Dividing two integers can be modeled by separating objects into new groups. In the example below, algebra tiles are used to represent the division of integers.
Find –6 ÷ 2. The expression
–6 ÷ 2 means to separate six negative tiles into 2 groups.
Therefore, –6 ÷ 2 = –3. Is a negative integer
divided by a positive integer always negative? Recall that division is related
to multiplication.
What if a negative integer is divided by a negative integer?
Study the pairs of related sentences in the table below. Look
for a pattern in the signs.
The pattern suggests the following rule for dividing
integers.
Example
Find each quotient.
1. –10
: 2
Alternative Solutions :
The
signs are different.
The
quotient is negative.
–10 :
2 = –5
2. –32
: (–8)
Alternative Solutions :
The
signs are the same.
The
quotient is positive.
–32 : (–8) =
4
Recall that fractions are another way of showing division.
Example
3. Evaluate 
if x = – 4 and y = 8
Alternative Solutions :
Example
Media Link
4. The
table shows the number of CDs and cassettes that were shipped in 1990 and 2000.
What was the average change in the number of cassettes that were shipped for
each of those ten years?
Alternative Solutions :
First,
find the change in the number of cassettes that were shipped.
76 – 442 = –366 There
were 366 million fewer cassettes
shipped
in 2000 than in 1990.
To
find the average change, divide –366 by 10.
–366 :
10 = –36.6
The average
change in the number of cassettes that were shipped was –36.6 per year. This
means that each year there were about 36,600,000 fewer cassettes shipped than
the year before.
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