1. MTH 231 Section 5.3 Multiplication and Division of Integers

2. Multiplication of Integers We will use counters to model multiplication. In a manner similar to addition and subtraction of integers using the number line, we must first establish the rules for multiplying two integers m x n: 1.Start with a “zero field” 2.m indicates the number of groups: if m is positive, the groups are being put in; if m is negative, the groups are being taken out. Note that taking out will require putting in zero pairs first. 3.n indicates the composition of each group: if n is positive, use positive counters; if n is negative, use negative counters.

3. Examples 1 – 4 Example 1: 5 x 6 means put in 5 groups of 6 positive counters. Example 2: 5 x -6 means put in 5 groups of 6 negative counters. Example 3: -5 x 6 means take out 5 groups of 6 positive counters (you must first put in 30 zero pairs). Example 4: -5 x -6 means take out 5 groups of 6 negative counters (again, you must first put in 30 zero pairs).

4. The Rules Positive x positive = positive Positive x negative = negative Negative x positive = negative Negative x negative = positive

5. Division of Integers Use the “missing factor” model along with the rules for multiplying integers.

6. The Rules Positive divided by positive = positive Positive divided by negative = negative Negative divided by positive = negative Negative divided by negative = positive

7. The Rules, Restated Same Signs = Positive Different Signs = Negative