# Ratios, Proportions, and Direct Variation

by Sara
(USA)

Ratios

What are ratios?

What are three ways ratios can be written?

What types of problems do ratios help solve? Give at least one example.

### Comments for Ratios, Proportions, and Direct Variation

 Feb 10, 2013 Ratios by: Staff AnswerPart IA ratio is a comparison of two numbers using division. A ratio can be written in three different ways:1. A ratio can be written using the colon symbol.2. A ratio can be expressed as a fraction.3. A ratio can be expressed using odds notation.1. A ratio can be written using the colon symbol.The ratio of the numbers 3 and 5 can be expressed as 3:5.The ratio of the variables A and B can be expressed as A:B.2. A ratio can be expressed as a fraction.The ratio of the numbers 3 and 5 can be expressed as 3/5.The ratio of the variables A and B can be expressed as A/B.3. A ratio can be expressed using odds notation (gamblers notation). The ratio of the numbers 3 and 5 can be expressed as 3 to 5.The ratio of the variables A and B can be expressed as A to B.A constant ratio between variables defines a direct mathematical proportion. For example:It takes three cups of berries to bake one berry pie. (It takes six cups of berries to bake two berry pies. It takes nine cups of berries to bake three berry pies. It takes twelve cups of berries to bake four berry pies.. . . and, so on . . .) It always takes three cups of berries for every pie.Using colon notation."Cups of Berries Needed" : "Number of Pies""3 Cups" : "1 Pie"3 : 1Using fraction notation."Cups of Berries Needed" / "Number of Pies""3 Cups" / "1 Pie"3 / 1Using odds notation."Cups of Berries Needed" to "Number of Pies""3 Cups" to "1 Pie"3 to 1How is a constant ratio between variables used in mathematics? Using our berry pie example, it is obvious that the number of cups of berries needed can be computed by multiplying the number of pies to be baked by 3 (since 3 cups are needed for each pie)."Cups of Berries Needed" = 3 * "Number of Pies"This is the formula for a direct variation.          The equation for a “proportional relationship” ALWAYS looks like this:              y = kx          k is a constant. It is called the “constant of variation”.In the case of the berry pie, k = 3 -------------------------------------------------

 Feb 10, 2013 Ratios by: Staff ------------------------------------------------- Part II A proportion can be graphed. In the case of the berry pie, the equation is: y = 3x y = cups of berries x = number of pies Thanks for writing. Staff www.solving-math-problems.com