RATIO is two "things" (numbers or quantities) compared to each other. or quantities.For example, "3 dollars per gallon" is a ratio.Or, "40 miles per 1 hour".Or, 15 girls versus 14 boys.Or, 569 words in 2 minutes.Or, 23 green balls to 41 blue balls, etc.
PROPORTION is when you have two ratios set to be equal to each other.For example, 3 dollars per gallon equals 6 dollars per two gallons. Or, 3/1 = 6/22 teachers per 20 kids equals 3 teachers per 30 kids. Or, 2/20 = 3/30
Hey! That look's like a pair of equivalent fractions. Right, fractions are rational numbers. When two fractions represent the same amount, they are equivalent fractions. Two ratios that are equivalent to each other are a proportion.
How do you know if two ratios are a proportion?
An equation such as 5/8 = 60/96 is a proportion if the two ratios are equivalent to each other. Either reduce one ratio to lowest terms or raise the other ratio to equivalent terms.
5 x 12 = 60 8 x 12 = 96 therefore 5/8 = 60/96
60 / 12 = 5 96 / 12 = 8 therefore 5/8 = 60/96
Another way to test a proportion for is to use cross multiplication.
Multiply 3 by 35. 3 x 35 = 105
Multiply 21 by 5. 21 x 5 = 105
Both products are 105, therefore the ratios are proportional.
Of course for it to be a PROBLEM, one of the four numbers is missing or ends up being the famous x.What if one term in a proportion is missing? How can you find the missing term?
27 is a multiple of 9 by 3, therefore do the same to the numerator. 3 times 3 equals 9, therefore x is 9.
One way to find a missing term in a proportion is to find the equivalent fraction.
A second way to find a missing term in a proportion is to use cross multiplication.
- Maps, blueprints, and scale models. An appropriate ratio, or scale, is chosen. Large objects or areas can then be shown in a considerably smaller size or space. Movies frequently use scale models of ship, planes, buildings.
Recipes or formulas may be increased or decreased by using proportions.
- Economic and sociological predictions based on the relationship of two quantities.