1. Commercial arithmetic
8th Grade Maths
Chapter 1 – Unit 4

2. How to deal with percentage problems
Sale 50% Reductions
How to deal with percentage problems

3. How to change percentages, into fractions and decimals
A percentage is a special fraction.
The % says, “per hundred.”
For example, 50%, is simply another way of writing the fraction 50/100

4. You can almost see the 100 in the percentage sign%
The noughts
The 1
Percentage
Fraction
17%
17/100
20%
20/100
75%
75/100
Etc.

5. Yes, but remember to try to write the fraction in its simplest terms
So to write a percentage as a fraction, you simply put it over 100 like this:
24% = 24/100
Yes, but remember to try to write the fraction in its simplest terms
24% = 24/ / /25

6. Copy and complete this chart
Percentage
Fraction
1. 23%
23/100
7. 80%
2. 24%
8. 84%
3. 55%
9. 12%
4. 20%
1/5
10. 48%
5. 17%
11. 71%
6. 78%
12. 36%

7. To change a fraction into a decimal, you divide the bottom number (the denominator) into the top number (numerator). For example, to change ¾ into a decimal, you would divide the 3 by the 4.
3 ÷ 4 = 0.75
Remember that a percentage is a fraction always has 100 as its denominator

8. So, to change a percentage into a decimal, you always divide by 100
For example, 35% as a fraction is 35/100 so to change this into a decimal, you divide 35 by 100
35%
÷ 100

9. To change decimal into a percentage
To change a decimal into a percentage, you X by 100
X 100 %

10. ÷ 100 You Should Know X 100 Decimal to a percentage
A a percentage is a special fraction.
23% = 23/100
Percentage to a decimal
÷ 100

11. Copy and complete this chart
Percentage
Decimal
1. 27%
2. 2%
3. 55%
4. 5%
5. 17%
6. 98%

12. Finding one quantity as a percentage of another quantity
Science 23/32
Megha obtained a score of 23 out of 32 in a science test. She wants to know what this will be as a percentage?
To do this, you
Write the result as a fraction 23/32
4. 72%
Change the fraction into a decimal (23 ÷ 32 = )
Change the decimal into a % ( X 100 = 71.9%)

13. The quantity that you want as a %
There are lots of similar problems and all of these can be tackled in the same way
Write the quantities as a fraction
23/32
2. Change the fraction into a decimal (23 ÷ 32 = ). It’s probably a good idea to round off to 2 decimal places.
3. Change the decimal into a % (0.72 X 100 =72%)
4. So, 23 is 72% of 32
The total quantity
The quantity that you want as a %

14. What percentage of the cars are green?
Car Par Survey
Colour
Frequency
Green 2
Silver 4
Black 5
What percentage of the cars are green?
Total is Want 2/11 as a percentage
Change 2/11 into a decimal =
(round off to 2 d,p Change 0.18 into a %
(0.18 X 100 = 18%) Answer 18%

15. Try these:
1 Work out your percentage if you got 12 out of 25
2  Work out your percentage if you got 15 out of 25
3 Work out your percentage if you got 17 out of 20
4 Work out your percentage if you got 19 out of 24
5 Work out your percentage if you got 17 out of 31
6 A player scores 3 times out of 6 shots.What is their score percentage
7 A player scores 4 times out of 10 shots. What is their score percentage
8 A player scores 44 times out of 69 shots. What is their score percentage
9 Work out out of 26 as a percentage
10 Calculate the score percentage if out of 15 shots 12 are successful

16. The ‘percentage of’ problem
What is 12% 0f 34?
What is 13% of 56?
What is 78% of 57?

17. To answer these questions
First: Change the percentage into a decimal
Second: Change the word ‘of’ into a X sign
Third: Workout
Example: What is 23% of 45
23% = 0.23 and ‘of’ X
0.23 X 45 = 10.35

18. Finding Percentages of Different Numbers
Problem:
In a survey of 120 pupils it was found that 20% had personal stereos. How many pupils had personal stereos?
Change the percentage to a decimal, then multiply by the number of children.
20% = 0.20
0.20 times 120 = 24

19. Try these 25% of 32 2. 75% of 36 3. 80% of 35 10% of 142 20% of 60

20. Profit & Loss Statement

21. Profit & Loss Statement
A basic profit and loss statement reports the following for a specified period of time:
Sales
Expenses
Profits/losses

22. Theory and Concepts Manufacturer or Producer Whole-saler or Dealer
Retailer or sales person
Customer
A Customer can get things in above sequences.

23. Cost Price (CP) Definition:-
The money paid by Shopkeeper to the manufacturer or Whole-saler to buy the goods is called the cost- price(CP) of the goods purchased by the shopkeeper.

24. Selling Price (SP) Definition:-
The price at which the Shopkeeper sells the goods is called the selling price(SP) of the goods sold by shopkeeper.

25. Profit(gain)
Definition:- If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit(or gain).
Profit = SP-CP; SP>CP

26. LOSS
Definition:-If the selling price of an article is less than its cost price, then the dealer suffers a loss.
Loss=CP-SP; CP>SP

27. Important Formulae Profit=SP-CP Loss=CP-SP
Loss or Profit is always based on CP.
Profit% = (Profit*100)/CP.
Loss% = (Loss*100)/CP
Selling Price(SP)=[(100+Profit%)/100]*CP
Selling Price(SP)=[(100-Loss%)/100]*CP
Cost Price(CP)=[100/(100+Profit%)]*SP
Cost Price(CP)=[100/(100-Loss%)]*SP

28. Marked Price
Definition:- Basically to avoid loss due to bargaining by the customer and to get the profit over the cost price trader increases the cost price by certain value, this increase in value over cost price is known as markup and the increased price(CP+markup) is called the marked price or printed price.

