Lessons · Teaching · ratio and proportion
A ratio compares parts; a proportion says two ratios match
A ratio of 3 to 2 says that for every three of one thing there are two of another. A proportion is a statement that two ratios are equal, and it is solved by cross multiplying. The trap is that a ratio's parts are not automatically the whole.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Mixing paint, scaling a recipe, reading a map and staffing a trip are all the same arithmetic, and a class of 30 split 3 to 2 is the question every teacher gets wrong once. Three to two is five parts, not thirty parts, and each part is six children.
How to think about it
Add the parts of the ratio to get the total number of parts. Divide the actual total by that to get the size of one part. Multiply back up. For a proportion, write the two ratios as fractions, set them equal, and cross multiply.
Worked example
30 children split 3:2 is 5 parts in totalAdding the parts first is the step that gets skipped.
30 / 5 = 6 children per part, so the groups are 18 and 12And 18 + 12 = 30, which is the check.
A recipe for 4 scaled to 10: the scale factor is 10/4 = 2.5Every ingredient multiplied by the same factor, not the same amount.
3/4 = x/20: cross multiply, 3 x 20 = 4x, so x = 15A proportion is one equation with one unknown.
Your turn
Name what the parts of a ratio must be added to find.
Add the parts to get the total number of
Solve one, graded on the server
The trap
Reading 3:2 as three out of two, or as three out of five without checking. It is three for every two, a total of five parts, and whether the question wants a part or the whole has to be read off the words.