4.2+Studying+Multiplication+Patterns+0910

MM April 26th 2010 Block 7E Problem 4.2: Big Idea: Multiplying and Dividing Integers Essential questions: How do I multiply and divide integers? Notes: If you multiply two negative integers you will always get a positive product. If you multiply a positive and negative integer the product will be negative. 5 X 5: 25 5 X 4: 20 5 X 3: 15 5 X 2: 10 5 X 1: 5 5 X 0: 0 A. Describe any patterns you see as the integers divided by 5 get smaller: Whenever the integer that five is multiplying by goes down one, the product goes down by 5. B1. Use patterns you observed to predict 5 X -1. Explain your reasoning: 5 X -1 = -5. I know this because as I said before, every time the integer that five is multiplying goes down one, the product goes down by five. So five times zero is zero. What’s one less than zero? Negative one. So what’s five less than zero? Negative five. B2. Write the next four equations in the pattern: 5 X -2 = -10 5 X -3 = -15 5 X -4 = -20 5 X -5 = -25 C. Complete the equations below, and use your answers to help you solve part D and E: 5 X -4 = -204 X -4 = -163 X -4 = -122 X -4 = -81 X -4 = -40 X -4 = 0 D. Describe any patterns in the way the products change when the integers multiplied by -4 get smaller: As the integers multiplied by -4 get smaller the products actually increase by 4 each time or decrease by -4 each time. E. Use the patterns you observed to predict -4 X -1. Explain your reasoning: -4 X -1 = 4. I know this because if you multiply two negative integers, the product will be positive. I also know because every time the value of the integer multiplied by -4 goes down one, the product goes up four. So if zero times negative four is zero. Then -1 (one less than zero) times negative four is positive four. (0 + 4 = 4) F. Find the following products: -3 X 7 = -21. 5 X -8 = -40. -11 X 12 = - 132 -3.6 X 2.7 = -9.7

Follow Up: 1ab: Find -6 X 7 and 7 X -6:The answer to both of them is -42. Even if you switch the numbers around and your working with positive or negative integers the product will still be the same. 2ab: Find -6 + 7 and 7 + -6:The answer two both of them is positive one. Same for addition, if you switch the order of the numbers around and even if your dealing with negative and positive integers the product will still be the same. 3ab: Find -6 - 7 and 7 - -6:The answer to the first one is -13 and the answer to the second one is positive thirteen. When working with subtraction the order of the numbers do matter, same with division. 4. When you add two negative integers you get a negative result. Is the same true when you multiply two negative integers? Explain:No this is not true. When multiplying two negative integers you will always get a positive integer. If there are two negative integers the negative signs cancel each other out. So basically it’s like multiplying the absolute value of the two negative integers together.Ex. -9 X -9. The two negative signs cancel each other out, so it becomes: 9 X 9. Which is 81.