Fractıons-Decımals-And-Percents-1-1P59Zel.ppt

Math

1. Fractions, Decimals,
and Percents
Parts of the whole

2. Let’s watch this clip to see how some people
can be confused on how fractions and percents
can be used as examples.

3. Percent comes from the Latin
per centum, or “per hundred”
Consequently, a number such as
32% can be written as “32 per
hundred” or the fraction 32/100.
This fraction is equivalent to the
decimal 0.32.
Percent –is a ratio of a number
to 100.

4. The word “percent” meaning “per hundred” is used to
show parts of a whole, the same as a fraction is used
to represent part of a whole.
If you had a pizza that was cut into 100 pieces, 25%
of the pizza would be 25 pieces!

5. Let’s begin with a simple concept. Consider the
blue square below. Let’s think of this blue square
as One Whole Square. How let’s divide it into 100
pieces—every piece just the same size as every
other piece. We can easily see that every one of
the 100 pieces is shaded blue. So we say 100% of
the square is shaded blue. So 100%and1 Whole
are the same thing.

6. Since percent means “per hundred” it tells us how
many for each hundred, 25% means 25 for each
hundred, or 25 out of each hundred.
Here is our One Whole Squarewith a portion
shaded green. What percent is shaded green. In
percent, every whole is divide into 100 pieces.
Now count the pieces shaded green. There are 50
pieces out of 100 shaded green, so 50% is green.

7. Once again our One Whole Squarehas a
portion shaded, this time it’s blue. What
percent is shaded blue. Remember, in
percents, every quantity is divided into 100
pieces. Now count the pieces shaded blue.
There are 86 pieces out of 100 shaded blue,so
86% of the pieces are shaded blue.

8. Can you calculate what percent of our “One
Whole” that is shaded red?

9. The Relationship
Between Fractions
Decimals and Percents
All represent part of a whole

10. How do we get from one
form to another?

11. A percentis based on the number in
terms of 100 or “per hundred”.
12%; 4%; 0.05%...
A fractionis based on
the number into which
the whole is divided
(the denominator).
The numerator(the top)
is the PART, the
denominator(the
bottom) is the whole.
½; ¼; ⅝…
A decimalis based on
the number in terms
of tenth, hundredths,
thousandths, etc…
0.5; 0.05; 0.005

12. Fraction to Decimal
Divide the denominator
(the bottom of the
fraction) into the
numerator(the top of
the fraction). Place a
decimal after the
number inside the
division “box” and attach
as many zeros as
necessary to complete
the division. If the
quotient does not come
out evenly, follow the
rules for “rounding off”
numbers.
numerator
denominator

13. Decimal to percent
.50 = 50%
(0.50 x 100 = 50.0)
Attach the % sign
Move the decimal point
two (2) places to the
right (this multiplies
the number by 100)

14. Percent to decimal
50% = .50
50 ÷100 = .50
Move the decimal point
two (2) places to the
left (this divides the
number by 100)

15. Percent to fraction
Place the number over
100 and reduce.

16. Fraction to percent
Multiply the number by
100, reduce and
attach a percent (%)
sign.

17. Decimal to fraction
You will be using place value to do this!Count the
decimal places of the decimal starting from the
decimal point. If there is one decimal point, place
the number over 10 and reduce. If there are two
decimal places, place the number over 100, and
reduce. If there are three decimal places, place
the number over 1000, and reduce…Etc.
(This is really just using your knowledge of place value to name
the denominator.)
1 decimal place = tenths,
2 decimal places = hundredths,
3 decimal places = thousandths

18. Remember that
fractions, decimals,
and percentsare
discussing partsof a
whole, nothow large
the whole is.
Fractions, decimals,
and percents are part
of our world. They
show up constantly
when you least expect
them. Don’t let them
catch you off guard.
Learn to master these
numbers.

19. Percents to
Remember

20. Problem Solving with
Percents
When solving a problem with a percent greater
than 100%, the partwill be greater than the
whole.

21. There are three types of percent problems:
1) finding a percent of a number,
2) finding a number when a percent of it is known,
and 3) finding the percent when the part and whole
are known
1) what is 60% of 30?
2) what number is 25% of 160?
3) 45 is what percent of 90?

