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Wednesday, December 18, 2013

Theresa's Percent Post

What is a Percent?


Percent is a fraction out of 100.
Here's how we find an equivalent fraction out of 100.

9/10 = 90/100
9 x 10 = 90
10 x 10 = 100

Why 100%? 100 is used because it's just right. It's also a number that's easily seen.

Percent was made by the French. Per means "out of" in french and Cent means "100". Together they make "out of 100". The percent sign %, the line in the middle represents 1 and the two little circles symbolizes the two zeros from 100.

Improper or Top Heavy fractions are fractions that have a greater numerator than the denominator. 

205/100 = 2 wholes, 205 out of 100, 205%
5/4 = 5 out 4, 125 out of 100, 125%

100% means all, whole, everything, 100/100, 6/6.
10% means 10/100, 1/10.
50% means half, part/whole, 50/100 or 20/40.
25% means 25/100, 1/4, one quarter.
1% means 1 out of 100, 1/100.

Representing Percents







Converting Decimals to Percents to Fractions

1) 26%

Decimal: 26% ÷ 100 = 0.26

Fraction: 0.26 / 1
0.26 x 100 / 100
26 / 100

2) 7 / 10

Decimal:÷ 10 = 0.7

Percent: 0.7 x 100 = 70%

3) 0.024

Percent: 0.024 x 100 = 2.4%

Fraction: 0.024 / 1
0.024 x 100 / 100
2.4 / 100


Percent of a Number

Mental Math                                                                    Calculator

                                                1) 20% of 60

             %  |  #                                                                  20 ÷ 100 = 0.20
           100 |  60                                                               0.20 x 60 = 12
÷5         20 |  12     ÷5
        20% of 60 = 12                                                       20% of 60 = 12

                                                 2) 0.1% of 40

              % | #                                                                  0.1 ÷ 100 = 0.001
           100 | 40                                                                0.001 x 40 = 0.04
÷100    10 |  4     ÷100
÷10     0.1 |  0.4     ÷10                                                   0.1% of 40 = 0.04
      0.1% of 40 = 0.4

                                                 3) 250% out of 400

            % | #                                                                    250 ÷ 100 = 2.50
          100 | 400                                                              2.5 x 400 = 1000
x 2     200 | 800    x 2
÷4        50 | 200   ÷4                                                      250% of 400 = 1000
          250 | 1000
 250% of 400 = 1000


Combining Percents

When working with money, you will often see discounts, sale prices or regular prices.

Discount - what you save
Sale Price - what you pay

To find the sale price,       Regular Price - Discount = Sale Price

To find the total price with taxes,

1) Calculate the total price of item(s) that were bought.

4.4 Pg. 149
7. A herd of 100 caribou was moved to a new location. The population increased by 10% the first year and then increased by 20% the second year.

a) Find the population after the second year.
b) Explain why there was not a 30% increase in population over the two years.




a) The population of the caribou herd after the second year was 132.

When finding the increase of the caribou, you add 100 + 10 because "increasing" means having more than you had before. So that means your answer will be more than what you started with.
The next thing you need to do is to take the percents from the question and convert them to a decimal. You do this by dividing the percent by 100.
Lastly, you have to multiply the decimal by the total amount of caribous.

100 + 10 = 110        110 ÷ 100 = 1.10        1.10 x 100 = 110

100 + 20 = 120        120 ÷ 100 = 1.20        1.20 x 110 = 132




b) There was not a 30% increase in population over the two years because the 100% changed when the second year increased by 20%. In the beginning, the population of the caribou was 100 but after the first year it became 110. 110 became the new 100%.

4.4 Pg.148 Show You Know

What is the final sale price at each store? Which is a better buy? Explain your thinking.

Store A: 50% off one day only
Store B: 25% off one day followed by 25% off the reduced price the second day

Example: you want to buy a $60 pair of boots.

Store A

For one day, there is a 50% off discount of $60.
The discount is what you save and the sale price is what you pay. Since it is just 50%, we can just half the number.


60 ÷ 2 = 30

The reduced price and what you now pay is $30 (without taxes).

Store B

Day 1: 25% off of $60
First, let's find the discount.

25 / 100    25 ÷ 100 = 0.25
0.25 x 60 = $15

Now that we've found the discount, we then have to find the sale price. We can find the sale price by subtracting the discount from the 100%. (25% of of $60)

$60 - $15 = $45

The sale price and what you pay is $45.

Day 2: 25% off of already reduced price ($45 new 100%)
We do everything again but with a new 100%.

25 / 100    25 ÷ 100 = 0.25
0.25 x 45 = $11.25

$45 - $11.25 = $33.75

Final Sale Price:
Store A - $30.00
Store B - $ 33.75

Which is a better buy?

Store A is a better buy because they're offering a $30 pair of boots while compared to Store B offering a pair of boots at $33.75.
You'll save $3.75 if you shop at store A compared to Store B. At Store B, you'd have to find the percent of a percent which means there will be a new 100%.


 

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