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Doing math

Problem

The bill at the table

You ordered three coffees at €2.50 and two croissants at €1.50. You pay with a €20 bill. How much is the bill, and how much change should you get?

You can do it in your head. But the register at the café does this math hundreds of times a day, with different prices and quantities. The program has to do the math by itself.

The idea

The arithmetic operators

You do math the way you would on paper: + adds, - subtracts, * multiplies, / divides. These signs are called operators.

double coffee = 2.5;
double croissant = 1.5;
double total = 3 * coffee + 2 * croissant;
double change = 20 - total;
System.out.println("Total: €" + total);
System.out.println("Change: €" + change);
Output
Total: €10.5
Change: €9.5

The order is the same as in math: first * and /, then + and -. That is why 3 * coffee + 2 * croissant is 7.5 + 3. If you want a different order, you add parentheses: (2 + 3) * 4 is 20.

There is a fifth operator too, %. The next idea is about it.

More precisely, if you are curious
  • Operators with the same precedence are evaluated left to right: 20 - 5 - 3 is 12, not 18.
  • - in front of a number makes it negative: -total.
  • With text, + does not add, it glues. Once there is text on the left, everything after it is glued on as text. That is the trap in the next card.

Try it

Concert tickets

Three tickets at €8 and a €5 order fee.

What will the program print?

int tickets = 3;
int fee = 5;
System.out.println("Total: " + tickets * 8 + fee);
Answer

Problem

An average grade of 5, not 5.67

You have grades 5, 6 and 6. The average is 17 / 3 = 5.67. The program says something else:

int math = 5;
int physics = 6;
int english = 6;
double average = (math + physics + english) / 3;
System.out.println("Average grade: " + average);
Output
Average grade: 5.0

You store the result in a double, and the decimal part is still missing. Where did it go?

The idea

Whole divided by whole gives whole

When both sides of / are int, the division is integer division: the result is a whole number, and the decimal part is cut off. 17 / 3 is 5. Only after that is the 5 stored in the double, where it becomes 5.0.

Here is the average grade from the last card, step by step:

int math = 5;
int physics = 6;
int english = 6;
double average = (math + physics + english) / 3;
System.out.println("Average grade: " + average);
Step by step, in words
  1. Three grades, each in an int: 5, 6, 6.
  2. First the parentheses: 5 + 6 + 6 = 17. The sum is an int too.
  3. 17 / 3: both sides are int. How many whole groups of 3 are in 17? 5.
  4. The remainder 2 (that is 17 % 3) is cut off. The result is the whole number 5.
  5. Only now is 5 stored in double average, where it becomes 5.0.
  6. It prints "Average grade: 5.0". 5.67 does not show up anywhere.

What is cut off is not completely lost. The % operator gives the remainder of the division: 17 % 3 is 2, because 17 = 5 · 3 + 2.

Together the two split an amount into whole parts and a remainder. The movie is 135 minutes:

int minutes = 135;
int hours = minutes / 60;
int rest = minutes % 60;
System.out.println(hours + " h " + rest + " min");
Output
2 h 15 min

You will need % often. A number is even if n % 2 is 0. The last digit of a number is n % 10.

More precisely, if you are curious
  • With negative numbers the result is cut off toward zero, and the remainder has the sign of the dividend. % also works with decimal numbers:
System.out.println(-7 / 2);
System.out.println(-7 % 2);
System.out.println(7.5 % 2);
Output
-3
-1
1.5
  • A whole number divided by 0 stops the program with an error: ArithmeticException: / by zero. With double there is no error: 5.0 / 0 gives infinity, and 0.0 / 0 gives NaN ("not a number").

Try it

Bottles in cases

A case holds 6 bottles. You have 17.

What will the program print?

int bottles = 17;
int perCase = 6;
System.out.println(bottles / perCase + " cases");
System.out.println(bottles % perCase + " left over");
Answer

The idea

Converting between types

For the division to give a decimal result, at least one side has to be a double. If you have an int, you convert it: you write the type in parentheses in front of the value. This is called a cast.

int sum = 5 + 6 + 6;
double average = (double) sum / 3;
System.out.println(average);
System.out.printf("%.2f%n", average);
int whole = (int) 9.99;
System.out.println(whole);
Output
5.666666666666667
5.67
9

(double) sum turns 17 into 17.0, and then the division gives a decimal result. If the number is written in the code, it is enough to make it a decimal: sum / 3.0.

The other way, from double to int, cuts off the decimal part: (int) 9.99 is 9, not 10. That is why the compiler does not do it by itself: if you write int whole = 9.99;, the program does not compile. From int to double nothing is lost, and the conversion happens by itself: double price = 10; is 10.0.

