Grade 9 Integer Review Review Day 1.

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Presentation transcript:

Grade 9 Integer Review Review Day 1

Can be visualized on a number line: 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

First Remove Double Signs!! Eg: (-3) + (-4)

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) - 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 = -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 = + #1. -33 ÷ (-3) - Negative divide negative = + = +11 #2. -90 ÷ (+10) - Negative divide a positive = (-) = -9

Solve the following problems: Mixed Practice Solve 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