Topic: Percents
Aim: How do we convert fractions to decimals to percents?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Percent
Fraction
a ratio comparing a
part to 100
a ratio comparing a
part to a whole
Example:
#1
Percents and Fractions
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Topic: Percents
Aim: How do we convert fractions to decimals to percents?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Fraction
3
8
Decimal
.375
divide numerator
by denominator
Multiply by 100
.375
(or move decimal point two spaces to the right)
Tip: Move toward % symbol to get percent
Percent
#2
37.5%
Converting FRACTION to DECIMAL to PERCENT
Alternate Method!
Can you quickly go straight from a fraction to a percent?
Hint: A percent is a
part compared to 100
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Topic: Percents
Aim: How do we convert fractions to decimals to percents?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Percent
5%
Divide by 100
5
(or move decimal point two spaces to the left)
Tip: Move away from % symbol to get rid of
Decimal
.05
Fraction
5
100
#3
put digits in numerator
over place value
reduce!
Converting PERCENT to DECIMAL to FRACTION
To quickly go from a percent to a fraction:
1. Write percent over 100
2. Reduce!
26%
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Topic: Percents
Aim: What is the percent proportion?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
The percent proportion compares part of a
quantity to the whole or total quantity.
The other ratio is the percent out of the total percent 100.
This IS the
part of total
percent is always
the part of 100
OF represents
TOTAL
#4
100 is always the
TOTAL percent
The Percent Proportion
Find a percent
____ = ____
Find a part
____ = ____
Find a total
____ = ____
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Topic: Percents
Aim: What is the percent equation?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
This equation comes from the percent proportion. as decimal
or fraction
is: equal sign
what: your
variable
x = .50
#5
of: multiplication
What is 50% of 60
60
or
x=1
2
The Percent Equation
.
60
Topic: Percents
Aim: How do we apply multiple strategies to find % of a #?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Commission
Tip/Gratuity
Tip or gratuity is the extra amount you give for good service on top of the total bill. It is usually a percentage of the total bill BEFORE discounts or taxes.
Commission is a percentage of the sales a person earns that is given to the seller as a BONUS in addition to their regular salary.
Commission = % of SALES
Paycheck = salary + commission
*Note: If the question tells you to tip on amount after tax, then do that even though it's wrong for real life math.
#6
Tip/Gratuity/Commissions
Example: Your salary is $700 a week. You have sold $1,500 in merchandise this week. Example: Calculate the tip you should leave. [Give 15%]
Bill: $47.00
Groupon: $10.00
New Total: $37.00
Tax: $3.19
Total Due: $40.19
PART A If you earn a 3% commission, how much did you make in commission this week?
PART B What is your total earnings for the week?
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Topic: Percents
Aim: How do we apply multiple strategies to find % of a #?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Remember that "OF" means to multiply.
Example: Find 20% of 750
Use a decimal.
Use a fraction.
Use the percent proportion.
Percent of a Number
#7
Round to nearest hundredth.
Find
of 3
Find 200% of 79
.
Find .25% of 50
Aim: How can two amounts of change be the same but the
percent of change can be different?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Percent of Change - a ratio that compares the
change in quantity to the original amount.
The percent of change could be a
percent INCREASE or a percent DECREASE
(SUBTRACT original and new amount)
#8
Percent of Change
If you wanted to see the movie Coraline in
1961 you would have paid $2.00. Today
you have to pay $12.00 in most NY theaters!
What is the percent of change?
Set up word fraction to help you.
how much did it change
original amount
________ = ________
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Aim: How can two amounts of change be the same but the
percent of change can be different?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Relative Error is Relative!!!!
15 lbs
Jack guessed the puppy was 65 pounds.
50 pounds too much!
Jill guessed the dinosaur was 4050 pounds.
50 pounds too much!
Do you think the error was the same? 4000 lbs
Percent of Error - a ratio that compares the inaccuracy of an estimate to the actual amount.
subtract actual amount and guessed amount
difference/error
actual
#9
=
% error
100
Relative Error/Percent of Error
Kevin estimates the mass of an object to be 120 grams.
The actual mass is 138 grams. What is the percent of error?
Set up word fraction to help you.
how much was the error? ________ = ________
actual amount
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Aim: How does sales tax, discounts, tips and markups effect
the final cost of an item?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Raises Final Cost
Lowers Final Cost
Under 100%
Over 100%
Sales tax, markups, tip
discount
Percent you pay is
(100% + % increase)
Percent you pay is
(100% - % decrease)
(%less)($ original)=$ less
(%more)($ original)=$ more
$ original + $ more = $ you pay $ original - $ less = $ you pay
or
or
(%you pay)($original)=$ you pay (%you pay)($original)=$ you pay
#10
Sales Tax, Tips, Markups, Discounts
Example: Find the final cost of a $50 pair of sneakers...
A. After a 40% markup.
B. After a 15% discount
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Aim: How does sales tax, discounts, tips and markups effect
the final cost of an item?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Tip/Gratuity: take percent of total bill BEFORE discounts or tax.
note: always follow directions of question. If the question tells you to calculate tip on total after tax, then do it, even though in real life that is wrong!
Tax: tax is ALWAYS on price you pay. So if you get a discount
the tax is on the sale price NOT the original price.
# 11
Rules of Tax and Tip
Example: Find the total due on a $35 bill after a 30% discount, 8% tax and 15% tip
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Aim: How does sales tax, discounts, tips and markups effect
the final cost of an item?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Find original cost after Markup
Find original cost after Discount
A game costs $48.75 after a 25% discount. What was the original cost of the game?
A game costs $53.00 after 6% sales tax. What was the cost of the game before tax?
discount ______ = ______
100
original
sales tax ______ = ______
100
original
final cost ______ = ______
100
original
final cost ______ = ______
100
original
# 12
Finding Original Cost
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Topic: Percents
Aim: How can you estimate the percent of a number?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
Use multiples of 10%
Use a fraction
reduce number by 1 decimal place
1.
62% of 503
Approximating!
# 13
3.
35% of 42.74
2.
Estimate 122% of 50
4.
100% + 20%
Estimate ¼% of 789
1% take away two decimal spaces
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Topic: Percents
Aim: How can you use a formula to find simple interest?
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
the percent
(expressed as a decimal)
the amount earned or paid
for the use of money.
the amount of money
deposited or borrowed.
the amount of time that
passes in YEARS!!
(divide the months by 12
to turn it into years!)
Balance = principal + interest
# 14
Simple Interest
Find the balance:
Find the interest:
1. $1500 at 4.25% for 4 years
2. $580 at 42% for 6 months
Find the interest rate:
3. $12,000 for 5 years paid $3,600 in interest
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Topic: The Assessment/Our Final... It's Coming!
Major
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