Download 1.2 Adding and Subtracting Whole Numbers The Commutative

Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
The Commutative Property of Addition
If a and b represent whole numbers, then
ab  ba
Ex) Simplify the left side and then right side.
23  3 2
55
With addition, the order of numbers can be interchanged and will yield the same result.
Grouping Symbols ( ), [ ], { }
Grouping symbols (parentheses, brackets, braces, etc.) are used to group an expression.
Expressions inside grouping symbols should always be simplified first.
The Associative Property of Addition
If a, b, and c represent whole numbers, then
 a  b   c  a  b  c 
Ex) Simplify the left side and then right side.
 2  3  4  2   3  4 
5  4  2   7 
99
With addition, the grouping symbols can be moved and will yield the same result.
The Additive Identity Property
The whole number zero is called the additive identity.
If a is a whole number, then
a0  a
Adding zero to a number, does not change the identity of the number. It will remain
the same number.
Important Notes:
 There is no commutative property of subtraction. If you interchange the order
of the numbers in subtraction, you will get a different result.
 There is also no associate property of subtraction. If you move the grouping
symbols in a subtraction, you will get a different result.
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2015 Worrel
Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
How to Add Whole Numbers
1) Align the numbers on the right side, making sure to stack digits so that all the
ones digits are in one column, all the tens digits are in the next column, etc.
2) Begin with the ones column (the farthest right column).
3) Add the digits.
-If the sum is ten or higher, “carry” the tens digit into the next column to the left.
4) Move to the next column on the left and repeat step 3, until finished.
Adding zero to a number, does not change the identity of the number. It will remain the
Example 1:
Simplify.
same
number.1, 234  498
Solution:
1 1
1234
+ 498
1732
1, 234  498  1,732
Example 2: Simplify. 378 1,706  957
Solution:
2 1 2
378
1706
+ 957
3041
378  1,706  957  3,041
You Try It 1: Simplify. 1, 286  349
You Try It 2: Simplify. 256  2,347  283
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2015 Worrel
Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
How to Subtract Whole Numbers
1) Align the numbers on the right side, making sure to stack digits so that all the
ones digits are in one column, all the tens digits are in the next column, etc.
2) Begin with the ones column (the farthest right column).
3) Subtract the digits (top digit – bottom digit).
-If top digit is smaller than the bottom digit, borrow (see example below) from
the column to the left.
4) Move to the next column on the left and repeat step 3, until finished.
Example 3:Adding
Simplify.
 328 does not change the identity of the number. It will remain
zero1,755
to a number,
the same number.
Solution:
4
1 7 515
328
1,755  328  1, 427
1427
You Try It 3: Simplify. 5,635  288
Order of Operations
Perform all additions and subtractions in the order they are presented, moving from left
to right.
Example 4: Simplify the expression. 15  8  4
Solution: As we read from left to right, we run into 15  8 first, so,
15  8  4
74
Note: You will get a different/wrong answer if you attempt to do the addition first.
 11
You Try It 4: Simplify the expression. 25  10  8
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2015 Worrel
Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
Perimeter
The sum of the lengths of the sides of a figure is called the perimeter.
Example 5: Find the perimeter of the figure shown.
3 yards
3 yards
4 yards
5 yards
Solution: To find the perimeter, find the sum of the lengths of the sides.
Perimeter = 3  3  4  5  15
Note: Remember to include your units in your answer.
Hence, the perimeter of the figure is 15 yards.
You Try It 5: A figure has sides that measure 4 inches, 3 inches, 5 inches, and 5 inches. Find its perimeter.
Rectangle
A rectangle is a quadrilateral (four sided figure) where all of its angles are right angles
and the opposite sides of a rectangle are equal.
Example 6: Find the perimeter of the rectangle.
3 meters
5 meters
Solution: To find the perimeter, find the sum of the lengths of the sides.
Since the opposite sides of a rectangle have equal measure, then we know there are two sides with a
length of 3 meters and two sides with a length of 5 meters.
Perimeter = 3  3  5  5  16
Note: Remember to include your units in your answer.
Hence, the perimeter of the figure is 16 meters.
You Try It 6: A rectangle has length 12 meters and width 8 meters. Find its perimeter.
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2015 Worrel
Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
Square
A square is a quadrilateral (four sided figure) where all of its angles are right angles
and all sides of a square are equal.
Example 7: Find the perimeter of the square.
12 feet
Solution: To find the perimeter, find the sum of the lengths of the sides.
Since all sides of a rectangle have equal measure, then we know there are four sides with a
length of 12 feet.
Perimeter = 12 12 12 12  48
Note: Remember to include your units in your answer.
Hence, the perimeter of the figure is 48 feet.
You Try It 7: A square has a side that measures 18 centimeters. Find its perimeter.
Example 8: Apple made $39 billion in profits in 2013. If Apple made $42 billion in profits in 2012, how much
profit did Apple make in 2012 and 2013 combined?
Solution: $39 billion + $42 billion
1
+
39
42
81
Apple made $81 billion in 2012 and 2013 combined.
Note: Remember to include your units in your answer. You must put $ as well as the word “billions”.
You Try It 8: Juan received 267 thousand likes on his first Facebook post. He then received 670 thousand likes
on his second Facebook post. How many likes did Juan receive on his first two Facebook posts
combined?
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2015 Worrel
Math 40
Prealgebra
Section 1.2 – Adding and Subtracting Whole Numbers
Example 9: Matt had 325 thousand Twitter followers. He then posted an unfavorable photo and lost 187
thousand Twitter followers. How many Twitter followers does Matt now have?
Solution: 325 thousand – 187 thousand
2 11
3 2115
187
138
Matt now has 138 thousand Twitter followers.
Note: Remember to include your units in your answer.
You Try It 9: The space shuttle usually orbits at 250 miles above the surface of the earth. To service the
Hubble Space Telescope, the shuttle had to go to 350 miles above the surface. How much higher
did the shuttle have to orbit?
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