Made By: Carlos Villalobos & Diego Samour

What is Ratio? A ratio is a way to compare amounts of something. Recipes, for example, are sometimes given as ratios. To make pie you may need to mix 2 parts of flour to 1 part of fat. This means the ratio of flour to fat is 2 : 1. If pie is 2 parts flour to 1 part fat, then there are 3 parts (2 + 1) altogether. Two thirds of the pie is flour; one third fat. Ratios are similar to fractions; they can both be simplified by finding common factors. Try to always divide by the highest common factor.

How to Simplify a Ratio There are 15 cats and 12 dogs in a farm, what is the ratio of cats to dogs, this answer is going to be in the simplest form. Cats 15 : Dogs 12 OR 15:12 With this ratio both numbers are divisible by 3 therefore the ratio in simplest form is (15/3): (12/3) Notice that 3 is the highest common factor, therefore the ratio will be 5:4 this being the simplest form. TRY THIS: es/flash/ratios/ratios.shtml es/flash/ratios/ratios.shtml

Writing a ratio in the form 1:n or n:1 When a ratio is in its simplest form, all the numbers are whole numbers. However, it is sometimes useful to write a ratio in the form 1:n or n:1 (where ¨n¨ is any number). This means we will not necessarily be dealing with whole numbers. For example, if we are asked to write the ratio 2:5 in the form 1:n, we need to make the left-hand side of the ratio equal to 1. We do this by dividing both sides of the ratio by 2: 2:5 = 2 / 2 : 5 / 2 = 1:2.5 If we were asked to write 2:5 in the form n:1, we would need to make the right-hand side equal to 1. So we would divide both sides by 5: 2:5 = 2 / 5 : 5 / 5 = 0.4:1

Direct Variations The term direct variation has the same meaning as direct proportion. Between two variables there is a direct proportion when one variable is a simple multiple of the other, that means their ratio is constant. When solving an examination question you first need to find the constant of proportionality which becomes the key base for solving the problem. The symbol for proportion is Example: the statement, the pay is directly proportional to time can be written by this, pay time.

Direct Proportion in a Problem By the cost of an article is directly proportional to the time spent making it, an article takes 6hours to make it cost $30 find: A)the cost of an article that takes 5hours to make. B) the length of time it takes to make an article costing $40. Solution: The cost will be represented by a C and time by T. C T C=KT (k is the constant of proportion) 30=6k K=30/6 K=5 so the formula is C=5T A) when T= 5hours C=5x5C=25, so the cost is $25 B) when C=$4040=5xT T=8hours

Inverse Proportion There is inverse variation between 2 variable, when 1 variable is directly proportional to the reciprocal of the other, which means the product of 2 variables is constant, therefore as 1 increases the other decreases. Ex..: The faster it travels over a distance the less time it takes, so speed and time are inversely proportional. S 1/TSO S=K/T

Example M R If M=9 and R=4 Find: A) M when R is 2 B) R when M= 3 Solution: M K/RWhen M=9 and R=4 9=K/4so K= 4x9K=46 The formula is M=36/R A) R=2 then M=36/2M=18 B) When M=3 then 3=36/RSO 3R=36R=12