Math 64
1.3 "Adding and Subtracting Whole Numbers, and Perimeter"
Objectives:
*
Add and subtract whole numbers.
*
Find the perimeter of a polygon.
*
Solve problems by adding or subtracting whole numbers.
Adding Whole Numbers
The operation of addition with whole numbers is indicated by writing the numbers horizontally, separated by (+)
signs. For example,
:
with instructions to add. For example,
of the addition is called the
:
:
Also, we can write the numbers vertically in columns
The numbers being added are called
;
and the result
Be sure to keep the digits aligned (in column form) so that we will be adding
units to units, tens to tens, and so on.
Example 1: (Addition with whole numbers)
Find the following sums.
a) 46 + 713
b) 4135 + 252
Adding by Carrying:
Note:
If the sum of the digits in one column is more than 9:
a. write the ones digits in that column, and
b. carry the other digits as a number to be added to the next column to the left.
Example 2: (Addition with whole numbers)
Find the following sums.
a) 46; 278 + 124; 931
b) 22; 781 + 186; 297
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Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
1.3
c) 1647 + 246 + 32 + 85
d) 121; 742 + 57; 279 + 26; 586 + 426; 782
Properties of Addition:
Addition Property of 0 :
The sum of 0 and any number is that number. For example,
Commutative Property of Addition:
Changing the order of two addends
does not change their sum. For example,
Associative Property of Addition:
Changing the grouping of addends
does not change their sum. For example,
Example 3: (Using the properties of addition)
Add:
a) 13 + 2 + 7 + 18 + 9
b) 22 + 54 + 8 + 16 + 5
Subtracting Whole Numbers
Subtraction is reverse addition. To subtract, we must know how to add. Subtraction
is not commutative nor
associative. For example,
Properties of Subtraction:
Subtraction Properties of 0 :
The di¤erence of any number and that same number is 0. For example,
The di¤erence of any number and 0 is that same number. For example,
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Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
1.3
Example 4: (Subtraction with whole numbers)
Find the di¤ erence and check the answer.
a) 893
52
b) 7826
505
Subtracting by Borrowing:
When subtracting vertically, if a digit in the second number (subtrahend) is larger than the corresponding digit in the
…rst number (minuend), borrowing is necessary.
Example 5: (Subtraction with whole numbers)
Subtract and check the answer.
a) 697
49
b) 7631
c) 400
164
d) 62; 222
152
39; 898
Finding the Perimeter of a Polygon
In geometry, addition is used to …nd the perimeter of a polygon. A polygon can be described as a ‡at …gure formed by
line segments connected at their ends. Geometric …gures such as triangles, squares, and rectangles are called polygons.
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Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
1.3
The perimeter of a polygon is the distance around the polygon. This means that the perimeter of a polygon is the
sum of the lengths of its sides.
Example 6: (Using the concept of perimeter)
Find the perimeter of each polygon.
a)
b)
Solving Problems by Adding or Subtracting
Often, real-life problems occur that can be solved by adding or subtracting. The …rst step in solving any word problem
is to understand the problem by reading it carefully. Descriptions of problems solved through addition or subtraction may
include any of these words or phrases:
Addition
Subtraction
(+)
( )
Key Words
Key Words
Examples
added to
plus
increased by
more than
total
sum
Examples
Symbols
Symbols
subtract
di¤erence
less
less than
take away
decreased by
subtracted from
To solve a word problem that involves addition or subtraction, we …rst use the facts given to write an addition or
subtraction statement. Then we write the corresponding solution of the real-life problem. It is sometimes helpful to write
the statement in words (brief phrases) and then translate to numbers.
Example 7: (Application)
In pricing a new car, Jason found that he would have to pay a base price of $15; 200 plus $1025 in taxes and $575 for license
fees. If the bank loaned him $10; 640; how much cash would Jason need to buy the car?
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Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
1.3
Example 8: (Application)
Airline executives are studying selected aircraft models and their seating capacity for possible equipment expansion and
replacement. In the following graph, each bar represents an aircraft model and the height of each bar represents the
corresponding seating capacity.
a. Which aircraft model shown contains the fewest seats?
b. Find the total number of seats for the B747-400, the F-100, and the B737-400
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Notes by Bibiana Lopez