|
Ratio and Proportion |
||||||
|
Chemistry is a quantitative subject, meaning chemistry deals with quantities: solids, liquids, and gases. The science and study of chemistry can be broken down into two groups, the information of Chemistry like chemical reactions, moles, and the four states of matter, and math problems such as balancing equations, mass-mass, and molarity problems. A lot of these problems found in chemistry contain ratios and proportions. The word ratio is derived from the Latin word "ratio" which means "computation." A ratio can be defined as the relative size of two quantities expressed as the quotient of one divided by the other. Ex. The ratio of 7 to 4 is written: 7:4 or 7/4. To solve this problem you would divide 4 from 7 To simplify a compound or an equation you take the coefficients of each element or compound and reduce them. Ex. C6H12O6 --> 6:12:6 --> 1:2:1 Here are some examples on how to determine the ratio from a chemical formula: Ex. 2H2 + O2 --> 2H2O From this example you can see that for every two molecules of hydrogen gas there is one molecule of oxygen gas. The ratio is 2:1. If you have fifty molecules of oxygen gas then from this ratio I would have one hundred molecules of hydrogen gas. Ex. 2Al(NO3)3 + 3H2SO4 --> Al2(SO4)3 + 6HNO3 In this chemical formula you can see that aluminum nitrate combined with hydrogen sulfate(sulfuric acid) yields aluminum sulfate and hydrogen nitrate. From this example you can see that for every two molecules of aluminum nitrate there are three molecules of hydrogen sulfate. The ratio is 2:3. If you have twenty molecules of aluminum nitrate then you would have thirty molecules of hydrogen sulfate. The word proportion is derived from the Latin word "proportio" which means "portion." A proportion can be described as an equation which states that two ratios are equal. Ex. 4 = 5 To solve a proportion you cross-multiply. In this example you multiply the 4 and the 10 together and the 5 and the 8 together. Ex. 6 = x To solve for x in this proportion you cross multiply the 6 and 10 together, and the 5 and x together: 5x = 60. Then divide the 60 by 5 to get your answer: 60/5 = 12. Ex. 4 = 8 To solve for x in this proportion you cross multiply the 4 and 16 together, and the 8 and x together: 8x = 64. Then divide the 64 by 8 to get the value of x: 64/8 = 8.
Ex. x+1 = 6 To solve for x in this proportion you must cross-multiply. In this example you multiply the x+1 with the x+4. When you multiply the two binomials together you will get one trinomial. (x+1)(x+4) = x2+5x+4. You can obtain this trinomial by using the F.O.I.L. method. First multiply the x's from each binomial together. Then multiply the outer numbers and variables together(X x 4), and the inner numbers and variables together(X x 1), and add the results: 4x and 1x together. Finally you multiply the last numbers and variables in the two binomials together (4 x 1). Your final answer is x2+5x+4. Next you cross-multiply the 6 with the (x+2). Distribute the 6 through the binomial (x+2). You multiply the 6 with the X and then the 6 with the 2. You final answer is 6x+12. Set the two equations equal to each other: x2+5x+4=6x+12. Move all the numbers and variables together on one side,--> x2-x-8=0. Break this equation into two binomials and you will have your answer. This is what you should get:(x+4) and (x-4). X is equal to 4.
An in-depth look at ratios and proportions, including practice problems of each.
Extra help with ratios and proportions from Dr. Math.
Extra help with ratios from "Modern Mathematics for Elementary School teachers."
Definitions and further information on proportions and ratios.
Please forward all questions, comments and criticisms to Gregory L. Curran. |
