Percentage of a Quantity: 10%, 25%, 50%, 75%

Fifty per cent of an amount is half of it; twenty-five per cent is a quarter, which is half of half; seventy-five per cent is three quarters. So fifty per cent of sixty is thirty, twenty-five per cent of eighty is twenty, and seventy-five per cent of eighty is three twenties, sixty — or the eighty with a quarter taken away, which is also sixty. This is exactly the fractions-of-a-quantity lesson with the fractions renamed.

Ten per cent is a tenth: divide by ten, which moves the digits one column right. Ten per cent of two hundred and fifty is twenty-five; of ninety, nine; of thirty-five dollars, three dollars fifty. And ten per cent is the workhorse, because the other percentages are built from it. Twenty per cent is two tenths: twenty per cent of ninety is eighteen. Thirty per cent of two hundred is three twenties, sixty. Five per cent is half a tenth: five per cent of four hundred is half of forty, twenty. Find ten per cent first, then multiply or halve.

A discount is a percentage of the price that you do not pay. An eighty-dollar jacket at twenty-five per cent off: the discount is twenty-five per cent of eighty, twenty dollars, and the price you pay is sixty. Questions ask for one or the other, so read which. The shortcut is that twenty-five per cent off means paying seventy-five per cent. When a second discount follows, it comes off the new price: sixty-dollar shoes at twenty-five per cent off are forty-five, and a further ten per cent off that is four dollars fifty, so forty dollars fifty — not thirty-five per cent off the original.

The backwards question gives a percentage and asks for the whole. Ten per cent of a number is seven: a tenth is seven, so the whole is seventy. Twenty-five per cent of a price is twelve dollars: a quarter is twelve, so the price is forty-eight. When the percentage is not a unit, get to one first: twenty per cent of a class is six students, so ten per cent is three, and the class is thirty. Seventy-five per cent is sixty, so twenty-five per cent is twenty and the whole is eighty. Find the unit, scale to a hundred, check forwards.

In a story, of tells you the amount, and not, off and left tell you to subtract from it. Thirty per cent of two hundred students walk: sixty walk, so one hundred and forty do not. A hundred and twenty dollar bike at twenty-five per cent off: the discount is thirty, you pay ninety. Five per cent of four hundred tickets: twenty. And a size check every time — a percentage under a hundred gives less than the amount, so thirty per cent of two hundred cannot be six hundred. Quiz and exercises now.