Bill F. answered • 01/02/13

Experienced Teacher & Tutor in Round Rock, TX

Ratio and proportion are slightly different viewpoints of the same idea: using what you know to quantify what you don't yet know. It's like having a replica model of the house you want ot build: if the length of your model house is 2 feet and the width is 1 foot, then you can know that your real house's width will be 30 feet if the length is 60 feet. Similar to using a map scale, such as 1" = 3 miles, in this house example 1 foot in the model = 30 feet in the real house. Proportion says we use the same multiplier for all measurements to keep the same ratios between different sized but similar objects, such as length, width, etc.

The easiest way to work with ratios and proportions is to set two fractions equal to each other, then cross-multiply to find the unknown part of one of the fractions. Using our house model example: Let's use W to represent our unknown width. We can say model width to model length = real house width to real house width:

1 ft / 2 ft = W ft / 60 ft; top-right X bottom-left = top left X bottom right: (2)(W) = (1)(60).

2W = 60; divide both sides by 2, and W = 60/2 = 20, or 30 feet width, since all measurements were in feet.

An important point: you need to convert ALL measurements used in the proportion fractions into the same measurement types. If you were using inches in your model and feet in your real house, then you need to convert the inches into feet, or the feet into inches. Otherwise, the results after you cross-multiply and divide will be incorrect.

You could set the proportions up differently, as long as you keep straight what is proportional to what. Above, we used Model Width to Model Length = Real House Width to Real House Length.

But we could also use something like Model Width to Real House Width = Model Length to Real House Length, or 1/W = 2/60; then cross-multiply and get 2W = 60, or W (width) = 30 feet. The important part is to compare width to width, and length to length - those measurements must be in the same equivalent parts (numerator or demonimator) of each fraction.

Rubal Hussain L.

01/02/13