1. ADDING, SUBTRACTING, MULTIPLYING AND DIVIDING INTEGERS By : Katie Kurth and Kateylnn Everhart

2. WHAT IS AN INTEGER?  Any whole number and 0  Can be positive or negative  A complete unit  Negative integer : Any integer that is less than 0  Positive integer : Any integer greater than 0

3. ADDING INTEGERS

4. WORDS TO REMEMBER  Inverse property of addition: The sum of a number and its opposite is 0.  Example: a + (-a) = 0 -a + a = 0

5. ADDING INTEGERS Step 1: start at 0 and move 3 over to the right Step 2 : begin at 3 and move 1 over to the right Step 3: write the sum. 3+1=4 since the number landed on was 4 after adding 1 to 3

6. ADDING INTEGERS  Practice Problems  4+3  3+2  6+1

7. ADDING INTEGERS SUMMARY  When a number is positive, move that many units to the right of zero or your starting point.

8. SUBTRACTING INTEGERS

9. WORDS TO REMEMBER  Opposites : Two numbers that are the same distance from 0 on a number line, but on opposite sides of 0  Subtraction Rule: To subtract an integer, add its opposite  5 – 8 = 5 + (-8) = -3  2 – (-3) = 2 + 3 = 5

10. SUBTRACTING INGETERS Step 1: move 6 units to the right from 0 Step 2: move 2 units away from 6 to the left Step 3: Use the subtraction rule of adding the opposite to check your answer

11. SUBTRACTING INTEGERS  Practice Problems  3-1  4-2  7-3

12. SUBTRACTING INTEGERS SUMMARY  To subtract an integer, add its opposite.

13. MULTIPLYING INTEGERS

14.  Multiplication is the same as repeated addition  4 x 2 = 2 +2 + 2 + 2 = 8  5(-6) = -6 + (-6) + (-6) + (-6) + (-6) = -30

15. MULTIPLYING INTEGERS  Find the product by rewriting it as repeated addition  3 x 15 = 15 + 15 +15 =45  5(-2) = -2 + (-2) + (-2) + (-2) + (-2)  3 x 1 = 1 + 1 + 1

16. MULTIPLYING INTEGERS  Practice problems  3 x 4  -7 x 2  -4 x (-5)

17. MULTIPLYING INTEGERS  Things to remember !  The product of a positive integer and a negative integer is negative  4 x (-4) = -16  The product of two negative integers is positive.  -3 x (-3) = 9

18. MULTIPLYING INTEGERS SUMMARY  The product of two negative integers is positive.  The product of a positive integer and a negative integer is negative

19. DIVIDING INTEGERS

20. WORDS TO REMEMBER  Quotient: The result of dividing two integers  Related problem: You can rewrite a division problem as the related multiplication problem.  Rules - The rules for multiplication of integers also hold true for division. The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.

21. DIVIDING INTEGERS  Solve 15 / 3  Step 1: Think? “What number times 3 gives you 15”  Step 2: Solve using mental math  Answer: 5 times 3 gives you 15

22. DIVIDING INTEGERS  Practice problems  4/2  8/4  9/3

23. DIVIDING INTEGERS SUMMARY  The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.  One method for finding the quotient of two integers is to begin by rewriting the division problem as a multiplication problem.