Percents Percents as Fractions Fractional Parts and Equivalent - - PDF document

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Percents

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Ratios as Percents Fractions as Percents Decimals as Percents Fractional Parts and Equivalent Names Three types of Percent Problems Percent of Change Applied Percent of Decrease Real-life Application Problems Percents as Fractions Percents as Decimals Relating Fractions, Decimals and Percents Applied Percent of Increase

Slide 3 / 194 Ratios as Percents

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What fraction of each grid is shaded? ___ 100 ___ 100 ___ 100

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What is the ratio of shaded boxes to total boxes? ______ to _______ ______ to _______ ______ to _______

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The fractions and ratios can also be written as percentages. Percent means per 100.

10 to 100 10 100 Fraction: Ratio: Percent: 10% Fraction: Fraction: Ratio: Ratio: Percent: Percent:

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What percent of the grid is shaded?

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Use the green stylus to shade 20% of the grid. How many squares will you shade? Use the black stylus to shade 5%

• f the grid.

How many squares will you shade?

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Use the red stylus to shade 100% of the grid. How many squares will you shade? 100% of something represents how much?

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1 1% of the grid is shaded.

True False

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2 100% of the grid is shaded.

True False

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3 What percent of the grid is shaded?

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4 6 to 100 is the same as what percent?

A

600%

B

60%

C

6%

D

100%

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5 15 is the same as what percent? 100

A 150% B

100%

C

15%

D

5%

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6 Express the ratio as a percent. 57 out of 100

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7 Express the ratio as a percent. 67 lacrosse team members in 100 students

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8 Express the ratio as a percent. $18 per $100

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decimals p e r c e n t s

Writing Decimals as Percents

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Multiply by 100 and add the percent symbol.

0.75

Example 1:

= 100 0.75 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.75 Writing decimals as percents... 75% Slide 20 / 194

Multiply by 100 and add the percent symbol. Example 2:

0.09 = 100 0.09 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.09 Writing decimals as percents... 9% Slide 21 / 194

Multiply by 100 and add the percent symbol. Example 3:

0.007 = 100 0.007 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.007 Writing decimals as percents... 0.7% Slide 22 / 194 0.4

Multiply by 100 and add the percent symbol. Example 4:

0.4 = 100 0.4 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

Writing decimals as percents... 40%

Slide 23 / 194 1.49

Multiply by 100 and add the percent symbol. Example 5:

1.49 = 100 1.49 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

Writing decimals as percents... 149%

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Multiply by 100 and add the percent symbol. Example 6:

8 = 100 8 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

8 Writing decimals as percents... 800%

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9 Write the decimal as a percent: 0.45 45%

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10 Write the decimal as a percent: 1.3 130%

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11 Write the decimal as a percent: 0.008 .8%

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12 Write the decimal as a percent: 5 500%

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13 Write the decimal as a percent: .2 20%

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percent decimal

Writing Percents as Decimals

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Divide by 100 and remove the percent symbol. Example 1:

28% = 100 28% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

28% Writing percents as decimals... 0.28 Slide 32 / 194

Divide by 100 and remove the percent symbol. Example 2:

8% = 100 8% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

8% Writing percents as decimals... 0.08 Slide 33 / 194

Divide by 100 and remove the percent symbol.

0.4%

Example 3:

= 100 0.4% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

0.4% Writing percents as decimals... 0.004 Slide 34 / 194

Divide by 100 and remove the percent symbol.

375%

Example 4:

= 100 375% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

375% Writing percents as decimals... 3.75 Slide 35 / 194

Divide by 100 and remove the percent symbol. Example 5:

=

Remember To divide a # by 100, move the decimal two places to the LEFT.

Writing percents as decimals... 0.235

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14 Write the percent as a decimal: 2% .02

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15 Write the percent as a decimal: 658% 6.58

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16 Write the percent as a decimal: 0.019% .00019

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.043 17 Write the percent as a decimal: 4.3%

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0.005 18 Write the percent as a decimal: .5%

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0.725 19 Write the percent as a decimal:

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0.2975 20 Write the percent as a decimal:

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f r a c t i

• n

s percents

Writing Fractions as Percents

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Write an equivalent fraction with a denominator

• f 100.

Example 1:

3 4 = 100 x 3 4 = 100 x 25 100 75

Writing fractions as percents... 75% 25

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Write an equivalent fraction with a denominator

• f 100.

Example 2:

4 5 = 100 x 4 5 = 100 x 20 100

80 Writing fractions as percents... 80% 20

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Write an equivalent fraction with a denominator

• f 100.

Example3:

9 4 = 100 x 9 4 = 100 x 25 100

225 Writing fractions as percents... 225% 25

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Write an equivalent fraction with a denominator

• f 100.

