Adding IntegersAdding IntegersSection 2.2 and 2.3Section 2.2 and 2.3
#10 If two wrongs don't make a right, try three. ~Author
Unknown#11 Arithmetic is where
numbers fly like pigeons in and out of your head. ~Carl
Sandburg, "Arithmetic"
The ConceptThe Concept► Today’s subject is not new to you, but Today’s subject is not new to you, but
rather a revisiting of an important topic rather a revisiting of an important topic from years previousfrom years previous
► Understanding the adding positive and Understanding the adding positive and negative numbers (integers) is negative numbers (integers) is imperative to the process of solving basic imperative to the process of solving basic algebraic equationsalgebraic equations
The number lineThe number line► The basic premise of adding these numbers is that the first number is plotted on the The basic premise of adding these numbers is that the first number is plotted on the
number line and then the answer is developed by moving either right or leftnumber line and then the answer is developed by moving either right or left e.g. 4+5=9e.g. 4+5=9
e.g. -3+10=7e.g. -3+10=7
0 55
0 55
Solve the followingSolve the followingAddAdd
► 5+105+10► -4+1-4+1► -10+3-10+3► 3+-103+-10► (4+3)+-3(4+3)+-3► 4+(3+-3)4+(3+-3)► 3+03+0► 4+-44+-4
PropertiesProperties
► Commutative Commutative ► AssociativeAssociative
► a + b = b + aa + b = b + a► (ab)c = a(bc)(ab)c = a(bc)
PropertiesProperties
► Identity Identity
► This will This will always make always make something something equal to it’s equal to it’s selfself
► a · 1 = a & a + 0 = aa · 1 = a & a + 0 = a
PropertiesProperties
Inverse Inverse
This will make This will make something go something go to 1 or zeroto 1 or zero
► a + (-a) = 0 & a · = 1a + (-a) = 0 & a · = 11
a
PropertiesProperties
► Commutative Commutative ► AssociativeAssociative
► Identity Identity ► Inverse Inverse ►DistributiveDistributive
► a + b = b + aa + b = b + a► (ab)c = a(bc)(ab)c = a(bc)► a · 1 = a & a + 0 = aa · 1 = a & a + 0 = a► a + (-a) = 0 & a · = 1a + (-a) = 0 & a · = 1► a(b + c) = ab + aca(b + c) = ab + ac
1
a
Lastly
ExampleExample
►What property is illustrated here?What property is illustrated here?
5 ( 5) 0
ExampleExample
►What property is illustrated here?What property is illustrated here?
0 ( 2) 2
ExampleExample
►What property is illustrated here?What property is illustrated here?
3 (1 4) (3 1) 4
ExampleExample
►What property is illustrated here?What property is illustrated here?
( 5) 8 8 ( 5)
The number lineThe number line
► The basic premise of subtracting is the addition The basic premise of subtracting is the addition of the opposite numberof the opposite number e.g. 4-5=e.g. 4-5= 4+(-5)=-14+(-5)=-1
e.g. -3-9=e.g. -3-9= -3+(-9)=-12-3+(-9)=-12
0 55
0 55
Re write using the Cm. Re write using the Cm. property property
►X+YX+Y
►5-45-4
►-4-4-4-4
►9- -49- -4
Solve the followingSolve the followingsubtractsubtract
► 5-105-10► -4-1-4-1► -10--3-10--3► 3--103--10► (4-3)-3(4-3)-3► 4-(3--3)4-(3--3)► 3-03-0► 4--44--4
exampleexample
►2-(-4)2-(-4)
►2+(-5)2+(-5)
►-3-5-3-5
Evaluate the expressionEvaluate the expression
►X=-9 Y=4X=-9 Y=4
►X+4-YX+4-Y
►-x-y-x-y
►-y-x-5-y-x-5
Practical ExamplePractical Example► This past weekend you started with $20 in your This past weekend you started with $20 in your
pocket. Over the course of the three days you pocket. Over the course of the three days you did the following thingsdid the following things Went to the movies for $6.50Went to the movies for $6.50 Bought candy for $2.50Bought candy for $2.50 Found $2 in the parking lotFound $2 in the parking lot Went to the football game for $1Went to the football game for $1 Stopped at QT on the way home and bought Stopped at QT on the way home and bought
a pop and M&M’s for $3.25a pop and M&M’s for $3.25 Gave a homeless person $1 and all the coins Gave a homeless person $1 and all the coins
you had in your pocketyou had in your pocket Bought a cookie at a coffee shop for $1.43Bought a cookie at a coffee shop for $1.43
How much money do you have left?How much money do you have left?
Most Important PointsMost Important Points► Addition on the number lineAddition on the number line► Properties of additionProperties of addition
Homework you must do bothHomework you must do both
2.22.2
Pg. 75Pg. 75
3-17, 26-31, 38-41 3-17, 26-31, 38-41
2.32.3Pg. 83Pg. 833-10, 17-22, 32-34, 3-10, 17-22, 32-34, 42,4342,43
