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COMBINING INTEGERS:Adding & Subtracting Negative & Positive
Whole Numbers
by S. Bradley
Definition
•Positive number – a number greater than zero.
0 1 2 3 4 5 6
Definition
•Negative number – a number less than zero.
0-1-2-3-4-5-6
Definition• Opposite Numbers – numbers
that are the same distance from zero in the opposite direction on a number line.
0 1 2 3 4 5 6-1-2-3-4-5-6
Definition
•Integers – Integers are all the whole numbers and their opposites.
7 opposite -7
Negative Numbers Are Used to Measure Temperature
Negative Numbers Are Used to Measure Below Sea Level
0102030
-10-20-30-40-50
Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5,000 to show they still owe the bank.
Positive & Negative Numbers
Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the driving rules.
Hint•If you don’t see a negative or positive sign in front of a number it is positive.
9 = 9+
Integer Addition Rules•Rule #1 – If the signs are the
same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.
9 + 5 = 14(-9) + (-5) = -14
Solve the Problems
•(-3) + (-5) = a•4 + 7 = b•(-6) + (-7) = c •5 + 9 = d•(-9) + (-9) = f
Solutions:
• a = -8• b = 11• c = -13• d = 14 • f = -18
Monday’s Problems:
•13 + 3 = a
•(-12) + (-5) = b
•(-2) + (-3) = c
Solutions to Monday’s Problems:
•16
•-17
•-5
Integer Addition Rules•Rule #2 – If the signs are
different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the larger one in front of your answer.
-9 + 5 =9 - 5 = 4Larger number
Answer = - 4
Solve These Problems
•3 + (-5) =•7 + (-4) =•3 + (-4) =•(-6) + 7 = •-9 + 5 =•(-9) + 9 =
-25 – 3 = 2
0
-41-1
3
9 – 9 = 0
9 – 5 = 47 – 6 = 14 – 3 = 1
7 – 4 = 3
How do I remember the addition rules? Simple! Let’s apply the rules to a song we all know – “Row, Row, Row Your Boat”
•Same sign – add & keep!•Different signs – subtract,
take the sign of the highest number, your answer will be exact!
Practice:
•(-4) + 5 = x
•(-13) + 3 = y
•-18 + 5 = z
Solutions to Practice:
•1
•-10
•-13
Tuesday’s Problems:
•-5 + (-2) = k
•10 + (-4) = j
•-23 + 7 = n
Solutions to Tuesday’s Problems:
•-7
•6
•-16
One way to add integers is using a number line…
0 1 2 3 4 5 6-1-2-3-4-5-6
When the number is positive, countto the right.
When the number is negative, countto the left.
+-
Here’s an example:
0 1 2 3 4 5 6-1-2-3-4-5-6+
-
3 + (-5) = -2
Using Integer Addition Rules or a Number Line – You choose!
•-150 + (-5) = g
•43 + (-20) = f
•24 + (-30) = v
Solutions to Practice:
•-155
•23
•-6
Wednesday’s Problem:
• The Georgia Bulldogs were playing the Auburn Tigers in a playoff game. Auburn’s offense received a penalty which resulted in a loss of 10 yards. If they were at the 25 yard line, what yard line would they be moved to after the penalty? (Write an equation, then solve.)
Wednesday’s Solution:
•-10 + 25 = h
•h = 15 yard line
Subtracting Integers
• Use the additive inverse. This simply means to change the problem to addition & follow the addition rules. How? Leave the first number “as is”; change subtraction to addition; lastly, change the SECOND number to its opposite…
Example:
• -18 – 5 = n*-18 remains “as is”*subtraction becomes +*change +5 to -5-18 + (-5) = n *Now, simply
follow the addition rules…n = -23
Example Problems for Subtraction:• -17 – 11 = d
-17 + (-11) = -28
• 25 – 32 = u25 + (-32) = -7
• 13 – (-5) = r13 + 5 = 18
You try it!
• 10 – (-6) = h
• -19 – 7 = w
• 9 – 11 = k
Solutions to Practice
• 10 – (-6) = h10 + 6 = 16
• -19 – 7 = w-19 + (-7) = -26
• 9 – 11 = k9 + (-11) = -2
Thursday’s Problems:
• 16 – (-5) = t
• -3 – 8 = p
• -14 – (-10) = q
Thursday’s Solutions:
• 16 – (-5) = t16 + 5 = 21
• -3 – 8 = p-3 + (-8) = -11
• -14 – (-10) = q-14 + 10 = -4
Practice for Friday:(Pay attention to the operation given…)
•-4 + 5 = a•-17 – 8 = b•-13 – (-7) = c•-12 + (-8) = d
Solutions for Friday’s Practice:
•a = 1•b = -25•c = -6•d = -20
Monday’s Problems:
• -11 + (-6) = m
• -16 – (-57) = c
• 8 + (-5) = h
Monday’s Solutions:
• m = -17
• c = 41
• h = 3
Tuesday’s Problem:
• A submarine is 33 feet below sea level. It rises 15 feet. What integer best represents the submarine’s location after its rise? (Write an equation, then solve.)
Tuesday’s Solution:
•-33 + 15 = ff = -18 feet
Wednesday’s Problem:
• You went to the bank and borrowed $200. One week later, you went back to the same bank and borrowed $250 more. How much are you in debt? (Write an equation, then solve.)
Wednesday’s Solution:
•-200 – 250 = d-200 + (-250) = d
d = -$450
Thursday’s Problems:
• -3 + (-19) = k
• 15 – (-7) = j
• 17 + (-10) = a
• -8 – 12 = f
Thursday’s Solutions:
• k = -22
• j = 22
• a = 7
• f = -20
GOOD LUCK ON FRIDAY’S ASSESSMENT!