Dividing by a 2-Digit Number

Dividing by a two-digit number is easy once you can see the multiples of it, so start by writing a short table: twelve times one, two, five, ten, twenty, fifty. You need no new facts — five is half of ten, twenty is double ten, fifty is half of a hundred. Then chunk. Nine hundred and thirty-six: take away six hundred, which is twelve fifties, leaving three hundred and thirty-six. Take away two hundred and forty, twelve twenties, leaving ninety-six. That is twelve eights exactly. Add the chunks: fifty plus twenty plus eight is seventy-eight. Check by multiplying: twelve times seventy-eight is nine hundred and thirty-six.

Some divisors are friendly because you already know their multiples. Twenty-five: four of them make a hundred, so twelve hundred holds four times twelve, forty-eight. Fifteen: two hundred and twenty-five is a hundred and fifty plus seventy-five, ten fifteens plus five fifteens, so fifteen. Twelve: eighty-four is seven twelves from the tables. Money shared by eighteen: eighteen fifties are nine hundred, leaving four hundred and fifty, which is eighteen twenty-fives, so seventy-five. When the divisor is friendly, use what you know; when it is not, write the table and chunk.

Before dividing, estimate the size of the answer. Eight thousand six hundred and seventy-five divided by twenty-five: round to eight thousand, and eight thousand divided by twenty-five is three hundred and twenty. So the answer has three digits and sits somewhere around three hundred to four hundred. Now chunk: three hundred twenty-fives are seven thousand five hundred, leaving one thousand one hundred and seventy-five; forty more are a thousand, leaving one hundred and seventy-five; seven more, exactly. Three hundred and forty-seven — three digits, near the estimate. An answer of thirty-four or three thousand four hundred would be the wrong size, and the estimate would say so.

With a remainder, the check matters even more. One thousand divided by thirty-two: thirty thirty-twos are nine hundred and sixty, leaving forty; one more thirty-two leaves eight; eight is less than thirty-two, so stop. Thirty-one remainder eight. Now check: thirty-two times thirty-one is nine hundred and ninety-two, plus eight is one thousand. If the check fails, a chunk was wrong. If the remainder is thirty-two or more, you stopped too early. Two thousand divided by forty-five works the same: forty-four remainder twenty, and forty-five times forty-four plus twenty is two thousand.

Division hides in stories as sharing, as rate, and as a missing factor. A seven hundred and twenty-eight page book read at twenty-six pages a day takes seven hundred and twenty-eight divided by twenty-six, twenty-eight days. One thousand three hundred and fifty dollars shared among eighteen is seventy-five each. A number times thirty-six is two thousand seven hundred and seventy-two: the number is two thousand seven hundred and seventy-two divided by thirty-six, seventy-seven. But a question like how many pages are left after twenty days is not a division at all — twenty days of twenty-six pages is five hundred and twenty, and seven hundred and twenty-eight minus that is two hundred and eight. Quiz and exercises now.