1. REV 00 BUSINESS MATHEMATICS
QMT 3301
BUSINESS MATHEMATICS
QMT BUSINESS MATHEMATICS

2. WHOLE NUMBERS AND DECIMALS
REV 00
CHAPTER 1
WHOLE NUMBERS AND DECIMALS
QMT BUSINESS MATHEMATICS

3. QMT 3301 BUSINESS MATHEMATICS
1.1 Whole Numbers
REV 00
1.1.1 Read and Write Whole Numbers
( )
Hundred Trillions
( )
Ten Trillions
( )
Trillions
( )
Hundred Billions
( )
Ten Billions
( )
Billions
Hundred Millions
( )
( )
Ten Millions
( )
Millions
Hundred Thousands
( )
Ten Thousands
(10 000)
Thousands
(1 000)
Hundreds
(100)
(10)
Tens
Ones
(1)
QMT BUSINESS MATHEMATICS

4. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example:
1. Write its word name given the number below: 28
346
2 335
11 007
QMT BUSINESS MATHEMATICS

5. QMT 3301 BUSINESS MATHEMATICS
REV 00
Write the number given its word name:
Four hundred twelve.
Thirty-three thousand, seven.
Ninety thousand, one.
Seven hundred thousand, eleven.
Fifteen million, three hundred sixty-two thousand, five hundred thirty-eight.
Eight hundred forty-two billion, five hundred thousand, twenty-nine.
QMT BUSINESS MATHEMATICS

6. QMT 3301 BUSINESS MATHEMATICS
REV 00
1.1.2 Round Whole Numbers
Example:
1. Round 2748 to the
(a) Nearest hundred
(b) First digit
2. Round 3596 to the nearest
(a) Ten
(b) Hundred
(c) Thousand
QMT BUSINESS MATHEMATICS

7. QMT 3301 BUSINESS MATHEMATICS
REV 00
1.1.3 Add, Subtract, Multiply and Divide Whole Numbers
Example:
1. Add and round the answer to the nearest hundred.
2. Subtract 27 from 64.
3. Multiply 127 by 53.
divided by 35 (answer in 1 decimal place).
QMT BUSINESS MATHEMATICS

8. QMT 3301 BUSINESS MATHEMATICS
REV 00
1.2 Application Problems
Many business-application problems require mathematics.
You must read the words carefully to decide how to solve the problems.
QMT BUSINESS MATHEMATICS

9. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example:
1. At a recent garage sale, the total sales were RM584. If the money was divided among Tom, Mina, Abu and Rashid, how much did each receive?
2. In May, the landlord of an apartment building received RM720 from each of eight tenants. After paying RM2180 in expenses, how much did the landlord have left?
QMT BUSINESS MATHEMATICS

10. QMT 3301 BUSINESS MATHEMATICS
1.3 Basics of Decimals
REV 00
1.3.1 Read, Write, and Round Decimals
Hundreds
(100)
(10)
Tens
Ones
(1)
Decimal Point
Tenths
(0.1)
Hundredths
(0.01)
Thousandths
(0.001)
Ten-thousandths
(0.0001)
Hundred-thousandths
( )
( )
Millionths
Ten-Millionths
( )
Hundred-Millionths
( )
QMT BUSINESS MATHEMATICS

11. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example:
Write the word name for the decimals below:
0.582
1.0009
782.07
3.12
$234.93
QMT BUSINESS MATHEMATICS

12. QMT 3301 BUSINESS MATHEMATICS
REV 00
1.3.2 Round to a Specified Decimal Place
Example:
1. Round to the nearest
Hundredth
Thousandth
Tenth
2. Round the number to the specified place
$ to the nearest dollar
$ to the nearest cent
QMT BUSINESS MATHEMATICS

13. QMT 3301 BUSINESS MATHEMATICS
REV 00
1.4 Addition, Subtraction, Multiplication and Divisions of Decimals
Example:
1. Add
2. Subtract 26.3 from 15.84
3. Multiply 3.5 by 3
4. Divide 95.2 with 14
5. Find the quotient of 37.4  24 to the nearest hundredth.
QMT BUSINESS MATHEMATICS

14. QMT 3301 BUSINESS MATHEMATICS
REV 00
CHAPTER 2
FRACTIONS
QMT BUSINESS MATHEMATICS

15. QMT 3301 BUSINESS MATHEMATICS
REV 00
2.1 Basics of Fractions
In the fraction ;
1 = numerator and 2 = denominator.
When a fraction has a value less than one, it is called a proper fraction.
If fraction  1, fraction = improper fraction.
QMT BUSINESS MATHEMATICS

16. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example: = proper fraction
= improper fraction
= whole or mixed number
Example:
1. Write as a mixed number.
2. Write as an improper fraction.
QMT BUSINESS MATHEMATICS

17. QMT 3301 BUSINESS MATHEMATICS
2.1.2 Change a Fraction to an
Equivalent Fraction
Example:
2.1.3 How to Reduce a Fraction to Lowest Term
1. Reduce to lowest term.
2. Write in lowest term.
3. Rewrite as a fraction with a denominator of 72.
REV 00
QMT BUSINESS MATHEMATICS

18. QMT 3301 BUSINESS MATHEMATICS
REV 00
2.2 Addition and Subtraction of Fractions
Adding and subtracting fractions with the same denominator:
Adding and subtracting fractions with the different denominator:
QMT BUSINESS MATHEMATICS

