Sharing Problems

One pie shared equally by four children: cut it into four equal pieces and each child gets one quarter. That is what a fraction is — the top is what is being shared, the bottom is how many ways. One divided by four is one quarter. One metre of ribbon shared by five is a fifth of a metre each, twenty centimetres. One dollar shared by four is a quarter of a dollar, twenty-five cents. Whenever a question shares something equally, the answer is a fraction, and the number of sharers is its bottom.

Two pies shared by eight children. Cut each pie into eight pieces: sixteen eighths altogether, so each child gets two eighths. Two eighths simplifies to one quarter — and that makes sense, because two pies among eight is the same as one pie among four. The rule is always things divided by sharers: three pizzas among four is three quarters each; four pizzas among six is four sixths, which is two thirds each. Things on top, sharers on the bottom, simplify at the end.

When there are more things than sharers, each share is more than one. Five bars shared by two: each gets two whole bars, four used, and the fifth is halved: two and a half each. That is five halves, or five divided by two — two remainder one, with the remainder shared as a half. Five pies among four: one whole each and the fifth pie in quarters, one and a quarter. Whole things first, then the leftover shared as a fraction with the sharers on the bottom.

Lengths and money share the same way, and the units give you a choice. Two metres of ribbon cut into five equal pieces: two fifths of a metre each, or, in centimetres, two hundred divided by five, forty. Three dollars among four is three quarters of a dollar, seventy-five cents. Six metres of rope in four pieces is a metre and a half each, one hundred and fifty centimetres. Convert to the smaller unit when the question wants a plain number; keep the fraction when it asks for one. Either way the sharers are on the bottom.

The words that mean share are share, divide equally, cut into equal pieces, and each. Whenever you see them, put the things on top and the sharers on the bottom. Eight children share two pies: two eighths, a quarter. Four pizzas among six: four sixths, two thirds. A three-metre plank in eight pieces: three eighths of a metre. And the reverse question — each of eight children gets a quarter of a pie, how many pies — multiplies instead: eight quarters, two pies. Quiz and exercises now.