29. Discount
Definition:- Discount means reduction of marked price to sell at a lower rate or literally discount means concession. Basically it is calculated on the basis of marked price.
Discount is always given on the marked price of the article.

30. Discount Formulae:- Discount = marked price – selling price
Marked price is sometimes called list price.
Discount = rate of discount times the marked price.
Net price = marked price - discount.

31. Commission Commission is percentage of sales price of an item.
Also, Transaction that are mediated by person other than buyer and owner.
The mediator who helps in buying and selling is Commission agent or Broker.
The money that the broker or agent receives in deal is brokerage or commission.

32. Commission Contd…
Commission in per hundred rupees is called Commission rate.
For e.g. If a salesperson receives a 10% commission on their sales and sells Rs1500 worth of merchandise, they would earn Rs150 in commission.

33. Simple Interest
Formula
I = PRT

34. What is Interest

35. INTEREST IS
If you DEPOSIT amount in a bank account then bank will pay you a percentage as INTEREST.

36. I = PRT I = interest earned (amount of money the bank pays you)
P = Principle amount invested or borrowed.
R = Interest Rate usually given as a percent (must changed to decimal before plugging it into formula)
T = Time (must be measured in years) or converted to years by dividing by 12 months

37. Converting Change % to decimal 1) 12% 2) 5% 3) 2 ½ % 4) 8.5%
Change from decimal to %
5) .098
6) .455
Answers
1) .12
2) .05
3) .025
4) .085
5) 9.8%
6) 45.5%
Move 2 places
to left & drop % sign
Move 2 places
to right & add % sign

38. I = PRT Solve for one of variables:
Solving for I
Write value for P, R, & T.
Then multiply
The result is required Interest.
Solving for other variables
Multiply the numbers that are on same side then divide by that answer.

39. Interest paid by bank is unknown Principle (invested)
1. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of Rs5,000 is invested at 4.5%, what is the total simple interest accumulated in the checking account after 2 years.
Interest paid by bank is unknown
Principle (invested)
Rate changed to decimal
Time is 2 years
Multiply
I = PRT I=
I=Rs450
(5,000)
(.045)
(2)

40. Interest paid by bank is unknown Principle (invested)
2. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of Rs7,000 is invested at 7.5%, what is the total simple interest accumulated in the checking account after 3 years.
Interest paid by bank is unknown
Principle (invested)
Rate changed to decimal
Time is 3 years
Multiply
I = PRT I=
I=Rs1575
(7,000)
(.075)
(3)

41. Principle (invested) is unknown Rate changed to decimal Time is 1 year
3. When invested at an annual interest rate of 6% an account earned Rs of simple interest in one year. How much money was originally invested in account?
I = PRT
180=
180 = .06P
3,000 = P
Interest paid by bank
Principle (invested) is unknown
Rate changed to decimal
Time is 1 year
Multiply
Divide P
(.06)
(1)

42. Principle (invested) is unknown Rate changed to decimal Time is 1 year
4. When invested at an annual interest rate of 7% an account earned Rs of simple interest in one year. How much money was originally invested in account?
I = PRT
581=
581 = .07P
Rs8,300 =P
Interest paid by bank
Principle (invested) is unknown
Rate changed to decimal
Time is 1 year
Multiply
Divide P
(.07)
(1)

43. Interest paid by bank Principle (invested) Rate is unknown
5. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of Rs7,000 accumulate Rs910 of interest in the account after 2 years, what was the annual simple interest rate on the savings account?
Interest paid by bank
Principle (invested)
Rate is unknown
Time is 2 years
Regroup & Multiply
Divide
Change to %
I = PRT
910=
910 = (7,000)(2)R
910 = 14,000 R
14, ,000
0.065 = R
6.5% = R
(7,000)
(R)
(2)

44. Interest paid by bank Principle (invested) Rate is unknown
6. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of Rs2,000 accumulate Rs360 of interest in the account after 4 years, what was the annual simple interest rate on the savings account?
Interest paid by bank
Principle (invested)
Rate is unknown
Time is 4 years
Regroup & Multiply
Divide
Change to %
I = PRT
360=
360 = (2,000)(4)R
360 = 8,000 R
8,000 8,000
0.045 = R
4.5% = R
(2,000)
(R)
(4)

45. Interest paid by bank Principle (invested) Rate is unknown
7. Mohan M. bought a 6-month Rs1900 certificate of deposit. At the end of 6 months, she received a Rs209 simple interest. What rate of interest did the certificate pay?
Interest paid by bank
Principle (invested)
Rate is unknown
Time is 6 months
(divide by 12)
Regroup & Multiply
Divide
Change to %
I=PRT
209=
209=(1900)(6/12)R
209=950R
950
0.22 = R
22% = R
1900
(R)
(6/12)

46. Interest paid by bank - Unknown
8. An investment earns 4.5% simple interest in one year. If the money is withdrawn before the year is up, the interest is prorated so that a proportional amount of the interest is paid out. If Rs2400 is invested, what is the total amount that can be withdrawn when the account is closed out after 2 months?
Interest paid by bank - Unknown
Principle (invested)
Rate is .045
Time is 2 months
(divide by 12)
Multiply
Now, since the money is being withdrawn, add the interest to the principal.
I=PRT I=
(2400)
(.045)
(2/12)
I=Rs18
Rs18 + Rs2400 = Rs2418
Rs2418 will be withdrawn