Decimals, Fractions and Benchmark Percentages

Per cent means per hundred, so a percentage is a fraction with a hundred on the bottom. Twenty-five per cent is twenty-five out of every hundred: twenty-five hundredths, which is zero point two five, which is a quarter. On a hundred-cell grid, twenty-five cells are shaded. One amount, three names. A hundred per cent is the whole thing; fifty per cent is half; zero per cent is nothing.

Every conversion goes through hundredths. Fraction to percentage: rename the fraction with a hundred on the bottom. Three quarters is seventy-five hundredths, seventy-five per cent. Decimal to percentage: multiply by a hundred, the digits move two columns. Zero point six is sixty per cent. Percentage to decimal: divide by a hundred. Thirty-five per cent is zero point three five. Percentage to fraction: put it over a hundred and simplify. Twenty per cent is a fifth. If the fraction's bottom does not go into a hundred, like thirds, the percentage recurs, and that is for later.

Six rows to know cold. Ten per cent is a tenth is zero point one. Twenty per cent is a fifth is zero point two. Twenty-five per cent is a quarter is zero point two five. Fifty per cent is a half. Seventy-five per cent is three quarters is zero point seven five. A hundred per cent is one whole. Most percentage questions on a test are one of these, and the next lesson builds every other percentage from ten and twenty-five. Say the rows as a set until they come without thinking.

A picture gives you the fraction — shaded parts over total parts — and from there the percentage is a rename. Seventy-five cells of a hundred is seventy-five per cent. Three of ten strip cells is three tenths, thirty per cent. Twelve out of fifty: twelve fiftieths is twenty-four hundredths, twenty-four per cent. That is also how a test score becomes a percentage: thirty-four out of forty is eighty-five per cent, because thirty-four fortieths is eighty-five hundredths.

When a question mixes the forms, convert everything into one form before comparing, and percentages are the easiest because they are whole numbers. Zero point three, a quarter and thirty-five per cent become thirty, twenty-five and thirty-five per cent, and the order is obvious. Three test scores of three quarters, seventy per cent and zero point eight are seventy-five, seventy and eighty per cent. Never compare across forms — zero point three looks smaller than a quarter because three is less than four, and it is actually bigger. Quiz and exercises now.