Math 6 High (Period 3)

Dividing Integers 4.6

According to your textbook, a useful way to divide integer  is to think of it as a multiplication problem. that is, when you consider   -15  ÷ 3  =?  rethink it as  3 · ? = -15.  

You know that  (3)(-5) = -15  so you can conclude that -15  ÷ 3  = -5   

Use similar reasoning for other division problems!

More generally, when dividing two integers, divide their absolute values and then use the same rules applied to multiplying integers:

Specifically:

The quotient of two positive integers is positive

The quotient of two negative integers is positive

The quotient of two integers with different signs is negative

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

Note: an expression with 0 in the divisor  such as 4 ÷ 0 is undefined. You cannot divide  a number by 0.

Evaluating an expression such as   -18/x 

a) when x = -3

1.  First substitute in using parentheses for the number     -18/(-3)

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

3.  The solution is +6.

b) when x = 3

1. First substitute in using parentheses for the number   -18/(3)

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

3. The solution is -6.

Finding an Average With Integers

To find the average,   always add the numbers first.

The example in the book uses the following measurements (in feet) taken from the bottom of Lake Michigan and find the average lake bottom’s elevation to its surface….

-844,  -865, - 900,  -893,  -888

so to add do the following

-844 + (-865) + (-900) +(-893) + (-888)

Now, I recommend stacking them to add carefully.  

Remembering the rule for adding integers—when adding integers with the SAME sign, just add them and USE THEIR sign… so we know the total must still be negative since they are ALL negative… and we get – 4390

Now, there are 5 numbers so we divide by +5   

            -4390/5

We see that we have a negative divided by a positive.  

We know our quotient will be negative

-4390/5 = -878

So  the average of the lake’s bottom elevation is -878 feet or you could state it is 878 feet BELOW the lake surface.