Example 4:

3

600 = 100 x 3 600 = 100 x 6 100 0.5 Writing fractions as percents... 0.5% 6

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21 Write the fraction as a percent: 19 20 95%

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22 Write the fraction as a percent: 9 1000 .9%

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23 Write the fraction as a percent: 8 100 8%

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24 Write the fraction as a percent: 5 2 250%

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25 Write the fraction as a percent: 3 500 .6%

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To write any fraction as a percent: METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Example 5:

7 8 0.875 7.000 87.5% 8 0.875 100 Slide 54 / 194

To write any fraction as a percent: METHOD 2: Write a proportion with the fraction as the first ratio and 100 as the denominator of the second ratio. Solve using cross products. Example 5:

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To write any fraction as a percent: METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Example 6:

12

9 1.333 12.000 133.3% 9 1.333 100

1

133 3

=

% Slide 56 / 194

To write any fraction as a percent: Example 6:

=

METHOD 2: Write a proportion with the fraction as the first ratio and 100 as the denominator of the second ratio. Solve using cross products.

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To write any fraction as a percent: METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Don't forget to add the whole number! Example 7:

5

8 0.625 5.000 362.5% 8 3.625 100

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26 Write the fraction as a percent: 5 8 62.5%

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27 Write the fraction as a percent. Round to the nearest whole percent. 4 7 57%

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28 Write the fraction as a percent: 3 5 360% 3

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29 Write the fraction as a percent: 2 500 .4%

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30 Write the fraction as a percent: 9 2 450%

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percents fractions

Writing Percents as Fractions

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Slide 65 / 194 Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 1:

75% = 75 = 100 3 4 Slide 66 / 194 Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 2:

120% = 120 = 100 1 5 1

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Multiply by 10 to eliminate the decimal

Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 3:

0.3% = 0.3 = 100 3 1000 Slide 68 / 194 Writing percents as fractions...

Express the % as a fraction with a denominator of 100, then simplify. Example 4:

% = = 100 1 4 2 9 4 100 2.25 = 10,000 225 = 400 9 Multiply by 100 to eliminate the decimal

Slide 69 / 194 Writing percents as fractions...another way

Express the % as a fraction with a denominator of 100, then simplify. Example 4: Convert the percent to a fraction. Divide the numerator by the denominator (100). Simplify.

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2 5 31 Write the percent as a fraction in simplest form: 40%

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32 Write the percent as a fraction in simplest form: 110% 11 10

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33 Write the percent as a fraction in simplest form: 0.5% 1 200

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34 Write the percent as a fraction in simplest form: 8% 2 25

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35 Write the percent as a fraction in simplest form: 5 % 4 75

1

3

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36 Write the percent as a fraction in simplest form: 9 % 3 32

3

8

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37 Write the percent as a fraction in simplest form: 54 % 191 350

4

7

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Fractional Parts and Equivalent Names

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Common Equivalents you should know like the back of your hand!

1 5 2 3 3 4 0.2 0.666... 0.75 20% 66.6% 75% Slide 80 / 194 1 2 1 3 1 4 0.5 0.3333... 0.25 50% 33.3% 25%

Common Equivalents you should know like the back of your hand!

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Relate Fractions, Decimals & Percents ...Tying it all together!

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Helping you remember... Fill in each box below with an example of the process described. % to a fraction

% to a decimal fraction to a % decimal to a %

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Order the numbers from least to greatest. 0.15 12.5% 0.095 In order to do this, they must all be in the same form. Let's turn them all into percents: 15% 12.5% 16% 9.5% So least to greatest: 9.5% 12.5% 15% 16% 0.095 12.5% 0.15

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38 Find the lowest value A 5% B 1/2 C .5% D .05

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39 Find the greatest value A 120% B 1.02 C .2% D 1.19

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40 Find the greatest value A 6% B .6 C 60 D 6

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41 Find the lowest value A 2% B .2 C .02 D .2%

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42 Find the lowest value A 50% B 500% C 50.0 D 50.01

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Express each fraction as a percent: 1) 2) 3) Click to Reveal Click to Reveal Click to Reveal

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43 Express as a fraction.

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44 Express as a decimal.

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45 Express as a percent.

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46 Express as a decimal.

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47 Express as a percent.

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48 Express as a percent.

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Remember, percents are "parts of a whole". The part is the numerator and the whole is the denominator. 17% means 17 parts per 100 or We are going to solve problems involving percents. There are 3 types of problems:

• 1. Find the part

What number is 54% of 34?

• 2. Find the whole

4 is 60% of what number?

• 3. Find the percent

18 is what percent of 28?

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Two words that will occur in these types of problems are "is" and "of". These words have specific meanings in math. · "Is" means equals (=) · "Of" means multiply To solve a percent problem, translate the words into an equation. Change the following:

• 1. Percent into a decimal
• 2. "is" to "="
• 3. "of" to " "
• 4. Unknown to "x"

Then, solve the equation.

