4.2+Studying+Multiplication+Patterns+0910

Ajwad Khan April 27, 10 Math 7B __Problem 4.2__ A. **Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.**
 * Big Idea: Negative numbers help us to model many real world situations. **
 * Essential Question: How do I multiply and divide integers. **

The products are decreasing by 5, as the multiplier is decreasing by 1.

B. **1. Use the patterns you observed to predict 5 x -1. Explain your reasoning.**

Since the product decreases by 5 each time, and -1 is just one unit below 0, I will subtract 5 from the previous product. The previous product was 0 so 0 – 5= -5. The answer is -5.

C. **Complete the equations below, and use them to help you answer parts D and E.**

5 x -4= -20 4 x -4= -16 3 x -4= -12 2 x -4= -8 1 x -4= -4 0 x -4= 0

D. **Describe any patterns you observe in the way the products change, as the integers multiplied by -4 get smaller.**

The products of the equations are increasing by 4 as the number being multiplied with -4 get smaller.

E. **1.** **Use the patterns you observed to predict -1 x -4. Explain your reasoning.**

Since the product increases by 4 each time, and -1 is just one unit below 0, I will add 4 to the previous product. The previous product was 0 so 0 + 4= 4. The answer is +4


 * 2. Write the next four equations in the pa****ttern.**

-2 x -4= 8 -3 x -4= 12 -4 x -4= 16 -5 x -4= 20 -6 x -4= 24 -7 x -4= 28

F. **Find the following products.**

1. -3 x 7= -21 2. 5 x -8= -40 3. -11 x -12= 132 4. -3.6 x 2.7= -9.72 __Problem 4.2 Follow-Up__ 1. **a. Find -6 x 7 and 7 x -6.** -6 x 7= -42 and 7 x -6= -42


 * b. When you multiply integers, does the order of the numbers matter?**

No, because whatever the order is, the product will always be the same.

2. **a**. **Find -6 + 7 and 7 + -6.** -6 + 7= 1 and 7 + -6= 1


 * b. When you add integers, does the order of the numbers matter?**

No, because whatever the order is, the sum will always be the same.

3. **a. Find -6 – 7 and 7 - -6.**
 * -**6 – 7= -13 and 7 - -6= 13


 * b. When you subtract integers, does the order of the numbers matter?**

Yes, the order does matter because switching the order will give you the opposite of the normal difference.

4. **When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.**

The same is not true because multiplying a negative integer with a negative integer will give a product that is positive.