2. Operations with Integers PowerPoint Created By: Mrs. Long

3. Pre-Test: 1. -5 + 4 = ____ 2. 5+ (-4) =____ 3. -14 + (-12) = ____ 4. 7- (-3) = ____ 5. -4 –(-1) = ____

4. Answers: 1. -1 2. 1 3. -26 4. 10 5. -3

5. 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:

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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!)

12. 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

13. 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!)

14. 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.

15. Subtracting Rules Put ( ) around second number & its sign Change SUBTRACTION sign to an ADDITION sign Change sign of 2 nd 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

16. 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 2 nd sign 9 + (-23) Step 4: 5 Follow adding rules -14 d Keep-Change-Change

17. 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!

21. 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.

22. 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 2 nd number to its ______________. 17. Subtracting Rule: What three words are the steps for subtracting integers? ________________-__________________-_____________

23. 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

24. 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

25. 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

26. Dividing - Examples #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

27. Mixed Practice Solve the following problems: -9 + - 9 -18 7 · -4 -28 -10 - (-19) 9 -35 ÷ -7 5 15 + -25 -10 -23 - 9 -32

28. Review What are the rules for the following operations?