1. Integer Operations Students will solve problems using addition, subtraction, multiplication, and division of positive and negative integers.

2. Number Line A number line can be used to show addition. -10 -5 0 5 10 ( - 4 ) + 8 Start at negative 4 on the number line. Move to the right 8 spaces. 1 2 3 4 5 6 7 8 The answer is… 4

3. Number Line (cont.) A number line can be used to show subtraction. -10 -5 0 5 10 ( 6 ) – 8 Start at positive 6 on the number line. Move to the left 8 spaces. 1 23 4 5 6 7 8 The answer is… - 2

4. Addition When adding positive and negative numbers, first look at the sign and determine if the signs are the same or different. ( -3 ) + ( -5 ) Are these the same sign or different signs? “THE SAME” ( -3 ) + ( -5 ) *** Since the signs are the same, add the numbers and keep the same sign. - ( 3 + 5 ) - 8 Example: Both signs are negative.

5. Addition Addition (cont.) ( -8 ) + ( 12 ) Are the signs the same or different? “DIFFERENT” subtract *** If the signs are different, subtract the 2 numbers and take the sign of the “biggest”. ( -8 ) + ( 12 ) Which number is bigger? 12 What sign is the 12? “POSITIVE” + ( 12 – 8 ) 4 Since our answer is positive we can leave off the sign. Example:

6. Addition Addition (cont.) ( 7 ) + ( -11 ) Are the signs the same or different? “DIFFERENT” subtract If the signs are different, subtract the 2 numbers and take the sign of the “biggest”. ( 7 ) + ( -11 ) Which number is bigger? 11 What sign is the 11? “NEGATIVE” - ( 11 – 7 ) - 4 Since our answer is negative we MUST write the sign. Example:

7. Addition (cont.) When the numbers have different signs, but are “the same”, what happens? Example: ( -5 ) + ( 5 ) Since the signs are different, subtract the numbers. 5 – 5 0 Since neither number is bigger, the answer gets neither sign. When you add two opposite numbers, they always equal ZERO.

8. Addition Summary Same sign – add and keep the same sign. Different signs – subtract and take the sign of the “biggest”.

9. Addition Guided Practice 1. ( - 8 ) + ( - 2 ) -10 2. ( - 9 ) + ( 2 ) -7 3. ( - 4 ) + ( 8 ) 4 4. ( - 9 ) + ( 9 ) 0 5. ( 7 ) + ( - 3 ) 4 6. ( 4 ) + ( - 8 ) - 4

10. Subtraction When you have a subtraction problem, re-write it as an addition problem and change the sign of the number AFTER the subtraction. Example: ( -4 ) – ( -8 ) Change it to addition. ( -4 ) +… ( -4 ) + ( 8 ) Change the sign of the 8. + ( 8 – 4 ) Since the signs are different, subtract and take the sign of the “biggest”. 4 After re-writing the problem, follow the rules for addition.

11. Subtraction (cont.) Example: ( - 8 ) – ( 7 ) Re-write the problem. ( - 8 ) + ( - 7 ) REMEMBER: When you change it to addition, change the sign of the number after the subtraction sign. Since the signs are the same, add and keep the same sign. - ( 8 + 7 ) - 15

12. Subtraction Summary Change subtraction to addition and change the sign of the number after the subtraction. Follow rules for addition.

13. Subtraction Guided Practice 1. ( - 9 ) – ( 9 ) Re-write ( - 9 ) + ( - 9 ) - 18 2. ( 14 ) – ( - 3 ) ( 14 ) + ( 3 ) 17 3. ( - 7 ) – ( - 7 ) ( - 7 ) + ( 7 ) 0 4. ( 4 ) – ( 9 ) ( 4 ) + ( - 9 ) -5

14. Multiplication & Division The rules are the same for multiplication & division. If the signs are the same, the answer is positive. ( - 5 ) ( - 2 ) NOTE: The dot means multiply. Multiply the numbers and make it positive. 10 Since the answer is positive, we can leave off the sign. Example: ( - 15 ) ÷ ( - 3 ) Divide the numbers and make it positive. 5

15. Multiplication & Division (cont.) If the signs are different, the answer is negative. Example: ( - 4 ) ( 3 ) NOTE: Parenthesis next to parenthesis means multiply. Multiply the numbers and make it negative. - 12 Example: ( - 18 ) ( 3 ) NOTE: The fraction bar means divide. Divide the numbers and make it negative. - 6

16. Multiplication & Division Summary Same sign – the answer is POSITIVE. Different signs – the answer is NEGATIVE.

17. Multiply & Divide Guided Practice 1. ( - 64 ) ÷ ( 8 ) - 8 2. ( - 10 ) ( 2 ) - 20 3.( - 20 ) ( - 2 ) 10 4. ( 7 ) ( - 4 ) -28 5. ( - 3 ) ( - 3 ) 9 6. - 9 9 - 1

18. Summary: Addition Same sign – add and keep the same sign. Different signs – subtract and take the sign of the “biggest”. Subtraction Change subtraction to addition and change the sign of the number after the subtraction. Follow rules for addition. Multiplication and Division Same sign – the answer is POSITIVE. Different signs – the answer is NEGATIVE.