Mathematical+Reflections,+p+66

 ** Big Idea ** Negative numbers help us to model many real world situations. ** Essential Question #4 ** How do I multiply and divide integers?
 * T.C.**
 * 28 April 2009**


 * Mathematical Reflection: p.66**


 * Write a strategy for multiplying two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following products:**

a. -13 x 7: -13 x 7 = -91 A strategy for solving this is that you always know that a negative times a positive equals a negative. So then you can a simple multiplication problem like 13 x 7 and then add the (-), because it will always be negative.

A strategy for solving this problem would be that you always know that a positive times a negative equals a negative. So then you can a simple multiplication problem like 11 x 20 and then add the (-), because it will always be negative.
 * b. 11 x –20: **11 x –20 = -220

A strategy is that if you times something by zero its always going to be zero. Because 12 times 0 is just twelve zeros, so 0,0,0,0,0,0,0,0,0,0,0,0 and all those added together equal… 0!
 * c. –12 x 0: **-12 x 0 = 0

d**. –18 x –22:** -18 x –22 = 396 A strategy for this is it will always be positive because the 2 negatives cancel each other out so you are left with a simple multiplication problem, which you can then solve.


 * Write a strategy for dividing two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following quotients:**

A strategy is that because a positive divided by a negative is always a negative, so you then just do a simple division problem.
 * a. 126 / -9:** 126 / -9 = -14

A strategy for this is that a negative divided by a negative is always a positive because the two negatives cancel each other out so then you can just do a simple division problem.
 * b. –36 / -12**: -36 / -12 = 3

A strategy for this is that a negative divided by a positive is always going to be a negative so then you can forget about the (-) or (+) signs and do a simple division problem and then just add a (-) sign.
 * c. –2592 / 32:** -2592 / 32 = -81

A strategy for this would be that if you ever have zero divided by something it will always be 0. Because 0 divided by 8 is 0 because you can’t divide 0 it will always be zero.
 * d. 0 / 8:** 0 / 8 = 0

There are different strategies for different multiplication problems and division problems but once you know what the out come has to be then you can just do a simple (x) or (/) problem and add a (-) or (+) on if needed.
 * Summary:**

(-) x (-) = (+) (+) x (-) = (-) (+) x (+) = (+) (-) x (+) = (-)


 * and the same for (/) except not a (x) and a (/) instead.


 * the symbol / is instead of a divide symbol.