This document provides an outline for a course on business mathematics. It includes 10 topics: number systems, set theory, linear equations and graphs, logarithms, matrices, mathematics of finance, linear programming, differential calculus, integral calculus, and permutation and combination. It also lists 3 references books on business mathematics, college algebra, and provides explanations and examples of key mathematical concepts like number systems, order of operations, properties of operations, and rules for positives and negatives.

1. Business Mathematics
Charls Darwin
Lecturer
Department of Business Administration-General
Bangladesh university of Professionals

2. Outline
1. Number system 6. Mathematics of Finance
2. Set theory 7. Linear Programming
3. Linear Equation and Graphs 8. Differential Calculus
4. Logarithms 9. Integral Calculus
5. Matrix 10. Permutation and
combination

3. References
• College Algebra by Raymond A. Barnett,
Michael R. Ziegler and Karl E. Byleen
• Business Mathematics by Qazi Zameeruddin,
Vijay K Khanna, Sk Bhambari
• Business Mathematics by Md. Rafiqul Islam,
Md Osman Gani.

4. NUMBER
SYSTEM

5. {1, 2, 3, 4, . . . }
If you were asked to count, the numbers you’d
say are called counting numbers. These
numbers can be expressed using set notation.
These are also called
the natural numbers.
{0, 1, 2, 3, 4, . . . }
If we include 0 we have
the set of whole numbers.
{ …, -3, -2, -1, 0,1, 2, 3, . . . }
Include the opposites of the whole numbers and
you have the set of integers.

6. rational numbers
Whole numbers are a subset of integers and
counting numbers are a subset of whole
numbers.
integers
whole numbers
counting
numbers
If we express a new set of numbers as the quotient of
two integers, we have the set of rational numbers
This means to
divide one integer
by another or
“make a fraction”

7. rational numbers
There are numbers that cannot be expressed as
the quotient of two integers. These are called
irrational numbers.
integers
whole numbers
counting
numbers
2
π
irrational
numbers
The rational numbers combined with the irrational
numbers make up the set of real numbers.
REAL NUMBERS

8. Translating English to Maths
sum of two numbers
difference between two numbers
The product of two numbers
the quotient of two numbers
is =
ab
a - b
a + b
b
a

9. ORDER OF OPERATIONS
When there is more than one symbol of operation in an
expression, it is agreed to complete the operations in a certain
order. A mnemonic to help you remember this order is below.
B I M D A S
rackets
ndices
ultiplication
ivision
ddition
ubtraction
Do any simplifying possible inside of brackets
starting with innermost brackets and working out
Apply IndicesComplete multiplication and division from left to rightComplete addition and subtraction from left to right

10. ( ) 423532
2
−×+−
BIMDASBIMDAS
brackets – combine these first
( ) 42322
2
−×+−
BIMDAS
indices – apply the indice now
( ) 42342 −×+
BIMDAS
complete multiplication and division, left to right
468 −+
BIMDAS
complete addition and subtraction, left to right
10
( ) 423532
2
−×+−

11. COMMUTATIVE PROPERTY
The operations of both addition and multiplication are commutative
abba +=+ 3223 +=+
When adding, you can “commute” or trade the terms places
abba ×=× 3223 ×=×
When multiplying, you can “commute” or trade the factors places

12. ASSOCIATIVE PROPERTY
( ) ( )cbacba ++=++
( ) ( )321321 ++=++
When adding, you can “associate” and add any terms first and
then add the other term.
( ) ( )cbacba ××=××
( ) ( )432432 ××=××
When multiplying, you can “associate” and multiply any factors
first and then multiply the other factor.
The operations of both addition and multiplication are associative

13. DISTRIBUTIVE PROPERTY
The operation of multiplication distributes over addition
( ) acabcba +=+
( ) 4323423 ×+×=+
The distributive property also holds for a factor that is multiplied
on the left.
( ) acabacb ×+×=+
( ) 2423243 ×+×=+

14. ( ) ( )abba −=−
A positive
times a
negative is
NEGATIVE
( ) ( )abba −=−
A negative
times a
positive is
NEGATIVE
( ) aa =−−
The negative
of a negative
POSITIVE
CAUTION: Remember that the value for a
and/or b could also be positive or negative.
b
a
b
a
b
a
−=
−
=
−
A positive
divided by a
negative or
A negative
divided by a
positive is
NEGATIVE
b
a
b
a
=
−
− A negative
divided by a
negative is POSITIVE