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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.