Lesson 1.5a - Basic
Math
Purpose: To learn how to write
statements involving basic arithmetic
Java Math Mathematics plays a large role in computer programming. Practically everything
boils down to math in some way. So Java has to have a way of performing
math operations. We will begin with basic arithmetic: addition,
subtraction, multiplication and division.
Java's Arithmetic
Symbols
operation |
symbol |
example of use |
addition |
+ |
a = b + c; |
subtraction |
- |
a = b - c; |
multiplication |
* |
a = b * c; |
division |
/ |
a = b / c; |
Order of
Operations Java has the same order of operations as in
Algebra. Remember PEMDAS?
Parentheses
Exponents
Multiplication and Division together
Addition and Subtraction together
Modulus The modulus operator is another arithmetic operation that you will find quite useful.
Modulus, or mod for short, gives the integer remainder of
division. The symbol for modulus is %, but it has nothing to do with
percents. Here are some examples of results of modulus calculations:
13 % 5 = 3
26 % 10 = 6
20 % 4 = 0
5 % 7 = 5
Note that modulus is an integer operator. It
does not work with decimal values. So you would never write a calculation
like 5.8 % 3.1. Modulus works
only with integer operands and its result is always an integer.
Application of
Modulus OK, mod gives the remainder of integer
division. So what? Well, it turns out that mod will be useful in a variety
of situations. One of these situations is breaking a measured value into
different units. For example, suppose we want to break total seconds down
into hours, minutes and seconds. Recall that there are 60 seconds in a
minute and 60 minutes in an hour. That means there are 3600 (60 * 60)
seconds in an hour. So here is how modulus would break 10,000 total
seconds into hours, minutes and seconds.
int totalSeconds = 10000;
int hours = totalSeconds / 3600; // the result is 2
int minutes = totalSeconds % 3600 / 60; // the result is 46
int seconds = totalSeconds % 3600 % 60; // the result is 40
So 10,000 seconds = 2 hours, 46 minutes and 40 seconds
Note the pattern of using / then % from each
equation to the next. This pattern will also be used in your programming
problems involving modulus (#'s 6-8). Secondly, recall that when dividing
integers, the result will be an integer. That is why the calculation for
hours and minutes works correctly here.
In Closing Remember to work with
only integers when using modulus. It doesn't work with
decimal values. Lastly, modulus falls in with multiplication and division in the order of operations.