22. Solving Equations
Containing
Percents
Most percent
problems are word
problems and deal
with data. Percents
are used to describe
relationships or
compare a part to a
whole.
Sloths may seen lazy, but their
extremely slow movement
helps make them almost
invisible to predators.
Sloths sleep an average of
16.5 hours per day. What
percent of the day do they
sleep?
Solution

23. Equation Method
What percent of 24 is 16.5.
n · 24 = 16.5
n = 0.6875
n = 68.75%
Proportional method
Part Part
Whole Whole24
5.16
100

n

24. Solve the following
percent problems
1) 27 is what percent of 30?
2) 45 is 20% of what number?
3) What percent of 80 is 10?
4) 12 is what percent of 19?
5) 18 is 15% of what number?
6) 27 is what percent of 30?
7) 20% of 40 is what number?
8) 4 is what percent of 5?

25. 9) The warehouse of the Alpha Distribution
Company measures 450 feet by 300 feet. If
65% of the floor space is covered, how many
square feet are NOT covered?
10) A computer that normally costs $562.00
is on sale for 30% off. If the sales tax is
7%, what will be the total cost of the
computer? Round to the nearest dollar.
11) Teddy saved $63.00 when he bought a CD
player on sale at his local electronics store.
If the sale price is 35% off the regular
price, what was the regular price of the CD
player?

26. Percent of Change
Markup or Discount

27. One place percents are
used frequently is in the
retail business. Sales are
advertised on television, in
newspapers, in store
displays, etc. Stores
purchase merchandise at
wholesale prices, then
markupthe price to get
the retailprice. To sell
merchandise quickly,
stores may decide to have
a sale and discount retail
prices.
Percent of change =
amount of change÷original
amount

28. When you go to the store
to purchase items, the
price marked on the
merchandise is the retail
price(priceyou pay). The
retail priceis the
wholesalepricefrom the
manufacturer plus the
amount of markup
(increase). Markupis how
the store makes a profit
on merchandise.

29. Using percent of
change
•The regular price of a portable CD player at
Edwin’s Electronics is $31.99. This week the CD
player is on sale at 25% off. Find the amount of
discount, then find the sale price.
25% · 31.99 = d Think: 25% of $31.99 is what number?
0.25 · 31.99 = dWrite the percent as a decimal.
7.9975 = d Multiply.
$8.00 = d Round to the nearest cent.
The discountis $8.00. To find the sale price
subtract the discountfrom the retail price.
$31.99 -$8.00 = $23.99
The sale price is $23.99

30. When solving percent problems there are two
ways to solve these problems. Take a look at
the problem below and see the two solutions.
A water tank holds 45 gallons of water. A new
water tank can hold 25% (+) more water.
What is the capacity of the new water tank?
25% · 45 = g25% of 45 gallons
0.25 · 45 = gWrite percent as a decimal
11.25 = gMultiply
Add increase to original amount
45 + 11.25 = 56.25 gallons
125% · 45 = g 125% of 45 gallons
1.25 · 45 = gWrite percent as a decimal
56.25 = gallons
The original tank holds 100% and the
new tank holds 25% more, so
together they hold;
100% + 25% = 125%

31. Find percent of
increase or decrease
1) from 40 to 55
2) from 85 to 30
3) from 75 to 150
4) from 9 to 5
5) from $575 to $405
6) An automobile dealer agrees to reduce the
sticker price of a car priced at $10,288 by 5%
for a customer. What is the price of the car for
the customer?
Remember,
Percent of changeis the
difference of the two numbers
divided by the original amount

32. Simple Interest
I= P· r· t

33. When you keep money in a savings account, your
money earns interest.
Interest–the amount that is collected or paid
for the use of money.
For example, the bank pays you interestto use
your money to conduct its business. Likewise,
when you borrow money from the bank, the bank
charges intereston its loans to you.
One type of interest, called simple interest, is
money paid only on the principal(the amount
saved or borrowed). To solve problems involving
simple interest, you use the simple interest
formula. I = Prt

34. Most loans and savings accounts today use
compound interest. This means that interest
is paid not only on the principal but also on all
the interest earned up to that time.
Interest rate of interest per year
(as a decimal)
I = P · r · t
Principal time in years that the
money earns interest

35. Using the simple
Interest Formula
I= ?, P = $225, r= 3%, t= 2 years
I = P· r· t Substitute. Use 0.03 for 3%
I = 225 · 0.03 · 2Multiply
I = 13.50
The simple interest is $13.50
I= $300, P= $1,000, r= ?, t= 5 years
I = P · r · t Substitute
300 =1,000 · r · 5 Multiply
300 = 5000r
300/5000 = 5000r/5000 Divide by 5,000 to isolate variable
r = 0.06 Interest rate is 6%

36. Solve the
following
Find the interest and total amount
1) $225 at 5% for 3 years.
2) $775 at 8% for 1 year.
3) $700 at 6.25% for 2 years.
4) $550 at 9% for 3 months.
5) $4250 at 7% for 1.5 years.
6) A bank offers an annual simple interest rate of
7% on home improvement loans. How much would
Nick owe if he borrows $18,500 over a period of
3.5 years.

