Business
Mathematics
I. Whole Numbers
What are numbers? What is the nature of arithmetical truth? - Friedrich
Ludwig Gottlob Frege
OUTLINE
Introduction to Whole Numbers
Operations on Whole Numbers
Order of Operations
Solving Word Problems
AFTER COMPLETING THIS CHAPTER, YOU ARE
EXPECTED TO:
USE THE PLACE VALUE TO READ AND WRITE
NUMERIC AND VERBAL WHOLE NUMBERS;
Learning
Objectives
ROUND OFF WHOLE NUMBERS TO INDICATED
POSITION;
PERFORM THE
NUMBERS;
OPERATIONS
ON
WHOLE
EVALUATE EXPRESSIONS USING THE RULES
FOR ORDER OF OPERATIONS; AND
SOLVE WORD PROBLEMS INVOLVING WHOLE
NUMBERS.
Introduction to Whole Numbers
Hindu-Arabic Numerals - the modern numeral
system or decimal system. It was developed by
Hindus in India and introduced by the Arabs in
Europe.
Counting - process used to measure any specific
measurable things.
Counting numbers/Natural numbers - numbers used
for counting (1, 2, 3, 4, ...).
Introduction to Whole Numbers
Whole Numbers - the set of natural numbers
including zero.
Numbers may be represented either by words or by
symbols called numerals.
Base-10 system - using the ten different digits to
write numbers. Ex: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
single-digit
numeral
two-digit
numeral
first ten
numerals
75
Introduction to Whole Numbers
Place values are separated into groups of
three. To help in reading the number, a
comma is used at every third place starting
from the right moving to the left side of
the number. The comma makes it easier to
identify the place value of the digit.
Introduction to Whole Numbers
Whole Number Place Value Chart
Examples: Give the place values of
each digit in the following numerals.
47
4 = tens
7 = ones
308 9,000
Examples: Read the numbers.
45,317
Forty-five
thousand,
three
hundred seventeen
1,256,092
Examples: Write the following
numbers as base ten
numerals.
Six
hundred
eighty thousand
680,000
Nine billion, four
hundred
sixty
million,
four
thousand
Rounding Whole Numbers
A lot of the whole numbers we read and hear
are rounded numbers. Government statistics
are usually rounded numbers. Some financial
reports of companies also use rounded
numbers. All rounded numbers are
approximate numbers. The frequent we round,
the more we approximate the number.
Steps in Rounding Whole Numbers
2.If
the
digit
to
the
1.Identify
3.Change all
right
of
the
identified
the place
the digits to
digit
is
5
or
more,
value of the
the right of
increase
the
identified
digit to be
the identified
digit
by
1,
otherwise
rounded.
digit to
do not change the
zeroes.
identified digit.
Examples: Round the following numbers as indicated:
4, 123 TO THE
NEAREST TENS
4, 120
46,968 TO
THE NEAREST
HUNDREDS
123, 456 TO THE
NEAREST TEN
THOUSANDS
47, 000
9, 876, 543 TO THE
NEAREST HUNDRED
THOUSANDS
18, 123, 456 ALL THE
WAY
Operations on Whole Numbers
Addition - unite two or more numbers called
“addends”to make one equivalent number
called “sum” (or total) and the process is
called “addition”.
Example:
Operations on Whole Numbers
Subtraction - process of taking away a
certain number from another number. When
one number is subtracted from another the
result is called “difference”. The number
that is subtracted is called “subtrahend”,
and the number from which it is subtracted
is called “minuend”.
Operations on Whole Numbers
Example:
Operations on Whole Numbers
Multiplication - two numbers are multiplied,
the result is “product“. The numbers
multiplied are called “factors“ of the
product. The top number is the
“multiplicand“ and the bottom number is
“multiplier“.
Operations on Whole Numbers
Example:
Operations on Whole Numbers
Division - process of finding out how many
times one number is contained in another
number. When a number is divided by
another number, the result is “quotient“.
The number divided is called “divisor“
while the number being divided is called
“dividend“.
Operations on Whole Numbers
It is set up in the form:
Example:
Order of Operations
The rule for order of operations is
abbreviated as “PEMDAS“.
Parenthesis,
Exponent,
Multiplication,
Division, Addition, Subtraction
Order of Operations
Example:
Order of Operations
Example:
Solving Word Problems
Example: The distance from Sta. Mesa, Manila
to Tanay, Rizal is 58 kilometers. Pagsanjan,
Laguna is 47 kilometers farther from Sta
Mesa to Tanay. Find how far it is from Sta.
Mesa to Pagsanjan.
Solving Word Problems
Example: The distance from Sta. Mesa, Manila to
Tanay, Rizal is 58 kilometers. Pagsanjan, Laguna is
47 kilometers farther from Sta Mesa to Tanay. Find
how far it is from Sta. Mesa to Pagsanjan.
Solution:
58 + 47 = 105
Solving Word Problems
Example: A stadium bleachers has 42 rows
with each row having 64 seats. How many
seats are there?
Solving Word Problems
Example: You need to rent a moving truck. if
it cost $25 per day and $2 per mile, how
much will the rental cost be if you need to
truck for 4 days and plan to drive a total of
150 miles?