1、Fractions as Ratios and ProportionsA 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.Ratio Comparison of two numbers Expresses the relative size of two quantities as the quotien
2、t of one divided by the other Written in 3 ways:a:b or a/b or a to bExample 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 0.481481 Would be the opposite putting the value for men first.The order in which th
3、e ratio is written is important because it defines the comparison Ratios should be left in their original form to represent the size of the sample compared In our example Ratio of women to men is 78 to 162 Notice that,in the expression the ratio of women to men,“women came first.This order is very i
4、mportant,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 78Reducing RatiosLets return to the 162 men and 78 women in our original group.162e had expressed the ratio as a fraction,nam
5、ely,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.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
6、numbers of women and men,respectively.But“13 to 27 just tells you that,for every 13 women,there are 27 men.This also tells you that,in any representative set of 40 people(13+27=40)from this group,13 will be women and 27 men.Using Ratios to Solve Word Problems In a certain class,the ratio of passing
7、grades to failing grades is 7 to 5.How many of the 36 students failed 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.So in a class of 36 students 5 X 36 =180 =15 12 1 12 =15 students failed.Units in Ratios Ratios may o
8、r may not have units it depends on what you are comparing In some cases units may cancel outExpress the ratio in simplest form:$10 to$45 This means that you should write the ratio as a fraction,and you should then reduce the fraction:10/45=2/9Note that the units canceled on the fraction,since the un
9、its,$,were the same on both values.So there is no unit on the answerRatios 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 miles per gallon.Properly,this answer should have units o
10、n it,since the units,miles and gallons,do not cancel out.Write two equivalent ratios for each ratio 3 1754 to 24 11:19 Write each ratio in simplest form.32:2015:33 149 21 48 Ratios are said to be in proportion when their corresponding fractions are equal78/162=13/27OR78:162=13:27What is a Proportion
11、?A statement that two ratios are equal.A comparison of one fraction to anotherFor example:78 =X 162 193Solve the Problem Cross Multiply and set up an equation78 women =X women162 men 193 men(78)(193)=(162)X 15054=162 X15054=X 162X =92.9259 women X=93 womenCheck your answer to see if the equations ar
12、e equal 78 =92.93 162 19378/162=0.4892.93/193=0.48The Proportion is true if the both fractions reduce to the same value.Check your answer to see if the equations are equal78 X 193=1505492.9259 X 162=15054 15054 1505478 =92.9259162 193=1State whether the ratios are proportional.yes or no8=27 28 2 =611 33 7 =3010 2140 =450 5Practice1.If 18 plums weigh 54 ounces,then 27 plums weigh _ ounces.2.If 40 nails hold 5 rafters,then 96 nails hold _ rafters.3.If 60 sliced mushrooms are on 4 pizzas,them _ sliced mushrooms are on 15 pizzas.Making Pancakes This many?OR This many?
