and Dening Interpreting Percents
Percents and Change
Interest
Conclusion
MATH 113 Section 6.2: Percents
Prof. Jonathan Duncan
Walla Walla University
Winter Quarter, 2008
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Outline
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Dening and Interpreting Percents Percents and Change Interest Conclusion
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Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
What are Percents?
The term percent is from the Latin per centum which translates per one hundred. Percents Percents are related to fractions as follows. A percent (written A A%) stands for 100 . Example Write 30%, 112%, and 0.5% as both fractions and decimals. Example Write
14 100 ,
0.003, and
5 4
as percents.
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Relating Percents and Proportions
Once we have learned how to express percents as fractions, we are able to use proportions to solve problems related to percents. Example You score 80% on a 20-point paper. What is your raw score on the paper? Example You score 10 on a homework assignment. To what percent does 12 your score translate?
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Applications of Percents
While scores on exams and assignments are a big part of your current life, there are other important ways in which percents are useful in the real world. Applications of Percents Weather Forecasting (30% chance of rain) Probability (0.01% chance of being struck by lightening) Rates of Change (annual ination of 3%) Interest Rates (CD earns 5.5% APR) others?
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Percents and the Whole
In percent problems, the whole is always 100%. So you must identify the whole in order to solve such problems. Example Property taxes are assessed at a rate of 1.2%. How much property tax would be due on a $142,500 home? Estimated Solution This is close to 1% which is by 100 to get $1,425. Computed Solution
1.2 t Solve the proportion 100 = 142,500 or simply multiply .012 142, 500 to get $1710. 1 100 .
So, divide the whole, $142,500,
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Modeling Percents
Since percents are fractions with denominators of 100, the same modeling techniques as used with fractions will still work. Example Banks usually require that no more than 28% of a households monthly income be spent on a mortgage payment. How much must a household make to aord a $1200 monthly payment? Use a 10 10 grid to model 100% and shade in 28%. The shaded area also represents $1200. Determine how much each box is worth. Now how much is the whole? Quicker Solution This can also be solved using the proportion
28 100
=
1200 x .
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Types of Change
Using percents to describe change can be quite confusing. need We to be sure we understand how the percents are being used. Example A citys 1.2% property tax rate will see a 1% increase in the new year. What will the new rate be? Additive Change If the change is additive, we are adding 1% to 1.2% so the new rate is 2.2%. Multiplicative Change If the change is multiplicative, the new rate is: 101 100 1 1.2% = 1.2% + 1.2% = 1.2% + .012% = 1.32%. 100 100 100
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Percents and Fairness
Example A state experiences a budget shortfall. To raise the missing revenue they decide to raise everybodys income taxes by $1000 a year. Is this fair? Compare the percent increase in tax for somebody paying $2000 a year to somebody paying $18,000 a year. Example Instead the state decides to raise everybodys taxes by 10% a year. Is this any better? How do the two taxpayers above fair? Cutting Taxes What about tax cuts? Is it fairer to cut taxes by set dollar amounts or by percents?
Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Percent Increases/Decreases
Another confusing aspect of percents and change is that the meaning of a percent increase or decrease depends on the whole. Example A local clothing store marks its clothing up 32%. In other words, they charge 32% more for an item than they paid their supplier.
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If you purchase a $100 outt, how much prot did they make? During a sale, they mark a certain item down 32% and claim they are selling it below cost. Could this be true? Solve x + 0.32x = 100 Solve 100 0.32(100) = x
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Dening and Interpreting Percents
Percents and Change
Interest
Conclusion
Simple Interest
One important use of percents is in calculating interest. This can be interes...