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Topic 14 Guided Notes
Understanding Percent
Information, Definitions, Solutions
Key Words/Topic
and Assignments
14.1
Understanding
Percent
New Terms
Percent A special kind of _____ in which the first ______ is compared to
____.
Review Terms
Ratio
Today’s Concept Since percents are comparing the 1st term to 100, the second term
must always be 100. If the original ratio does not have a bottom
term of 100, you must come up with a proportion to make the
second term 100. If the original ratio has 100 for a secon term,
but you do not know the value of the top term, you must also use
a proportion.
You can use the methods we learned about in the last unit; cross
multiplication, scale factor, and unit rates.
1.
Group Work
1-6 on page 345.
2.
Show work when
3.
appropriate.
Use complete sentences
when appropriate.
4.
Don’t forget your labels.
HOMEWORK: 7-15, 18 5.
P. 345 in textbook.
6.
Key Words/Topic
and Assignments
14.2
Fractions,
Decimals, & Percents
Information, Definitions, Solutions
New Terms
Review Terms
Percent A special kind of _____ in which the first ______ is compared to
____.
Today’s Concept Fractions, decimals, and percents are all related to each other.
They each show a part of a whole. Let’s look at an example.
25/100 = .25 = 25%
At times you will need to change a type of number (fraction,
decimal, percent) into another type of number (fraction, decimal,
percent) using what you’ve already learned this year.
How do you turn a decimal into a percent? Multiply the
number by 100 (move the decimal two places to the right)
and put a % sign after the number. .75 * 100 = 75%
Group Work
1- 8 on page 348.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-20
even 21 P. 348 in
textbook.
How do you turn a fraction into a decimal? Divide the
numerator by the denominator. 3/4 = .75
How do you turn a decimal into a fraction? Say the decimal-the
numerator is the number you said and the denominator is the
place value of the number.
1.
2.
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4.
5.
Group Work
1- 8 on page 348.
6.
Show work when
appropriate.
Use complete sentences 7.
when appropriate.
Don’t forget your labels.
8.
HOMEWORK: 10-20
even 21 P. 348 in
textbook.
Key Words/Topic
and Assignments
14.3 Percents Greater
than 100 and Less than
1
Information, Definitions, Solutions
New Terms
Review Terms
Today’s Concept Often times percents can be greater than 100 or less than 1.
Group Work
1-7 on page 350.
When you have a percent that is less than 1, you need to know
how to change the percent into a fraction and decimal.
What are the fraction and decimal equivalents of 1/4%?
1. Change the fraction into a decimal equivalent WITHOUT
dropping the percent sign.
1/4% =.25%
2. Put the .25 over 100; .25/100
3. Remember you can’t have a decimal in a fraction so you
have to change the numerator to a whole number. In this
case we must multiply the top and bottom by 100.
.25*100 = 25__
100*100 10,000
4. Then you can convert the fraction to a decimal.
25/10,000 = .0025
so 1/4% = 25/10,000 = .0025
Show work when
When you have a percent that is greater than 100, you need to
appropriate.
Use complete sentences know how to change the percent into a fraction and decimal.
when appropriate.
Don’t forget your labels.
What are the fraction and decimal equivalents of 125%?
HOMEWORK: 14-22 P.
350 in textbook.
1. Put the .125 over 100; 125/100
2. Divide the numerator by the denominator to change the
fraction to a decimal (move the decimal two places to the
left). 1.25
3. Put the fraction into simplest form by dividing the
numerator and denominator by the GCF (25) 125/100 = 5/4 or 1
1/4.
1.
2.
Group Work
1-7 on page 350.
Show work when
appropriate.
3.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 14-22 P.
350 in textbook.
4.
5.
6.
7.
Key Words/Topic
and Assignments
14.4
Estimating
Percent
Information, Definitions, Solutions
New Terms
Review Terms
Today’s Concept This topic combines what you know about rounding, compatible
numbers, and benchmark fractions to estimate percents.
Estimating percents is good to use when you want to quickly
analyze information and the answer doesn’t have to be precise.
Benchmark fractions and rounding are two good tools to use
when estimating percents.
Sometimes you will need to round the percent, the fraction, or
the decimal. Sometimes you will need to round more than one.
You should always round your numbers to compatible numbers.