Slide 101 / 194 Finding the Part... Slide 102 / 194

Examples: Find 40% of 60

.40

60 = 24 20% of 90 .20 90 = 18

Write a mathematical sentence Write a mathematical sentence

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What is 10% of 88?

Write a mathematical sentence

X = .10 88 X = 8.8 Try these: Find 12% of 70 What is 40% of 28? PULL PULL

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Let's try these examples again, but solve them with a proportion this time! Examples: Find 40% of 60

.40

60 = 24 20% of 90 .20 90 = 18

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What is 10% of 88? X = .10 88 X = 8.8 Try these: Find 12% of 70 What is 40% of 28? PULL PULL

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49 Find 30% of 45

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50 What is 15% of 90?

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51 Find the greater value.

A

20% of 16

B

10% of 90

C

25% of 40

D

100% of 7

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52 Find the greater value.

A

2% of 1000

B

5% of 500

C

10% of 300

D

15% of 100

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53 Identify any values that are equal.

A

What is 40% of 80?

B

60% of 70

C

25% of 128

D

200% of 16

Slide 113 / 194 Finding the Whole... Slide 114 / 194

Remember, you can solve this by:

• 1. Translating into an equation
• 2. Setting up a proportion

40% of what number is 50? .40 X = 50

X = 50 .40 X = 125

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Try This: 100 is 20% of what number? 100 = .20 X

100 = X .20 X = 500

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54 What is 70% of 80?

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55 12% of 50 is what number?

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56 65% of what number is 10?

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57 What number is 150% of 18?

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58 1% of what number is 12?

Slide 121 / 194 Finding the Percent... Slide 122 / 194

What percent of 80 is 24?

x 80 = 24

X = 24 80

X = .30 X = 30%

Remember, you can solve this by:

• 1. Translating into an equation
• 2. Setting up a proportion

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60 is what percent of 15?

60 = X 15

60 = X 15

4 = X 400% = X

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59 What percent of 3 is 12?

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60 30 is what percent of 36?

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61 What percent of 18 is 180?

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62 2 is what percent of 1?

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63 What percent of 25 is 20?

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You have just studied three different types of percent problems. Try all 3 types: What number is 40% of 60? 42 is what percent of 840? What is 30% of 45? PULL

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64 Find the largest value.

A

What is 50% of 50?

B

What number is 45% of 60?

C

30 is 60% of what number?

D

25% of what number is 150?

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65 Find the greatest percentage value.

A

What percent of 30 is 18?

B

60 is what percent of 90?

C

What percent of 70 is 210?

D

1,000 is what percent of 100?

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66 Find 20% of 78.

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67 8 is what percent of 28?

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68 What number is 3% of 17?

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69 Find 27% of 54.

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70 23 is what percent of 200?

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71 What percent is 35 of 20?

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72 56% of what number is 40?

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73 45 is 30% of what number?

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74 62% of 40 is what number?

A

24.8

B

.0155

C

24.8%

D

15.5

Slide 141 / 194 Percent of Change

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Percent of Change: The ratio of the amount of increase or decrease to the

• riginal amount

It is an increase when the new amount is larger than the

• riginal and a decrease when the new amount is smaller

than the original. To find the percent of change, use the following proportion: Percent of change: Amount of increase or decrease = % Original Amount 100

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Find the percent of change (be sure to label your answer as an increase or decrease). Examples: Original amount: 20 Original amount: 40 New amount: 30 New amount: 10 Percent of change= Percent of change=

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Identify the percent of change as an increase or

• decrease. Then find the percent of change.
• 1. Original: 45

New: 75

• 2. Original: 100

New: 42

• 3. Original: 58

New: 75 PULL

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Try This! A CD's original price was $12.99. It is now on sale for $10.99. What is the percent of change? PULL

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Try This! A student's first test grade was 60. The second test grade was an 85. What was the percent of change? PULL

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75 In 2005, the price of a McDonald's hamburger was $0.89. In 2010, the price of a McDonald's hamburger was $1.19. What was the percent of change?

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76 Original Amount: 500 New: 700 Find the percent of change.

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77 Original Amount: 52 New: 17 Find the percent of change.

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78 The number of students who attended FHS in 2010 was 1405. In 2011, 1380 students attended FHS. What was the percent of change in student enrollment?

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79 Find the percent of change. Original price: $120 Sale price: $75

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80 Find the percent of change. Original price: $80 Sale price: $50

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81 A stereo, originally priced at $360, is on sale for $200. What is the percent of change?

