Ratio and Proportions
Ratios and Proportions is a very important subject in a branch of mathematics. Ratio is nothing but thecomparison of two numbers. The numbers could be anything for example 5/13,12/15, 6/4 is a ratio. Soratio is comparison of numbers.
Next important thing to know is that ratios are writtenas, a: b, a/b, a divided by b all of these meanssame. Here a, in numerator is antecedent and b the denominator is called as consequent. Duplicateratios are written as a square: b square.
For example in duplicate ratio 2 square: 3square so this is a perfect duplicate ratio. Triplicate ratio isnothing but in cubes. It is written as, acube: bcube. When exponents is 2 then it will be called duplicateratio but when exponent will become 3 it will be called as triplicate ratio. Like we have duplicate andtriplicate ratio, we also have Sub duplicate and Sub triplicate ratios.
In sub duplicate ratio is opposite of duplicate that is square of a number; here sub duplicate is squareroot of a number. Same with sub triplicate ratio. It will be cube root of a is to cube root of b. If a ratio bis greater than the unity which is one, that is only possible when a is greater than b. also the opposite isif a ratio b is less than unity that is one, only if b is greater than a. for example we have 2:3, then in thiscase the solution would be less than 1 as b is less than 1.
If a: b is equal to unity, only if a and b are equal. Let us learn some of the properties of ratio. Themost important is in ratio, if quantities compared they must be of same kind. We talk about Ratio and Proportion in our daily lives.
A proportion is a state where two ratios are equal. Each quantity is called term or proportion. Extremesare the first and last terms. If we call two ratios are equal then product of middle term is equal toproduct term of extremes. There are many Ratios and Proportions Word Problems which we havestudied in our elementary classes. Ratio Proportion is used when we do scaling for painting our house,for preparing recipes.
Somemore examples of Proportions and Ratios are for converting large objects and areas into aconsiderably small size.