Game Development Reference
In-Depth Information
Multiplication and Division
When you combine positive and negative numbers through division, results vary
according to the signs of the numbers. There are two general ways to view the
results of multiplication and division operations involving numbers with dif-
ferent signs. First, consider multiplication and division problems involving only
two numbers. Then consider multiplication and division problems involving
more than two numbers.
Multiplication and Division with Two Numbers
When you carry out multiplication and division operations that involve two
numbers, you deal with a few basic possibilities:
n
Both numbers are positive. If both numbers are positive, then the result of
the multiplication or division is positive. Here are a few examples:
2
2
1
2
¼
2
4
¼
1
2
,
2
5
¼
10
5
¼
2
2
2
¼
4,
2
2
¼
1,
5
n
Both numbers are negative. If the two numbers are negative, then the result
is positive. Here are a few examples:
4
2
¼
2,
4
3
3
4
¼
1,
ð
4
Þð
4
Þ¼
16,
4
2
4
16
4
¼
4
2
¼
In the last example, when you multiply the numerators,
4and
4, you
arrive at a positive value of 16. Along the same lines, multiplying the deno-
minators,
2and
2, results in a positive number. Alternatively, you can first
carry out the divisions. In both cases,
4
2, the quotient is positive 2.
n
One number is negative and the other is positive. If you multiply a
negative number by a positive number, then the result is negative.
4
2
¼
2,
4
3
3
4
¼
1,
ð
4
Þð
4
Þ¼
16,
3
3
4
4
¼
12
12
1
