1. Copyright © Ed2Net Learning, Inc.1 Integers Grade 6

2. Copyright © Ed2Net Learning, Inc. 2 Comparing and Ordering Integers Integers are all of the positive whole numbers, their opposites and zero  Example:..-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,… Integers consist of positive numbers, negative numbers and zero (which is neither positive nor negative)

3. Copyright © Ed2Net Learning, Inc. 3 Comparing and Ordering Integers Two numbers that are the same distance from zero on the number line are called opposites  Example: -6 and 6 The absolute value of a number is its distance from zero on the number line. Absolute value is always positive!  18 = 18  -32 = 32

4. Copyright © Ed2Net Learning, Inc. 4 Comparing and Ordering Integers -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -4 is smaller than -1 If we compare two numbers on a number line, the number that is furthest to the left is the smaller number!

5. Copyright © Ed2Net Learning, Inc. 5 Try these! 1. What is the opposite of -8? 8 2. Is -8 an integer? Yes 3. 19 = 19 4. Which number is larger… -15 or -11? -11 5. -76 = 76

6. Copyright © Ed2Net Learning, Inc. 6 Adding Integers There are 3 methods to Add Integers Method 1: We can add integers using Zero Pairs. -+ These two chips equal zero. These 2 chips form a Zero Pair.

7. Copyright © Ed2Net Learning, Inc. 7 Adding Integers Example: Add (-5) + 3 - + - --- ++ 1) We begin with 5 red chips 2) We add 3 yellow chips 3) We circle the Zero Pairs and remove them! 4) We are left with 2 red chips. Therefore; (-5) + 3 = -2

8. Copyright © Ed2Net Learning, Inc. 8 Adding Integers Method 2: Using a Number Line  Example: (-6) + 8 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 1.Start at 0 and move to the left (in a negative direction) 6 spaces. 2.Then move 8 spaces to the right in the positive direction. 3.The answer is 2. (-6) + 8 = 2

9. Copyright © Ed2Net Learning, Inc. 9 Adding Integers Method 3: Adding with Absolute Values  Same Sign: Add the absolute values and use the common sign. Example:  13 + 18 = 31  -8 + (-6) = -14  Different Signs: Subtract the lesser absolute value from the greater absolute value and use the sign of the integer with the greater absolute value. Example:  17 + (-9) = 8  -15 + 8 = -7

10. Copyright © Ed2Net Learning, Inc. 10 Adding Integers  Opposites: The sum of an integer and its opposite is 0. Example:  -6 + 6 = 0  -15 + 15 = 0

11. Copyright © Ed2Net Learning, Inc. 11 1) Use the number line to solve -5 + 8 = 3 0 -2 -3-4 -5 12 34 5 2)Use zero pairs to solve 4 + -3 = 1 3)Use the Addition Rules to solve (-16) + (-5) = -21 (Sum of two negative integers is negative) Try Some! + - +++ ---

12. Copyright © Ed2Net Learning, Inc. 12 Subtracting Integers There are 2 methods to Subtract Integers Method 1: We can subtract integers using Zero Pairs. -+ These two chips equal zero. These 2 chips form a Zero Pair.

13. Copyright © Ed2Net Learning, Inc. 13 Subtracting Integers Sometimes we need to add zero pairs in order to subtract or take away chips.  Example: 3 – (-1) = + - ++ 1) We begin with 3 positive yellow chips 2) We add 1 Zero Pair 3) Now we can take 1 negative red chip. 4) We are left with 4 positive yellow chips. Therefore; 3 – (-1) = 4 +

14. Copyright © Ed2Net Learning, Inc. 14 Subtracting Integers Method 2: When we subtract an integer we add its opposite and follow the rules for adding integers.  Example: Find (-10) – 7 We add the opposite of 7: -7 (-10) – 7 = (-10) + (-7) = (-17)

15. Copyright © Ed2Net Learning, Inc. 15 Try Some! 1. (-8) - 12 = (-20) 2. 22 - (-6) = 28 3. 13 - 20 = (-7) 4. -9 - (-10) = 1

16. Copyright © Ed2Net Learning, Inc. 16 Multiplying Integers Method 1: Use of Zero Pairs  Example: 2 x (-3) -- - --- 1)Place 2 sets of 3 negative chips. 2)So, 2 x (-3) = -6

