Upload
scarlett-fisher
View
215
Download
0
Embed Size (px)
Citation preview
42510011 0010 1010 1101 0001 0100 1011
April 28, 2009
“Nobody can go back and start a new beginning, but anyone can start today and make a new ending.”
~Maria Robinson
4251
0011 0010 1010 1101 0001 0100 1011
Final Exam
Tuesday, May 12
11am – 1pm
In our usual classroom
Cumulative (covers material from entire semester).
As always, you may use a calculator and/or manipulatives from your own pack.
4251
0011 0010 1010 1101 0001 0100 1011
April 28, 2009
• Section 6.1 (finish)
• Exploration 6.3
• Section 6.2 – Percents
• Course evaluations
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Ratios and Rates
• If a : b = c : d, then a/b = c/d.
• If a/b = c/d, then a : b = c : d.
Example:
• 35 boys : 50 girls = 7 boys : 10 girls
• 5 miles per gallon = 15 miles using 3 gallons
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d) Proportional word problems:
Start easy:• I can buy 3 candy bars for $2.00.• So, at this rate, 6 candy bars should cost…• 9 candy bars should cost…• 30 candy bars should cost…• 1 candy bar should cost… this is called a
unit rate.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Proportional word problems:
Here’s another.
• 7 small drinks cost as much as 5 large drinks. At this rate…
• How much should 14 small drinks cost?
• How much should 21 small drinks cost?
• How much should 15 large drinks cost?
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Ratios are not the same as fractions
• The ratio of males to females is 3 : 2.
• That means 3/5 of the people are male, and 2/5 of the people are female. The ‘whole’ is the group of 5 people.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Ratios are not the same as fractions
• The mixture is 3 parts water and 1 part green dye.
• That means that 3/4 of the mixture is water and 1/4 of the mixture is green dye. The ‘whole’ is the mixture, which consists of 4 total parts.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Ratios are not the same as fractions
• A school’s enrollment increases by 25 students per year.
• This one can be expressed as a fraction – sort of: 25 students/1 year. There is no ‘whole’, though, since the two quantities being compared have different units!
4251
0011 0010 1010 1101 0001 0100 1011
Exploration 6.3
Do Part 1.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d) Reciprocal unit ratios
Suppose I tell you that 4 doodads can be exchanged for 3 thingies.
How much is one thingy worth? • 4 doodads/3 thingies means
1 1/3 doodads per thingy.How much is one doodad worth?• 3 thingies/4 doodads means
3/4 thingy per doodad.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
To solve a proportion:
If a/b = c/d, then ad = bc.
Show that this is true:
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
To set up a proportion:
Ex: I was driving behind a slow truck at 25 mph for 90 minutes. How far did I travel?
• Set up equal rates: miles/minute
• 25 miles/60 minutes = x miles/90 minutes.
• Solve: 25 × 90 = 60 × x; x = 37.5 miles.
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Strange looking problems:
Ex: I see that 1/4 of the balloons are blue, and there are 6 more red balloons than blue.
• Let x = number of blue balloons, and so x + 6 = number of red balloons.
• Also, the ratio of blue to red balloons is 1 : 3
• Proportion: x/(x + 6) = 1/3
• Alternate way to think about it. 2x + 6 = 4x
x x + 6
4251
0011 0010 1010 1101 0001 0100 1011
6.1 (cont’d)
Which rates are (equivalent) proportional?Ex:
1. 6/10 mph
2. 1/0.6 mph
3. 2.1/3.5 mph
4. 31.5/52.5 mph
5. 240/400 mph
6. 18.42/30.7 mph
7. 60/100 mph
4251
0011 0010 1010 1101 0001 0100 1011
6.2 – Percents
• Percent means per hundred.
• 50% means 50 per hundred, or 50/100.
• 95% means 95 per hundred, or 95/100.
• 2% means 2 per hundred, or 2/100.
• 315% means 315 per hundred, or 315/100.
4251
0011 0010 1010 1101 0001 0100 1011
6.2 (cont’d)
Percents you should know:
1 = 100%
1/4 = 25%, 1/2 = 50%, 3/4 = 75%
1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%
1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%
1/10 = 10%, 2/10 = 20%, etc…
%3.333/1 %6.663/2
4251
0011 0010 1010 1101 0001 0100 1011
6.2 (cont’d)
Fractions, decimals, percents
• To write fractions as decimals or percents:
• a/b means a ÷ b. Divide, and write the answer to get the decimal. Then, multiply by 100 to get the percent.
Ex: 48/60 = 48 ÷ 60 = 0.8 = 80%
You try: 4/9, 4 3/20
4251
0011 0010 1010 1101 0001 0100 1011
6.2 (cont’d)
Fractions, decimals, percents
• To write decimals as fractions or percents:
• Consider using expanded form, then combine fractions and simplify.
• To write a percent, multiply by 100.
Ex: 0.09 = 9/100 = 9%
You try: 7.007, 0.59
4251
0011 0010 1010 1101 0001 0100 1011
6.2 (cont’d)
Fractions, decimals, percents
• To write a percent as a decimal, divide by 100.
• From there, you can convert the decimal to a fraction.
Ex: 591% = 5.91 = 5 91/100
You try: 3%, 62%, 0.4%
4251
0011 0010 1010 1101 0001 0100 1011
6.2 (cont’d)
What happens if...
What if you have 3 2/5%
Rewrite 2/5 as 0.4.
So 3 2/5% = 3.4%
4251
0011 0010 1010 1101 0001 0100 1011
HomeworkLink to online homework list:
http://math.arizona.edu/~varecka/302AhomeworkS09.htm
*Note: approximate grades are posted on D2L.