1. IMA 101: Basic Math
Lecture 5
IMA101: Basic Mathematics
6/17/2010

2. Lecture Outline Turn in HW1 and Journal
Where we’ve been and where we are going
Percents
Break
Ratios
IMA101: Basic Mathematics
6/17/2010

3. Just so you know How this week connects to Last week
A little signposting
Just so you know How this week connects to Last week
IMA101: Basic Mathematics
6/17/2010

4. Review: What we’ve covered so far
Different sets of numbers:
Whole numbers
Integers
Rational numbers
Real numbers
Different operations on numbers:
Addition and subtraction
Division
Multiplication & exponents
Square roots
Key methods:
Prime factorization
Using reciprocals
Rounding
The order of operations
IMA101: Basic Mathematics
6/17/2010

5. This week Discuss interpretations of these numbers Percents (decimals)
Ratios (fractions)
Proportions (fractions)
Unit conversion (multiplication/division)
Estimation (rounding)
Descriptive statistics (NEW!)
IMA101: Basic Mathematics
6/17/2010

6. Percents
IMA101: Basic Mathematics
6/17/2010

7. Percent: Definition A percent means parts per one hundred
We write it using the % symbol
Examples:
27 % is the same as 27 parts per 100
8% is the same as 8 parts per 100
IMA101: Basic Mathematics
6/17/2010

8. 100 square grid
When all the squares in the grid are shaded we say that 100% of the of the grid is shaded.
IMA101: Basic Mathematics
6/17/2010

9. 100 square grid
If only 83 of the 100 squares are shaded, then we have 83% of the grid shaded.
What percent of the grid is NOT shaded?
100% - 83% = 17%
IMA101: Basic Mathematics
6/17/2010

10. Percents as Fractions
We can convert a percent into a fraction by dropping the % symbol and writing the percent over 100, then simplifying
Examples
IMA101: Basic Mathematics
6/17/2010

11. 100 square grid 2/3 of the grid is shaded, so we have
66 2/3% of the grid shaded.
IMA101: Basic Mathematics
6/17/2010

12. Percents as Decimals Recall: a percent is just parts out of 100
To change a percent to a decimal, drop the % symbol, and divide the number by 100, leaving the answer in decimal notation
Examples
65% = 65/100 = 0.65
14.25% = 14.25/100 =
100% = 100/100 = 1.0
IMA101: Basic Mathematics
6/17/2010

13. Caution: Small and Large Percents
Write 0.6% as a decimal
Write 354% as a decimal
Important: Make sure that the 1’s place in a percent is in the 100th place in the decimal!
IMA101: Basic Mathematics
6/17/2010

14. Decimals as Percents
Recall: decimals can be written as a sum of fractions of different powers of 10, as well as one fraction over the largest power of ten
Decimals are fractions over 100. How can we write this as a fraction over 100, and then as a % ?
IMA101: Basic Mathematics
6/17/2010

15. Fractions as Percents Write the following as a percent 4/5 3/4
Note: these are easy because they multiply into 100 neatly
IMA101: Basic Mathematics
6/17/2010

16. Fractions as Percents
Recall: sometime we have a denominator that does not multiply neatly into 100, such as 3, 7, 11, etc. These are examples that give us repeating decimals
To write a fraction as a percent first convert to decimal notation, then convert to a percent
Example
4/3 as a percent
(approximate and exact answers)
IMA101: Basic Mathematics
6/17/2010

17. Some numbers to know and love
Fraction
Decimal
Percent
0.5
50%
~33.3%
0.25
25%
~66.6%
0.75
75%
0.1
10%
0.2
20%
0.01 1%
IMA101: Basic Mathematics
6/17/2010

18. Solving Percent problems
Recall: a percent is the number of parts out of 100
But really this is just a conversion of a different fraction into one with a denominator of 100
Using the conversion techniques we have just discussed, we can write any amount out of a base as a percent
Find the percent of female students in this class
IMA101: Basic Mathematics
6/17/2010

19. Percent Problems Student Practice
Amir International got a score 0f 81 out of a possible 150 on HW1*. Did Amir get a passing grade (at least 60%) on his first homework?
If Annie Globetrotter got a score of 126. Did she get a passing grade on her first homework?
*yay for those of you who got the bonus!
IMA101: Basic Mathematics
6/17/2010

20. Percent Problems
We can also solve for the amount necessary to get a certain percent
Example
What minimum score does Chetan have to get in order to get a passing grade on his first homework?
IMA101: Basic Mathematics
6/17/2010

21. Percent Problems
You are starting an intramural ultimate Frisbee team. The league rules require that at least 25% of the players be female. If you need at least 30 players, how many female players do you need?
IMA101: Basic Mathematics
6/17/2010

22. Percent Problems
Given a certain amount and a known associated percent, we can also find the base
Example
If 18% of students at Tonedeaf University are enrolled as music majors and there are 270 students in the music program, how big is the student body?
IMA101: Basic Mathematics
6/17/2010

23. Percent Problems Student Practice
An apartment building has 42 rooms currently rented out. If the occupancy rate is at 60%, how many rooms are currently empty?
If there are 360 motorcycles outside the international college and ~90% of students drive motorcycles, approximately how many students are in the international college? (assume all the motorcycles belong to students)
IMA101: Basic Mathematics
6/17/2010

24. Percentage Increase and Decrease
Sometimes we are interested in finding how much something changes as a percent of the original amount
Example
If the population of Imaginaria is 450,000 in 2008 and 486,000 in 2009, what was the rate of population growth?
IMA101: Basic Mathematics
6/17/2010

25. Percentage Increase and Decrease
Student Practice
You originally go to the store and see a pair of fly kicks for 5200, upon your return the next day, you see that the price has been changed to What was the percentage change in the price of the shoes?
Your dog used to weight 5.2 kg but it now weighs What percent of the original weight did your dog lose?
IMA101: Basic Mathematics
6/17/2010

26. Ratios and Proportions
Section 6.1
IMA101: Basic Mathematics
6/17/2010

27. Ratio: Introduction Definition:
A ratio is a relationship between two numbers that have the same units
Examples:
4:1
5:2
Equivalent to fractions
IMA101: Basic Mathematics
6/17/2010

28. Rates: Introduction A ratio of two different types of quantities
Example
If you drive 450 km in 9 hours then the rate of your driving is:
IMA101: Basic Mathematics
6/17/2010

29. Rates Student Practice
If you are paid a salary of 443,700 for at total of 255 work days with 8 hours of work each day, what is your hourly rate of pay?
If the fastest-growing flower plant on record grew 12 feet in 14 days, what was its daily growth rate?
IMA101: Basic Mathematics
6/17/2010