Bellwork Write an algebraic expression for each verbal expression. A. The sum of a number x and twenty-one B. The difference of twice a number x and 8. C. Five times a number x D. The quotient of a number x and 15

Operations with Integers

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 is a Number Line? A line with arrows on both ends that show 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) = ? ? = -13 6 + (8) = ? ? = 14

Adding (Same Signs) - Examples #1. -3 + (-10) Step 1: 13 Add the #s Step 2: -13 Keep same sign (Both #s are negative – Answer is negative!) #2. 6 + (8) Step 1: 14 Add the #s Step 2: 14 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) = ? ? = -6 23 + (-8) = ? ? = 15

Adding (Different Signs) - Examples #1. -13 + (7) Step 1: 6 Subtract the #s Step 2: -6 Use sign of bigger # (Bigger # is negative - Answer is negative!) #2. 23 + (-8) Step 1: 15 Subtract the #s Step 2: 15 Use sign of bigger # (Bigger # is positive - Answer is positive!)

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 = ? ? = 5 9 - 23 = ? ? = -14

Subtracting - Examples #1. -5 – -10 #2. 9 - 23 Step 1: -5 – (-10) Insert ( ) 9 – (23) Step 2: -5 + (-10) Change – to + 9 + (23) Step 3: -5 + (10) Change 2nd sign 9 + (-23) Step 4: 5 Follow adding rules -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 Examples: -3 · (-5) = ? ? = 15 -9 · (-10) = ? ? = 90 -7 · 7 = ? ? = -49 6 · -6 = ? ? = -36

Multiplying - Examples #1. -3 · (-5) #2. -9 · (-10) 15 Multiply the numbers 90 15 Same signs = Positive Answer 90 #3. -7 · 7 #4. 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) #2. -90 ÷ (-10) #1. -33 ÷ (-3) #2. -90 ÷ (-10) 11 Divide the numbers 9 11 Same signs = Positive Answer 9 #3. -20 ÷ 2 #4. 6 ÷ -6 10 Divide the numbers 1 -10 Different signs = Negative Answer -1

Solve the following problems: Mixed Practice Solve the following problems: -9 + - 9 7 · -4 -10 - (-19) -35 ÷ -7 15 + -25 -23 - 9

Review Visit the website below for additional information on integers: http://www.math.com/school/subject1/ lessons/S1U1L10GL.html