8:00 GED Math 4/19
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AGENDA 4/19/12
• 1. Review: Ratio/Proportion• 2. Discuss Ratio/Proportion Quiz• 3. Introduction to Percent– The Basics
• 4. The Percent Statement
• NO CLASS MONDAY
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PERCENT
• Percent means “out of 100”
• So, if you get 4 out of 5 questions right on a quiz, we generally give a percent to show a grade.
• Percentage is a way of putting numbers in the same terms so no matter what you compare, an understanding can me made.
45=80100
You can see these two fractions are equal, by multiplying diagonally.
400400
Because of this relationship, you can set up a proportion to calculate percentage, find the part, or find the whole.
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THE BASICS
• You will need to know how to convert:–A decimal to a fraction (place value)–A fraction to a decimal (division)–A fraction to a percent (division)–A percent to a fraction or decimal
(place value/division)
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EXAMPLE
CHANGING A PERCENT TO A DECIMAL
RULE
• 1. Drop the percent sign (%).
• 2. Move the decimal point two places to the LEFT.
45%...Percent Decimal
45%
8%
37 ½ %
250%
0.45
0.08
0.37 ½ or 0.375
2.5
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CHANGING A PERCENT TO A FRACTION
RULE• 1. Drop the %
sign.• 2. Write 100 as
the denominator.• 3. Reduce.
EXAMPLE 1• Change 35 % to a
fraction.
•
• Common denominator = 5
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CHANGING A MIXED NUMBER PERCENT TO A FRACTION
RULE• 1. Drop the % sign.
• 2. Change to an improper fraction.
• 3. Multiply by • 4. Reduce.
EXAMPLE 3• Change 16 2/3 % to a
fraction.
%
1
2
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THE PERCENT STATEMENT
15% of $25 is $3.75Percent
Whole
Part
$3.75 is 15% of $25Part
Percent
Whole
You will be asked to find the part, the percent, or the whole.
𝑖𝑠𝑜𝑓
=%100
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FINDING THE PART OF A WHOLE
• Two Strategies:• 1. Turn the percent into a decimal and then
multiply.
• Ex) Find 25% of 12.
• .25 x 12 = 3
• 3 is 25 % of 12.
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PROPORTION AND PERCENT
𝑝𝑎𝑟𝑡h𝑤 𝑜𝑙𝑒
=%100 This relationship is ALWAYS TRUE.
𝑝𝑎𝑟𝑡h𝑤 𝑜𝑙𝑒
=%100
Josh got 4 out of 5 questions right on a test. What is his percentage?
45=%100
45=
𝒙100
Step 1: Write a proportion statement.
Step 2: Find the cross products.
𝒙
5 𝑥¿ 400Step 3: Divide by 5 on both sides.
5 5 𝑥=80%4 is the part.
5 is the whole.
We are looking for the %.
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FINDING THE PART
• Find 25% of 12.
•Step 1: Set up a proportion.
•Step 2: Cross multiply.
•Step 3: Divide
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FINDING THE PART
• Option 1: Change the percent to a decimal, then multiply.
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FINDING THE PART• Option 2: Write a
proportion statement.
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WORD PROBLEMS (PART)• A state official predicts that 70% of the registered voters in
Montana will vote on election day. If there are 514,000 registered voters in Montana, how many are predicted to vote?
Step 1: Understand the question. “How many registered voters are predicted to vote?”Step 2: What info do you need? Use the % of voters predicted to vote and the number of registered voters.Step 3: Choose the operation. What is 70% of 514,000?
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EXAMPLE FROM P 135
• 6. Randi’s property tax bill is increasing by 3% this coming year. She now pays $890 a year in property tax.
• A) By how much is her property tax going to increase?
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EXAMPLE FROM P. 135
• 6. Randi’s property tax bill is increasing by 3% this coming year. She now pays $890 a year in property tax.
• B) How much will she pay next year?
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FINDING WHAT PERCENT ONE NUMBER IS OF ANOTHER
RULE• 1. First make a
fraction. Put the part (is) over the whole (of) and reduce.
• 2. Change the fraction to a percent.
EXAMPLE 3• 27 is what percent
of 45?
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Casio fx-260 Calculator- Example 2
• Use the calculator to find what percent 27 is of 45.
AC1. Press
2. Press 2 7 5
The display should read 60.
÷ SHIFT4
The answer is 60%.
