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1、Fractions as Ratios and Proportions,A ratio is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the ratio of men to women in the group.,Fractions as Ratios and Propor,Ratio,Comparison of two numbers Expresses the relative
2、size of two quantities as the quotient of one divided by the otherWritten in 3 ways:a:b or a/b or a to b,RatioComparison of two numbers,Example,Suppose there are 240 people in a class, 78 are women and 162 are men.Numerically 78 : 162 78 to 162 78/162Could reduce to 13/27 or decimal of 0.481481Would
3、 be the opposite putting the value for men first.,ExampleSuppose there are 240 p,The order in which the ratio is written is important because it defines the comparisonRatios should be left in their original form to represent the size of the sample comparedIn our example Ratio of women to men is 78 t
4、o 162Notice that, in the expression the ratio of women to men, “women came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been the ratio of men to women, then the ratio would have been “162 to 78,The order in w
5、hich the ratio i,Reducing Ratios,Lets return to the 162 men and 78 women in our original group.162e had expressed the ratio as a fraction, namely, 15/20. This fraction reduces to 3/4. This means that you can also express the ratio of men to women as 3/4, 3 : 4, or 3 to 4.,Reducing RatiosLets return
6、to,However,This points out something important about ratios: the numbers used in the ratio might not be the absolute references. The ratio “78 women to 162 men refers to the absolute numbers of women and men, respectively. But “13 to 27 just tells you that, for every 13 women, there are 27 men. This
7、 also tells you that, in any representative set of 40 people (13 + 27 = 40) from this group, 13 will be women and 27 men.,HoweverThis points out someth,Using Ratios to Solve Word Problems,In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed
8、the course? The ratio, 7 to 5 (or 7 : 5 or 7/5), tells you that, of every 7 + 5 = 12 students, five failed. That is, 5/12 of the class flunked.,Using Ratios to Solve Word Pro,So in a class of 36 students 5 X 36 = 180 = 15 12 1 12 = 15 students failed.,So in a class of 36 students ,Units in Ratios,Ra
9、tios may or may not have units it depends on what you are comparingIn some cases units may cancel outExpress the ratio in simplest form: $10 to $45 This means that you should write the ratio as a fraction, and you should then reduce the fraction: 10/45 = 2/9Note that the units canceled on the fracti
10、on, since the units, $, were the same on both values. So there is no unit on the answer,Units in RatiosRatios may or m,Ratios and Units,Express the ratio in simplest form: 240 miles to 8 gallons In this case, you would have (240 miles)/(8 gallons) = (30 miles)/(1 gallon)In more common language, 30 m
11、iles per gallon.Properly, this answer should have units on it, since the units, miles and gallons, do not cancel out.,Ratios and UnitsExpress the ra,Write two equivalent ratios for each ratio,3 17,54 to 24,11:19,Write two equivalent ratios fo,Write each ratio in simplest form.,32:20,15:33,149,21 48,
12、Write each ratio in simplest f,Ratios are said to be in proportion when their corresponding fractions are equal78/162 = 13/27OR78:162 = 13:27,Ratios are said to be in propo,What is a Proportion?,A statement that two ratios are equal. A comparison of one fraction to anotherFor example:,= X 162 193,Wh
13、at is a Proportion?A statem,Solve the Problem,Cross Multiply and set up an equation,women = X women162 men 193 men,(78) (193) = (162) X 15054 = 162 X15054 = X 162X = 92.9259 women X = 93 women,Solve the ProblemCross Multipl,Check your answer to see if the equations are equal,78 = 92.93 162 19378/162
14、 = 0.4892.93/193 = 0.48The Proportion is true if the both fractions reduce to the same value.,Check your answer to see if th,Check your answer to see if the equations are equal,78 X 193 = 1505492.9259 X 162 = 15054 15054 15054,= 92.9259162 193,= 1,Check your answer to see if th,State whether the rat
15、ios are proportional. yes or no,= 27 28,2 = 611 33,7 = 3010 21,40 = 450 5,State whether the ratios are p,Practice,If 18 plums weigh 54 ounces, then 27 plums weigh _ ounces.If 40 nails hold 5 rafters, then 96 nails hold _ rafters.If 60 sliced mushrooms are on 4 pizzas, them _ sliced mushrooms are on 15 pizzas.,PracticeIf 18 plums weigh 54 o,Making Pancakes This many? OR This many?,Making Pancakes This many?,