Slide 154 / 194 Applied Percent of Decrease

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There are situations when the percent of change is going to be a decrease. Examples are: · Discounts · Sales · Reduction in Population

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When finding a discount, there are two different methods you can use. Method 1: Find the percent of the original price (discounted amount in $) Subtract the discount from the original price. Method 2: Subtract the percent from 100% (percent you are paying) Find the percent of the original price.

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82 A $710 computer is to be discounted 30%. What will be the sale price?

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83 A necklace, priced at $120, is to be marked down 15%. What will be the sale price?

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84 The student population of the high school will decrease by 5% next year. The current population is 1407

• students. How many students will attend next year?

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85 The store is having a 40% off sale. What percent will the customers pay?

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86 $80 boots are on sale for 20% off. After the sale, the manager raises the price 20%. What will be the selling price of the boots after the sale?

Slide 167 / 194 Applied Percent of Increase

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There are situations when the percent of change is going to be an increase. Examples are: · Tips · Sales Tax · Increase in Population

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When finding an increase, there are two different methods you can use. Method 1: Find the percent of the original price (increased amount) Add the increase to the original price. Method 2: Add the percent to 100% (percent you are paying) Find the percent of the original price.

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Find the new amount Increase 60 by 10% Increase 68 by 12% PULL

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87 Increase 36 by 25%.

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88 Increase 40 by 15%

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Tip: An amount added to a bill for services provided. Customers traditionally tip 18 - 20% for good service in restaurants and salons. Example: If the restaurant bill is $45 and you want to leave a 20% tip, how much money should you leave? 45 + .20(45) = 54 or 45(1.20) = 54 The customer will leave $54 on the table. The waitress will receive a $9 tip and the restaurant will receive $45. To calculate the amount of the tip only: .20(45) = 9

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Calculate a 20% tip on a $75 bill. PULL What will the customer leave in total? PULL For poor service, my friend will leave a 5% tip. How much less will this waitress earn than the waitress above? PULL

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Sales tax: An amount of money that is calculated by applying a percentage rate to the taxable price of a sale. Sales taxes are collected by the buyer from the seller, who turns it over to the

• government. In NJ the sales tax rate is 7%.

To calculate Sales Tax alone find the percent (tax) of the price. That is the amount that you owe in addition to the cost of the item. To find the total cost of an item, you must add the sales tax to the cost. There are 2 ways to do this:

• 1. Find the percent of the item and add it to the original amount.
• 2. Find 100% + tax% of the original amount.

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A car costs $23,500. How much sales tax will the customer pay? 23,500(0.07) = $1645 What will the customer pay altogether for the car? 23,500 + 1645 = 25,145 The total cost of the car, including tax, can be calculated as follows: 23,500 + .07(23,500) = 25,145 or 23,500(1.20) = 25,145

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Discuss: How are tips and sales tax alike?

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89 What is the total cost of a $250 stereo in the state of NJ?

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90 Calculate the sales tax on a $125 bicycle.

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91 Mike wants to leave a 20% tip. His bill is $35.50. How much is the tip?

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92 A $65 restaurant tab is put on the table. The couple plans on leaving an 18% tip. How much should be left altogether?

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93 What is the total cost of a $123 ipod, including tax?

Slide 184 / 194 Real Life Application Problems

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A store owner pays $12 for a particular bracelet. To cover expenses, the owner will mark up the price by 150%. Find the selling price of the bracelet. PULL

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The store is having a 20% off sale on all CD's. With the sale, you pay $12 for a CD. What was the original price? PULL A couple left their waiter a 20% tip in the amount of $18. What was the cost of their meal? PULL

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A group of friends had dinner at a restaurant. The cost of their meals is $62. They want to leave a 15% tip. Calculate the tip. When they arrive at the register the cashier will calculate the sales tax on the meal at a rate of 7%. Determine the sales tax. Calculate the total cost of the meal for each of the 3 friends. PULL

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A store is having a 25% off sale on ipods. You want to purchase an ipod with an original price of $249. The sales tax is 7%, which will be applied to the sale price of the

• ipod. What is the total cost of the ipod?

PULL A computer is on sale for 10% off the original price of $325. When it doesn't sell, the manager marks it down another 20% off the sale price. · What is the new sale price of the laptop? · Is the new sale price the same as it would be had the manager taken 30% off of the original price? Explain. PULL

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94 Wholesale price: $56 Markup percent: 50% New price ?

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95 Tickets cost $7 at the door. If purchased in advance, the tickets cost $5. What is the percent of discount for purchasing tickets in advance?

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96 560 people were surveyed. 25% said they prefer

• Coke. How many people prefer Coke?

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97 Increase 50 by 25%. What is the new amount?

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98 What is the original price on a pair of boots that sell for $72 after a 25% discount?

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99 An ipod costs $176. It is on sale for 20% off and will be taxed at a rate of 7% on the sale price. What will be the total cost of the ipod?