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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 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
Adding (Same Signs) - Examples
#1. -3 + (-10)- Change the double sign + (-)
to a (-)- Same signs - add and keep
sign!= -13
#2. 6 + (8)- Same sign so add and keep
sign!= 14
Adding Rules – Different Signs• If the integers have DIFFERENT signs: SUBTRACT
the numbers & use sign of the BIGGER( further from zero) number!
•Bigger # is Positive = Positive Answer
•Bigger # is Negative = Negative Answer
Adding (Different Signs) - Examples #1. -13 + (7)
- Subtract the numbers- Keep the sign of the number
furthest from zero (bigger number)
= -6
#2. 23 + (-8)
- Subtract the numbers- Keep the sign of the number
furthest from zero (bigger number)
= +15
Subtracting Rules• Make sure to change any double signs
•Follow the rules for ADDITION:
-SAME signs: Add & keep the same sign -
DIFFERENT signs: Subtract & use sign of bigger #
Subtracting - Examples #1. -5 – -12
- Change double signs to a +- Subtract the two numbers and
keep the sign of the number further from zero (bigger number)
= +7
#2. 9 – 23- Subtract the two numbers and
keep the sign of the number further from zero (bigger number)
= -14
d
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
Multiplying - Examples• #1. -3 · (-5)
- negative times negative = +
= +15
#2. -9 · (+10)
- Negative times a positive = (-)
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
Dividing - Examples• #1. -33 ÷ (-3)
- Negative divide negative = +
= +11
#2. -90 ÷ (+10)
- Negative divide a positive = (-)
= -9
Mixed PracticeSolve the following problems:
-9 + - 9
-18
7 × -4
-28
-10 - (-19) 9
-35 ÷ -7
5
15 + -25
-10
-23 - 9-32
Review
• Visit the website below for additional information on integers:http://www.math.com/school/subject1/ lessons/S1U1L10GL.html
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