What is 31% of 294 ≈ 90
31% ≈ 30% & 294 ≈ 300
.3 * 300 = 90 so 30% of 300 = 90
Group Work
1-8 on page 352.
1.
Show work when
appropriate.
2.
Use complete sentences
when appropriate.
Don’t forget your labels.
3.
HOMEWORK: 12-21
P. 352 in textbook.
4.
5.
6.
Group Work
1-8 on page 352.
7.
Show work when
appropriate.
Use complete sentences
when appropriate.
8.
Don’t forget your labels.
HOMEWORK: 12-21
P. 352 in textbook.
Key Words/Topic
and Assignments
14.5
Finding the
Percent of a Number
Information, Definitions, Solutions
New Terms
Review Terms
Today’s Concept There are two key ways we will use to find the percent of a
number. One way involves converting the percent to a decimal
and multiplying the decimal times the number. The other way
uses proportions and cross multiplication.
What is 34% of 234?
Method 1. 34% = .34. .34 * 234 = 79.56
Method 2. 34 = X cross multiply to solve 34*234=100x
100 234
7956=100x so x=79.56
100 100
Group Work
1-7 on page 354.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
You can also uses estimation to get you close to the answer and
to check the reasonableness of your answer.
Sometimes you want to know what percent one number is of
another number. This is how you can find out how well you do
on a quiz! All you have to do is divide the numbers.
Mr. Levine scored a 17 out of 21. What percent is 17 out of
21?
Divide the 1st number by the 2nd number – 17/21 ≈ .8095 *
100 = 80.95%
HOMEWORK: 9-29
odd P. 355 in textbook.
1.
Group Work
1-7 on page 354.
2.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels. 3.
HOMEWORK: 9-29
odd P. 355 in textbook.
4.
5.
6.
7.
Key Words/Topic
and Assignments
14.6
Tips, Taxes,
Discount, and Simple
Interest
Information, Definitions, Solutions
New Terms
Principal The ____________ of ______________ you deposit.
Interest What the bank _________. It is a ______________ of your
deposit.
Simple Interest This is used when _________ is paid only on the __________
originally invested.
Review Terms
Today’s Concept You will use percent calculations your whole life. Three uses are
for calculating tips, taxes, and discounts.
To calculate tips use this formula Tips = Percent * Cost or T=pc
A meal at Cheese Cake Factory costs $23.49. You want to
leave a 20% tip. What is the tip amount AND the total cost?
1. Convert the tip percent to a decimal; 20% = .2
2. Plug what you know into the formula; T = .2*23.49
3. Solve for T; T=4.698-remember to round for problems
involving money. T=4.70
4. Total Cost = 23.49 + 4.70 = $28.19
Group Work
1-5 on page 359.
Oops. You forgot about taxes. There is a 6.75% tax rate on
your meal. What are the tax amount and the total cost for
the meal including your tip.
1. Convert the tax percent to a decimal; 6.75%=.0675
2. Multiply the tax rate times the cost; .0675 * 23.49
=1.585575 (remember to round for money) = 1.59
3. Total Cost = $23.49 + $1.59 + $4.70 = $29.78
Show work when
appropriate.
Use complete sentences
when appropriate.
You want to buy the latest shirt from Abercrombie. There is
Don’t forget your labels. a 20% off sale on shirts. The shirt you want to buy is $19.99.
How much does the shirt cost after the discount is taken off?
1. Use the discount formula; discount = rate * cost or d=r*c
HOMEWORK: 6-12 P.
2. Convert the discount rate percent to a decimal; 20% =.2
359 in textbook.
3. Plug what you know into the formula; d=.2*19.99
4. Solve for d; d=3.998 (remember to round for money) =
$4.
5. Subtract the discount from the cost of the shirt; $19.99 $4 = $15.99
In order to pay for your meal, you took out a $50 loan for 2
years. The loan has an interest rate of 5%. How much
interest will you pay on your loan?
1. Use the formula for simple interest; Interest = principal x
rate x time (I=prt)
2. Convert the interest rate percent to a decimal; 5% = .05
3. Plug in what you know; I=50*.05*2
4. Solve for I; I=5 or $5
You can use these formulas, and what you know about solving
equations to find the value for any of the variables.
Group Work
1-5 on page 359.
1.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 6-12 P.
359 in textbook
2.
3.
4.
Group Work
1-5 on page 359.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 6-12 P.
359 in textbook
5.