MTH 231

Section 5.3Multiplication and Division of

Integers

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.

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).

The Rules

• Positive x positive = positive• Positive x negative = negative• Negative x positive = negative• Negative x negative = positive

Division of Integers

• Use the “missing factor” model along with the rules for multiplying integers.

20____4____420

20____4____420

20____4____420

20____4____420

The Rules

• Positive divided by positive = positive• Positive divided by negative = negative• Negative divided by positive = negative• Negative divided by negative = positive

The Rules, Restated

• Same Signs = Positive• Different Signs = Negative