4.2+Studying+Multiplication+Patterns

22/04/09 A.M

Big Idea: Multiplying and Dividing Integers

Essential Question: How do I multiply and divide integers?

Notes from Class: (no notes were taken)

Problem 4.2 Multiplying and Dividing Integers

5x5=25 5x4=20 5x3=15 5x2=10 5x1=5 5x0=0

A: Describe any patterns you observe in the way the products change, as the integers multiplied by 5 get smaller. As the integers multiplied by 5 get smaller the products also get smaller.

B1: Use the patterns you observed to predict 5x -1. Explain your reasoning. 5x -1= -5, I got this answer because firstly as the integers multiplied by 5 get smaller the products also become smaller and if 5x0=0 then 5x -1 should equal something less than 0, and -5 is less than 0. Moreover multiplying is like adding that number with its self several times, in this case 5 times. And -1+-1+-1+-1+-1= -5. B2: Write the next four equations in the pattern. 5x-2= -10, 5x-3= -15, 5x-4= -20, 5x-5= -25

C: Complete the equations below, and use them to help you answer parts D and E. 5x-4= -20 4x-4= -16 3x-4= -12 2x-4= -8 1x-4= -4 0x-4= 0 D: Describe any patterns you observe in the way the products change, as the integers multiplied by -4 get smaller. As the integers multiplied by -4 get smaller the products become larger.

E1: Use the patterns you observe to predict -1x -4. Explain your reasoning. -1x -4=4, this is because as the integers multiplied by negative 4 get smaller the product gets larger. If 0x -4= 0 than -1x -4 should equal something more than 0.

F: Find the following products.

1. -3x7= -21 2. 5x-8= - 40 3. -11x-12=132 4. -3.6x2.7= -9.72

Follow Up

1a: Find -6x7 and 7x-6 -6x7= -42, 7x-6= -42

b: When you multiply integers the order of the numbers doesn’t matter

2a: Find -6+7 and 7+-6 -6+7= -1 and 7+-6= 1 b: When adding the order of the numbers does matter.

3a: Find -6-7 and 7- (-6). -6-7= -13 and 7- (-6)= 13 b: When subtracting integers he order of the numbers does matter.

4: When you add two negative integers you get a negative result. Is the same true when you multiply two negative integers? Explain. This is not true when you multiply two negative integers. This is because when you multiply a negative integer the smaller the integer you multiply it with the larger your result gets. And whenever you multiply a negative integer by another negative integer you always get a positive product. Ex: -4x-1= 4, -5x-3= 15, and -8x-5= 40
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