Ratio and proportion worksheets

A proportion is two ratios saying the same thing at different sizes, which is the math behind a recipe doubled, a map's scale and a price per kilo. The question to ask of each pair is what the first was multiplied by to get the second, and the answer is always the same multiplier on both halves.

Everything here comes out in whole numbers. A ratio is only in its lowest terms one way — 12 : 18 and 2 : 3 are the same ratio and only one is marked right — so the arithmetic is done with a greatest common divisor rather than by dividing a decimal that would not have come out exactly.

The answers were worked out when the problems were, so the key is the same page with the answers drawn in rather than a second attempt at the same questions — there is no way for the two to disagree. The number in the footer is the seed the sheet was built from: it is printed so that the identical sheet can be had again next week, rather than one that merely looks like it.

This page is one sheet out of a family that can print thousands, and the settings behind it — how many problems, how big the numbers get, how they are laid out, whether there is room to work — are all switches. The builder link at the top of the page carries this sheet’s own settings, so the bench opens on exactly the sheet here rather than on a blank one.

The configuration travels in the address bar rather than on a server, so the link can be bookmarked or sent to somebody as it stands — and what they open is this sheet, down to the seed, rather than another one like it.

Not in the games. The multiplication and division either side of a proportion are, in The Grid.