Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Ch. 6.3 Proportions Ratio – a fraction, or quotient of two quantities with the same units. A ratio of length to width would be calculated by finding length/width (also can be calculated by doing length ÷ width) A ratio of 16 oz to 2 lbs would first have to be converted to the same units. 16 oz = 1 lb. 16 oz to 2 lbs = 1 lb to 2 lbs = 1 lb / 2 lbs = ½ Rate – a ratio of two quantities with different units. 60 miles/ 2 hours , $500/2 weeks, etc… A unit rate is a rate with 1 as the denominator. Example 1 Find the unit rate of miles per hour. 60miles/2 hours can be converted to a unit rate by doing the division 60/2 = 30. 60 miles /2 hours = 30 miles/1 hour = 30mph Example 2 Find the unit cost of a pound of fruit $3 for 2 pounds of fruit. $3 2lbs 3 $ 2 lb 1.5 $ lb 1.5 $ 1 lbs $1.50 lb $1.50 per pound Proportion – a statement with two ratios set equal to one another. Ratios are “proportional” if they are equal. 1 2 136 272 How do we know they are equal? Cross-multiply to prove it. 2*136 = 272 ? Yes. Solving Proportions Use cross-multiplication to solve an equation where one fraction equals another. 3 7 12 x 3 x 12 7 84 84 x 28 3 Check: Put x = 28 into the original proportion. 3 12 7 28 Are these ratios equivalent ? Do cross - multiplying to check. 3 28 12 7 84 84 Example 3 a) 21 n 12 8 If possible, simplify the fractions first to make the cross - multiplication easier. 21 7 12 4 7 n 4 8 7 8 4n 56 4n 56 4n 4 4 14 n Check : put n 14 back into the original proportion. 21 14 12 8 21 8 12 14 If you don' t want to do the math, break all the numbers down into their prime - factored form and compare. 3 7 2 2 2 2 2 3 2 7 When doing application problems, make sure to write down the units that go along with the numbers. Example 5 Yusef can wash 6 windows in 21 minutes. How many minutes will it take him to wash 10 windows? What are we being asked to find? How many minutes. Let m = number of minutes to wash 10 windows. Put given info into a mathematical proportion. 6 windows in 21 minutes 6 windows 21 minutes 10 windows in ? Minutes. 10 windows Let m = the unknown number of minutes. m minutes Set up a proportion and solve it. 6 windows 10 windows 21 minutes m minutes 6 10 21 m Simplify, then solve 2 10 7 m Cross - multiplication : 2m 7 10 2m 70 2m 70 2 2 m 35 Check : 6 10 21 35 6 35 21 10 210 210 UNIT ABBREVIATIONS Money Volume dollars $ cents ¢ or $0._ _ teaspoon tsp tablespoon tbsp Time cup c years yr pint pt months wks quart qt weeks wks gallon gal days dys liter l hours hr milliliter ml minutes min cubic feet ft3 seconds sec or s Area square miles mi2 Length miles mi square feet ft2 yards yd Weight feet ft inches in. or “ meters m pounds lb ounces oz grams g kilometers km kilograms kg Rates are usually stated with the word “per” in between two quantities with different units. Miles per Hour = miles/hours = mph Feet per second = feet/seconds = ft/s Dollars per pound = $/lb Dollars per ounce = $/oz Inches per week = in./wk