Download File - Mrs. Long`s 7th Grade Pre

Operations with
Integers
PowerPoint
Created By:
Mrs. Long
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Pre-Test:
-5 + 4 = ____
5+ (-4) =____
-14 + (-12) = ____
7- (-3) = ____
-4 –(-1) = ____
Answers:
1. -1
2. 1
3. -26
4. 10
5. -3
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What is an Integer?
• A whole number that is either greater
than 0 (positive) or less than 0 (negative)
• Can be visualized on a number line:
What is a Number Line?
•A line with arrows on both ends that
shows the integers with slash marks
•Arrows show the line goes to infinity in
both directions ( + and -)
•Uses a negative sign (-) with negative
numbers but no positive sign (+)
with positive numbers
•Zero is the origin and is neither
negative nor positive
What are Opposites?
•Two integers the same distance from the
origin, but on different sides of zero
•Every positive integer has a negative
integer an equal distance from the origin
•Example: The opposite of 6 is -6
•Example: The opposite of -2 is 2
What is Absolute Value?
•Distance a number is from zero on a number
line (always a positive number)
•Indicated by two vertical lines | |
•Every number has an absolute value
•Opposites have the same absolute values
since they are the same distance from zero
•Example: |-8| = 8 and |8| = 8
•Example: |50| = 50 and |-50| = 50
What Can We Do to Integers?
•Integers are numbers, so we can add,
subtract, multiply, and divide them
•Each operation has different rules to follow
Adding Rules – Same Signs
•If the integers have the SAME signs:
ADD the numbers & keep the same sign!
•Positive + Positive = Positive Answer
•Negative + Negative = Negative Answer
• Examples: -3 + (-10) = ?
•
6 + (8) = ?
? = -13
? = 14
Adding (Same Signs) - Examples
#1. -3 + (-10)
Step 1:
13
Step 2:
-13
Add the #s
Keep same sign (Both #s are
negative – Answer is negative!)
#2. 6 + (8)
Step 1:
14
Step 2:
14
Add the #s
Keep same sign (Both #s are
positive – Answer is positive!)
Adding Rules – Different Signs
•If the integers have the DIFFERENT signs:
SUBTRACT the numbers & use sign of the
BIGGER number!
•Bigger # is Positive = Positive Answer
•Bigger # is Negative = Negative Answer
• Examples: -13 + (7) = ?
•
23 + (-8) = ?
? = -6
? = 15
Adding (Different Signs) - Examples
#1. -13 + (7)
Step 1:
6
Step 2:
-6
Subtract the #s
Use sign of bigger # (Bigger # is
negative - Answer is negative!)
#2. 23 + (-8)
Step 1:
15
Step 2:
15
Subtract the #s
Use sign of bigger # (Bigger # is
positive - Answer is positive!)
Integer Song
(Sing to the tune of row,
row, row your boat)
Same sign add and keep,
Different signs
Subtract.
Keep the sign of the
higher number, then it’ll
be exact.
Subtracting Rules
•Put (
) around second number & its sign
•Change SUBTRACTION sign to an
ADDITION sign
•Change sign of 2nd number to its opposite
•Follow the rules for ADDITION:
-SAME signs: Add & keep the same sign
-DIFFERENT signs: Subtract & use sign of bigger #
• Examples: -5 – -10 = ?
•
9 - 23 = ?
?=5
? = -14
Subtracting - Examples
#1. -5 – -10
#2. 9 - 23
Step 1:
-5 – (-10)
Step 2:
-5 + (-10)
Change – to +
9 + (23)
Step 3:
-5 + (10)
Change 2nd sign
9 + (-23)
Step 4:
5
Insert ( )
Follow adding rules
Keep-Change-Change
9 – (23)
-14
d
Subtracting Integer Song
Sing to the tune of row,
row, row, your boat.
Change the minus to a
plus,
Change the sign of the
next,
Then all you do is add
them up,
Like you did in the past!
1. A whole number that is greater than zero is called _________.
2. A whole number that is less than zero is called ____________.
3. Arrows on a number line show that the line goes to
___________ in both directions.
4. True or False: Zero is a positive number.
5. True or False: Negative numbers have a negative sign (-) and
Positive numbers have a positive sign (+) on a number line.
6. True or False: 5 and -5 are opposites. Explain your answer.
7. ________________ is the distance a number is from zero on a
number line (always a positive number).
8. What does this symbol represent? | |
9. True or False: Every number has an absolute value.
10._________________ have the same absolute values since they
are the same distance from zero.
Adding Rules: (same signs)
11. Positive + Positive = _________________ Answer
12. Negative + Negative = __________________ Answer
Adding Rules: (different signs)
13. If the integers have the DIFFERENT signs: _____________ the
numbers & use sign of the ____________ number!
14. If the Bigger # is Positive = _______________ Answer
15. If the Bigger # is Negative = _________________ Answer
Subtracting Rules:
16. Change SUBTRACTION sign to an _______________ sign
Change sign of 2nd number to its ______________.
17. Subtracting Rule: What three words are the steps for
subtracting integers?
________________-__________________-_____________
Multiplying Rules
• Multiply the numbers like usual
•If the integers have the SAME signs:
ANSWER will be POSITIVE
•If the integers have DIFFERENT signs:
ANSWER will be NEGATIVE
• Examples: -3 · (-5) = ?
? = 15
-9 · (-10) = ?
? = 90
•
-7 · 7 = ?
? = -49
•
6 · -6 = ?
? = -36
•
Multiplying - Examples
• #1. -3 · (-5)
•
15
•
15
#2. -9 · (-10)
90
Multiply the numbers
Same signs = Positive Answer
#3. -7 · 7
#4.
90
6 · -6
49
Multiply the numbers
36
-49
Different signs = Negative Answer
-36
Dividing Rules
• Divide the numbers like usual
•If the integers have the SAME signs:
ANSWER will be POSITIVE
•If the integers have DIFFERENT signs:
ANSWER will be NEGATIVE
• Examples: -33 ÷ (-3) = ?
? = 11
-90 ÷ (-10) = ?
?=9
•
-20 ÷ 2 = ?
? = -10
•
6 ÷ -6 = ?
•
? = -1
Dividing - Examples
• #1. -33 ÷ (-3)
•
11
•
11
#2. -90 ÷ (-10)
Same signs = Positive Answer
#3. -20 ÷ 2
10
-10
9
Divide the numbers
#4.
Divide the numbers
Different signs = Negative Answer
9
6 ÷ -6
1
-1
Mixed Practice
Solve the following problems:
-9 + - 9
7 · -4
-10 - (-19)
-18
-28
9
-35 ÷ -7
15 + -25
5
-10
-23 - 9
-32
Review
• What are the rules for the following
operations?