17. Copyright © Ed2Net Learning, Inc. 17 Multiplying Integers Method 1: Use of Zero Pairs  Example: -2 x (-4) - 1)Since -2 is the opposite of 2, -2 x (-4) means to remove 2 sets of 4 negative chips. 2)Since there are no negative chips, place 8 Zero Pairs. 3)Now you can remove 2 sets of 4 negative counters. 4)So, -2 x (-4) = 8 + -+ -+ -+ -+ -+ -+ -+

18. Copyright © Ed2Net Learning, Inc. 18 Multiplying Integers Method 2: There are 3 rules for multiplying integers: Same sign: The product of two integers with the same sign is positive.  Example: 6 x 7 = 42 (-5) x (-4) = 20 Different signs: The product of two integers with different signs is negative.  Example: 8 x (-4) = -32 (-9) x 3 = -27 Zero: The product of an integer and 0 is 0.  Example: 9 x 0 = 0 (-16) x 0 = 0

19. Copyright © Ed2Net Learning, Inc. 19 Multiplying 3 or more Integers Example: (-4) x 5 x (-2) (-4) x 5 x (-2) = +40 (-20) x (-2) +40 We begin by multiplying two at a time and inserting appropriate sign.

20. Copyright © Ed2Net Learning, Inc. 20 Multiplying Multi-digit Integers Example: 583 x (-47) 583 x 47 4081 2332_ -27,401 5 2 3 1 Larger number of digits goes on top Multiply from right to left Multiply first then add the appropriate sign. Also, remember to add comma.

21. Copyright © Ed2Net Learning, Inc. 21 Try Some! 1. (-12) x 3 = (-36) 2. (-6) x (-11) = 66 3. 4 x (-9) x 2 = (-72) 4. (-45) x 57 = (-2565)

22. Copyright © Ed2Net Learning, Inc. 22 Dividing Integers Method 1: Use of Zero Pairs  Example: -8 ÷ 4 -- - --- - - 1)Place 8 negative red chips. 2)Division means to divide into groups; so we need to divide the 8 chips into 4 groups. 3)So, -8 ÷ 4 = -2 Think: 4 times what number equals -8?

23. Copyright © Ed2Net Learning, Inc. 23 Dividing Integers Method 2: The rules are similar to the rules for multiplying Same Sign: The quotient of two integers with the same sign is positive.  Example: 24 ÷ 6 = 4 (-12) ÷ (-3) = 4 Different sign: The quotient of two integers with different signs is negative.  Example: 32 ÷ (-8) = -4 (-27) ÷ 3 = -9 Zero: The quotient of 0 and any nonzero integer is 0.  Example: 0 ÷ 7 = 0 0 ÷ (-5) = 0

24. Copyright © Ed2Net Learning, Inc. 24 Dividing Integers Example: (-195) ÷ 13 (-195) ÷ 13 = -15 Divide first and then add the appropriate sign to the answer.

25. Copyright © Ed2Net Learning, Inc. 25 Try Some! 1. (-45) ÷ (-9) = 5 2. 72 ÷ (-8) = (-9) 3. (-36) ÷ (-9) = 4 4. 732 ÷ (-12) = (-61)

26. Copyright © Ed2Net Learning, Inc. 26 Assessment 1. -73 = 73 2. Insert a) -32 __ -42 b) -21 __ -20 c) 0 __ 16 > > <

27. Copyright © Ed2Net Learning, Inc. 27 Assessment 3. 92 + (-102) = (-10) 4. (-85) + (-15) = (-100) 5. (-13) x 6 = (-78) 6. (-22) x -10 = (-220)

28. Copyright © Ed2Net Learning, Inc. 28 Assessment 7. (-96) ÷ (-6) = 16 8. 2,142÷ (-34) = (-63)

29. Copyright © Ed2Net Learning, Inc. 29 Assessment 9. Ben had borrowed $300 from each of his four friends last year. He now has $600 to return back. Find out the amount he can return to each of his friends and the amount of total loan still remaining. Total money borrowed 4 x $300 = $1200 He has $600 which he has to return to 4 friends so each friend gets $600 / 4 = $150 Money left to return to each $300 - $150 = $150 Total Loan still remaining $150 x 4= $600

30. Copyright © Ed2Net Learning, Inc. 30 Assessment 10. Sarah went for a drive with her father. On the onward journey they sped at an average speed of 60 miles per hour. After 5 hours they turned back and as it was uphill this time they drove at an average speed of 50 miles an hour. Find out the time it would take them to get home. Total distance travelled in onward Journey 60 x 5 =300 Miles. On return speed is 50 miles per hour and They need to travel 300 miles so time taken is 300 / 50 = 6hours

31. Copyright © Ed2Net Learning, Inc.31 Great Job today!