifteen, so the price is thirty-five. Or pay seventy per cent directly. When two shops offer different prices and different discounts, work out both final prices — eighty dollars at twenty-five per cent off is sixty, ninety dollars at thirty per cent off is sixty-three, so the bigger discount is the dearer shirt. The percentage alone never tells you which is cheaper.

An increase is the same calculation added on. A ticket at eighty dollars goes up ten per cent: ten per cent is eight, the new price is eighty-eight. Rent of two hundred up five per cent is two hundred and ten. Backwards is a little harder: a price rose twenty per cent to seventy-two dollars, so seventy-two is a hundred and twenty per cent of the original, ten per cent is six, and the original was sixty. Read the direction — up or off — and notice that a rise and a fall of the same percentage do not cancel, because the fall is taken from a bigger number.

Turning a score into a percentage is the fraction lesson in reverse: part over whole, then rename to hundredths. Thirty-four out of forty: forty goes into a hundred two and a half times, so thirty-four becomes eighty-five, eighty-five per cent. When the whole does not go into a hundred nicely, simplify first: eighteen out of twenty-four is three quarters, seventy-five per cent. Percentages exist so that scores out of different totals can be compared — thirty-four out of forty and forty-three out of fifty are eighty-five and eighty-six per cent. Quiz and exercises now.