19. Example: 1. Find the sum 2. Solve
REV 00
QMT BUSINESS MATHEMATICS

20. 2.3 Addition and Subtraction of Mixed Numbers
REV 00
Example:
1. Solve
QMT BUSINESS MATHEMATICS

21. 2.4 Multiplication and Division of Fractions
REV 00
Multiplying fractions:
Dividing fractions:
QMT BUSINESS MATHEMATICS

22. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example:
1. Multiply Divide
QMT BUSINESS MATHEMATICS

23. QMT 3301 BUSINESS MATHEMATICS
REV 00
CHAPTER 3
PERCENT
QMT BUSINESS MATHEMATICS

24. QMT 3301 BUSINESS MATHEMATICS
REV 00
3.1 Writing Decimals and Fractions as Percents
Example: Write those numbers as percent
i i.
ii ii.
iii iii.
iv iv.
v v. (in 2 decimal places)
QMT BUSINESS MATHEMATICS

25. QMT 3301 BUSINESS MATHEMATICS
REV 00
3.1.1 Write a Percent as a Decimal
Example:
1. Write the percent as a decimal
37% iv.
26.5% v.
0.9%
QMT BUSINESS MATHEMATICS

26. QMT 3301 BUSINESS MATHEMATICS
3.2 Finding the Part
REV 00
B = Base – the whole or the total.
R = Rate – a number followed by “%” or
“percent”.
P = Part – the result of multiplying base times rate.
QMT BUSINESS MATHEMATICS

27. QMT 3301 BUSINESS MATHEMATICS
REV 00
B = Base – sales
R = Rate – sales tax rate
P = Part – sales tax
Example:
1. If the sales tax rate is 5%, what is the sales tax and total sales on $133 of merchandise?
Solution:
QMT BUSINESS MATHEMATICS

28. 3.2.1 Identifying the Base and the Part
REV 00
3.2.1 Identifying the Base and the Part
Usually the Base
Usually the Part
Sales
Sales Tax
Investment
Return
Savings
Interest
Retail Price
Amount of Discount
Value of Real Estate
Rents
Total Sales
Commission
Value of Stocks
Dividends
Earnings
Expenditures
Original
Change
QMT BUSINESS MATHEMATICS

29. QMT 3301 BUSINESS MATHEMATICS
3.3 Finding the Base
REV 00
Using the Basic Percent Equation to solve for Base.
Example:
is 30% of _____
Solution:
QMT BUSINESS MATHEMATICS

30. QMT 3301 BUSINESS MATHEMATICS
REV 00
Finding sales when sales tax rate is given.
Example:
1. The 5% sales tax collected by a store was $380. What was the total amount of sales?
Solution:
QMT BUSINESS MATHEMATICS

31. QMT 3301 BUSINESS MATHEMATICS
REV 00
Finding the amount of an investment.
Example:
1. The yearly maintenance cost of an apartment is 2.5% of its value. If maintenance is $37,000 per year, what is the value of the apartment complex?
Solution:
QMT BUSINESS MATHEMATICS

32. QMT 3301 BUSINESS MATHEMATICS
REV 00
Finding the base if rate and part are different quantities.
Example:
1. United Hospital finds that 25% of its employees are men and 720 employees are women. What is the total number of employees?
QMT BUSINESS MATHEMATICS

33. QMT 3301 BUSINESS MATHEMATICS
Solution:
REV 00
Men = 25%, then women = (100-25)% = 75%
QMT BUSINESS MATHEMATICS

34. 3.4 Finding the Rate Using the percent equation to solve for rate.
REV 00
Using the percent equation to solve for rate.
Example:
45 is what percent of 180? Solution:
Note: Rate is always expressed as a percent.
QMT BUSINESS MATHEMATICS

35. QMT 3301 BUSINESS MATHEMATICS
Finding rate of return when the amount of return and the investment are known.
Example:
1. $3400 is invested in a new computer yielding additional income of $1700. What is the rate of return? Solution:
REV 00
QMT BUSINESS MATHEMATICS

36. QMT 3301 BUSINESS MATHEMATICS
REV 00
Solving for the percent remaining.
Example:
1. A car is expected to last 10 years before it needs replacement. If the car is 7 years old, what percent of the car’s life remains?
Solution: Years remain = 10 – 7 = 3 years
QMT BUSINESS MATHEMATICS

37. QMT 3301 BUSINESS MATHEMATICS
REV 00
Find the percent of increase/decrease.
Example:
1. Sales of digital cameras went from $40,000 to $100,000. Find the percent increase. Solution:
Increase = $100,000 - $40,000 = $60,000
QMT BUSINESS MATHEMATICS

38. QMT 3301 BUSINESS MATHEMATICS
REV 00
3.5 Increase and Decrease Problems
Increase problems:
Original + increase = new value
Phrases: after an increase of, more than, greater than
Decrease problems:
Original – decrease = new value
Phrases: after a decrease of, less than, after a reduction of
QMT BUSINESS MATHEMATICS

39. QMT 3301 BUSINESS MATHEMATICS
REV 00
Example:
1. The value of a home sold by Sally this year is RM , which is 10% more than last year’s value. Find the value of the home last year.
Answer: RM
2. At A company, production last year was 20% more than the year before. This year’s production is chairs, which is 20% more than last year’s. Find the number of chairs produced 2 years ago.
Answer: chairs
QMT BUSINESS MATHEMATICS

40. QMT 3301 BUSINESS MATHEMATICS
REV 00
3. After Sport About deducted 10% from the price of a tennis racket, Robert paid RM135. What was the original price of the racket?
Answer: RM 150
QMT BUSINESS MATHEMATICS