# AP Computer Science Java: Lesson 1.5a Math Operations - Basic Math

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.

 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

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.