Math 6 High (Period 3)

Multiplying Integers 4.5 

As we discovered any number multiplied by -1  is equal to its opposite.

-1 ∙ a = -a

We use this Multiplicative Property of -1  to develop general rules for multiplying integers.

 Specifically:

The product of two positive integers is positive

The product of two negative integers is positive

The product of two integers with different signs is negative

The product  of 0 and a non-zero integer is 0.

Examples

Multiplying Integers with the same sign:

(4)(7) = 28

(-11)(-4) = +44

Multiplying Integers with different  signs:

(5)(-5) = -25

(-8)(9) = -72

Evaluating an expression such as:

a)   x y     when x = -15 and y = -6

1.  First substitute in using parentheses for the numbers     (-15)(-6)

2.  Then DO THE MATH  remembering that the product of two negative numbers is positive. 

3.  The solution is +90.

b) ( -a)(b) when a = -4 and b = -8 

(Be careful with these types—they can be tricky)

1. First substitute in using parentheses for the number   -(-4)(-8)

2. Now look at –(-4) first  that really says to take the opposite of -4 and we know that the opposite of -4 is 4 so we really have (4)(-8)

3. Then DO THE MATH remembering that the product of two integers with different signs is always negative.   

4. The solution is -32.

Multiplying Three or MORE  Integers

The following is our textbooks instructions:

• To multiply three or more integers work from left to right, multiplying two numbers at a time.
•   Find the product of the first two numbers, the multiply that product by the next number to the right
•      Continue until all numbers have been multiplied to find the final product.

EXAMPLES:

(2)(-3)(4)  = (-6)(4) = -24

(-4)(5)(0) = (-20(0) = 0 

My Note:  But why even do the multiplication? Any number  multiplied by 0 is 0 so you know right away the solution is ZERO!!!

(-1)(-2)(-3)(-4) = (2)(-3)(-4) = (-6)(-4) = 24

We discussed in class to be a sign counter—If the number of negative signs (in your non-zero multiplication problem) is EVEN then your solution will be POSITIVE. If the number is ODD, then your solution will be NEGATIVE.  The sign of the product depends on the number of factors (assuming all are non-zero) that are negative.

The product of two integers with the same sign is POSITIVE

    The product of two integers with different signs is NEGATIVE