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42510011 0010 1010 1101 0001 0100 1011
April 30, 2009
“Nobody can go back and start a new beginning, but anyone can start today and make a new ending.”
~Maria Robinson
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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.
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April 30, 2009
• Section 6.2 (finish)
• Exploration 6.5
• If time – Exploration 6.7
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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
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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
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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%
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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%
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6.2 (cont’d)
Ways to estimate:
Ex: A newspaper story reports that 8% of 7968 students work full-time.
• Strategy 1: Use 10% as a benchmark10% of 7968 is 796.8, or about 797.
• Strategy 2: Use 1% as a benchmark1% of 7968 is 79.68, or about 80. So 8% is 8 • 1%: 8 • 80 = 640.
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6.2 (cont’d)
Ways to estimate:
A newspaper story reports that 8% of 7968 students work full-time.
• Strategy 3: find a close number:7968 is about 8000:10% of 8000 is 800; 8 • 1% is 8 • 80 = 640.
• Strategy 4: find a range.
8% is between 5% and 10%.5% of 8000 is 400. 10% of 8000 is 800. So 8% of 7968 is between 400 and 800.
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6.2 (cont’d) A newspaper story reports that 8% of 7968 students work
full-time.
For an exact answer:• Write and solve a proportion.
Percent = part 100 whole
8 = x 8 • 7968 = 100x
100 7968 63744 = 100x 637.44 = x
About 637 students work full time.
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6.2 (cont’d) Ex: Suzanne makes 68 baskets a week, and
wants to sell at least 30%. What is the minimum number of baskets she can sell?
Part = Percent Whole 100
30 = x 30 • 68 = 100x 100 68
x = 20.4, so Suzanne should sell at least 21 baskets. (Why did I round up here?)
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6.2 (cont’d) You try:A child has 72 stuffed animals on his bed, but he generally
only sleeps with 4 at a time. What percent of his animals does he sleep with?
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6.2 (cont’d) You try:A child has 72 stuffed animals on his bed, but he generally
only sleeps with 4 at a time. What percent of his animals does he sleep with?
4 = x 4 • 100 = 72x.
72 100
%5.5x
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6.2 (cont’d) You try:
There is a 20% off sale at the mall. I’ve wanted a particular sweater that is $120, but couldn’t afford it. How much less is the price with the sale? What is the sale price?
Can you explain how to do this in your head?
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6.2 (cont’d) Answer:
If the sale is 20% off, then the sweater is going to cost 100% – 20% = 80% of the original price.
New price: $96. Savings: $24.
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Exploration 6.5
Do the parts labeled “Sales” and “Percent Decrease and Increase”.
This will be due Tuesday, 5/5.
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6.2 (cont’d)
Ex: The college bookstore makes a profit by charging students 25% more than the book actually cost wholesale. If your book cost $140, how much did the bookstore pay for it?
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6.2 (cont’d) Answer:
The bookstore pays 100%,
and you pay 100% + 25% = 125%.
100% = $x 100 • 140 = 125x
125% $140
x = $112
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6.2 (cont’d)
Ex: In the course of a year, there has been a decrease of 0.5% in the number of cacti in a certain zip code. If there had been about 640,000 cacti at the beginning of the year, how many are left now?
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6.2 (cont’d) Answer:
100% in the beginning;
100% 0.5% = 99.5% now.
100 = 640,000 100x = 99.5 • 640000
99.5 x
About 636,800 cacti are left.
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HomeworkLink to online homework list:
http://math.arizona.edu/~varecka/302AhomeworkS09.htm
*Note: approximate grades are posted on D2L.