%
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• 1. 9 is what percent of 36?
• 7 is what percent of 35?
• 7. The Melino family was on vacation for 12 days. It rained 3 of those days. On what percent of their vacation days did it rain?
Exercise 9, page 160 1-8
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FINDING A NUMBER WHEN A PERCENT OF IT IS GIVEN (WHOLE)
RULE• 1. Change the
percent to either a fraction or a decimal.
• 2. Divide the number by that fraction or decimal.
EXAMPLE 1• 20% of what is 9?
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Casio fx-260 Calculator- Example 1
• Use the calculator to find 20% of what number is 9.
AC1. Press
2. Press 9 0
The display should read 45.
÷ SHIFT2 %
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• 1. 18 is 50% of what number?
• 25% of what number is 30?
• 6. Paul and Jane Bidwell pay $150 a month on their car loan. This is 5% of their monthly income. How much do they make each month?
Exercise 10, p161 1-7
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THE PERCENT CIRCLE
P
% x W
•P stands for the Part
•% stands for the Percent
•W stands for the WHOLE
•The horizontal line means divided by.
•The X means multipliedby
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The Percent Circle
P
% x W
To Use the Percent Circle:
1. Cover the symbol of the number you are looking for.
2. Do the math shown by the uncovered symbols.
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The Percent Circle
P
% x W
What is 50% of 8?
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The Percent Circle
P
% x W
4 is 50% of what number?
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Finding What Percent One Number is of Another
• To find a percent of a number:
• Step 1: Change the percent to a decimal or a fraction.
• Step 2: Multiply
• What is 62 ½ % of 56?
• Decimal• 62.5 x 56 = 3500
• Move decimal two places to the left.
• 62 ½ % of 56 is 35.
PART
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• What is 62 ½ % of 56?• Fraction
• To find a percent of a number:
• Step 1: Change the percent to a decimal or a fraction.
• Step 2: Multiply
Change to a mixed number
Finding What Percent One Number is of Another
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Finding What Percent One Number is of Another
• To find the part: • 1. First make a fraction.
Put the part over the whole and reduce.
• 2. Change the fraction to a percent.
• 27 is what percent of 45?
PERCENT
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• The Melino family was on vacation for 12 days. It rained 3 of those days. On what percent of their vacation did it rain?
• Write the fraction as
• Change the fraction to percent.
•
Finding What Percent One Number is of Another
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Finding a Number When a Percent is Given
• 1. Change the percent to either a fraction or a decimal.
• 2. Divide the number by that fraction or decimal.
• 20% of what number is 9?
• Change to a fraction
WHOLE
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REVIEW: THE PERCENT STATEMENT
15% of $25 is $3.75Percent
Whole
Part
$3.75 is 15% of $25Part
Percent
Whole
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PRACTICE
• Mrs. Jackson makes a week. She pays $90 a week for food. Money spent for food is what percent of her income?
$450 is her total income.
She spends $90 on food.
$90 is what percent of $450?
𝑖𝑠𝑜𝑓
=%10090450
=𝑥100
450𝑥=9000450 450
𝑥=20%
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PRACTICE
• 60% of what number is 45?
• Lois got a 6% commission for selling a house. She sold a house for $120,000. Find the commission.
𝑖𝑠𝑜𝑓
=%10045𝑥
=60100
4500=60𝑥60 60 𝑥=75
𝑖𝑠𝑜𝑓
=%100
𝑥$120,000
=6100
$720 ,000=100 𝑥100 100
𝑥=$7200
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THE PERCENT CIRCLE
P
% x W
•P stands for the Part
•% stands for the Percent
•W stands for the WHOLE
•The horizontal line means divided by.
•The X means multipliedby
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The Percent Circle
P
% x W
To Use the Percent Circle:
1. Cover the symbol of the number you are looking for.
2. Do the math shown by the uncovered symbols.
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The Percent Circle
P
% x W
What is 50% of 8?
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The Percent Circle
P
% x W
4 is 50% of what number?
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USING THE PERCENT CIRCLE
• Sally wants a new computer that costs $900. She has saved 75% of the price. How much has she saved?
P
% x W
I am looking for the part.
.75 x $900 = $675
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USING THE PERCENT CIRCLE
• Bill paid $2 sales tax on a $40 shirt. The tax was what percent of the list price?
P
% x W
I am looking for the percent.
2/40= 1/20=.05
5 %