37. Compound Interest Formula
A = Amount (new balance)
P = Principal (original amount
r = rate of annual interest
n = number of years, and
k = number of compounding
periods per year (quarterly)
Amount Principalratenumber of years
number of compounding periodskn
k
r
PA







1

38. Since simple interest is rarely used in real-
world situations today, it is important to
understand how compound interest is used.
The contrast between simple interest and compound
interest does not become very evident until the
length of time increase. Look at the comparison
below using simple versus compound interest.
$1000 at 8% for 1 year$1000 at 8% for 30 years
Simple interest $1,080.00 Simple $2,400.00
Compound interest $1,082.43Compound $10,765.16

39. Formula explained
A = P(1 + r/k)
n · k
Write down formula
A =1000(1 + .08/4)
30 · 4
Substitute values
A =1000(1 + .02)
30 · 4
Evaluate parenthesis
A
=
1000(1.02)
120
Evaluate parenthesis and exponents
A =1000(10.76516303…) Evaluate the power
A = 10765.16303 = $10,765.16
Remember, compound interest is computed on the
principal plus all interest earned in previous periods.
Compound interest is used for loans, investments,
bank accounts, and in almost all other real-world
applications.

40. Using Percents to Find
Commissions, Sales
Tax, and other taxes.
Percent of Money

41. Percents
Percents are used everyday to
compute sales tax, withholding tax,
commissions, and many other types of
monies.
Think about this, you go to Wal-Mart to buy a
new CD or video game. You make your
selections and go to the check out counter.
This happens when you make your purchase.
You pay for your CD, along with your purchase
you pay salestaxon what you bought, your
Wal-Mart associate that takes your money is
paid money to work there, they also may make
a commissionon what they sell. From her
salary, withholding taxesare taken out to pay
to the state and federal government.

42. Using Percents to Find
Commissions
A real-estate agent is paid
a monthly salary of
$900 plus commission.
Last month she sold one
condo for $65,000,
earning a 4% commission
on the sale How much
was her commission?
What was her total pay
last month?
First find her commission.
4% · $65,000 = c
0.04 · 65,000 = cChange percent to decimal.
$2,600 = c
She earned $2,600 on the sale.
Now find her total pay.
$2,600 + $900 = $3,500 Total pay
Total commission
earned
Monthly salary

43. Oct 1, 2009, NC Sales
Tax increased to
7.75%. Use percents
to find sales tax.
If the sales tax rate
is 7.75%, how much
tax would Daniel
pay if he bought
two CD’s at $16.99
each and one DV D
for $36.29? What
would his total
purchase cost him?
2 CD’s @ $16.99each $33.98
1 DVD @ $36.29
$33.98
$36.98
$67.96
Sales tax · total purchase = total tax
.0775 · 67.96 = $5.2669
Total purchase + sales tax = total due
$67.96 + $5.27 = $73.23

44. Use percent to
find withholding
tax
Anna earns $1,500
monthly. Of that,
$114.75 is withheld
for Social Security
and Medicare. What
percent of Anna’s
earnings are withheld
for Social Security
and Medicare?
Write an equation.
114.75 iswhat % of$1,500
114.75 =x ·1,500
114.75= 1500x
1500 1500Divide both sides by 1500
0.0765 = x Change to percent
7.65% = x
Anna pays 7.65% withholding
tax on her salary
Think!!!
$114.75 is what % of $1,500 or
What % of $1,500 is $114.75
Remember, when changing a decimal to
percent, move the decimal two places to
the right and add the percent sign %

45. Note:
Commissions and sales taxare based on the price of
an item.
Withholding taxesare also called income tax. This
tax is taken before you get your paycheck. This
is where the terms gross payand net paycomes
from.
Gross payis the amount of salary you earn before
taxes are remove.
Net payis the amount of your actual check you
receive after the taxes are remove.
When you get a job, which
would you prefer, a job that
pays commission or one that
pays a straight salary?