More precisely, if you are curious
  • A cast goes from a number to a number. You already turn text into a number with Integer.parseInt: that is something else.
  • A character (char) is actually stored as a number, its code. That is why it converts to int and back:
System.out.println((int) 'A');
System.out.println((char) 66);
int max = 2147483647;
System.out.println(max + 1);
Output
65
B
-2147483648
  • The third line is a surprise: int goes up to 2,147,483,647. One more does not give an error. It "wraps around" to the smallest negative number. For bigger numbers there is long.

Try it

Find the bug

The electricity bill is €125, split between three roommates. The program says each person pays €41.00, but it should be €41.67. Which line is the bug on?

Pick the line with the bug.

The idea

Shorthand: += and ++

You often change a value based on itself: the card balance goes down with every purchase, a counter goes up by one. There is a short way to write this:

double balance = 20;
int purchases = 0;
balance -= 4.5;
purchases++;
balance -= 3.5;
purchases++;
System.out.println(purchases + " purchases, €" + balance + " left");
Output
2 purchases, €12.0 left
You write It means
balance -= 4.5; balance = balance - 4.5;
total += price; total = total + price;
x *= 2;, x /= 2;, x %= 2; the same with *, / and %
purchases++; purchases = purchases + 1;
seats--; seats = seats - 1;

+= works with text too: message += "!"; glues an exclamation mark onto the end.

More precisely, if you are curious

++ can also go in front of the variable. On its own line there is no difference. Inside an expression there is: a++ gives the old value and then increases it, ++a increases it first and gives the new value.

int a = 5;
int b = a++;
int c = ++a;
System.out.println(a + " " + b + " " + c);
Output
7 5 7

Code like this is hard to read. Write ++ and -- on their own line.

The idea

Math: roots, powers, rounding

A pizza place sells a 30 cm pizza for the same price as two 20 cm pizzas. Which is more? The area of a circle is π · r². For the power and for π there is something ready in Math: you write the name and the numbers in parentheses. These are methods, ready-made pieces of code. You will write your own in the "Methods" module.

double big = Math.PI * Math.pow(15, 2);
double small = 2 * Math.PI * Math.pow(10, 2);
System.out.printf("One 30 cm pizza: %.1f sq cm%n", big);
System.out.printf("Two 20 cm pizzas: %.1f sq cm%n", small);
System.out.println(Math.sqrt(144));
System.out.println(Math.abs(-7.5));
Output
One 30 cm pizza: 706.9 sq cm
Two 20 cm pizzas: 628.3 sq cm
12.0
7.5

One big pizza is more than two small ones.

You write What it gives
Math.sqrt(x) the square root
Math.pow(x, n) x to the power n
Math.abs(x) the absolute value (without the sign)
Math.round(x) rounding to a whole number
Math.PI the number π, 3.14159…

The square root and the power return a double, even when the result is a whole number (that is why you see 12.0). If you need an int, convert it: (int) Math.sqrt(144).

More precisely, if you are curious
  • Rounding 2.5: Java and C# give different results.
System.out.println(Math.round(2.5));
System.out.println(Math.round(3.5));
System.out.println(Math.round(5.678 * 100) / 100.0);
Output
3
4
5.68
  • Math.round rounds "the half" up and returns a long, not an int. For two digits after the decimal point you multiply by 100, round and divide by 100.0. If it is only for printing, printf("%.2f") is easier.
  • printf follows the computer's language settings. On a computer with Bulgarian settings you will see 706,9, not 706.9.

Exercise

Let the program do the math

Solve the tasks in your editor. Each number in the input is on a separate line.

1. Average of three numbers. Read three whole numbers and print their average with two digits after the decimal point. Watch out for the division.

Input
5
6
6
Output
Average: 5.67

2. Seconds into hours. Read a number of seconds and split it into hours, minutes and seconds. Hint: an hour has 3600 seconds, and % gives what is left.

Input
3725
Output
1 h 2 min 5 s

3. Volume of a sphere. Read the radius and print the volume: V = 4/3 · π · r³. Think about what 4 / 3 is before you write it like that.

Input
10
Output
Volume: 4188.79 cubic cm

4. Celsius to Fahrenheit. F = C · 9 / 5 + 32. Read the temperature in degrees Celsius.

Input
37
Output
37.0 °C = 98.6 °F

More tasks

  • Inches to centimeters. One inch is 2.54 cm. For 12 inches: 30.48 cm.
  • Area of a rectangle. Read the length and the width, and print the area (length · width).
  • Area of a square. Read the side and print the area. Do it once with * and once with Math.pow.
  • Radians to degrees. Degrees = radians · 180 / π. For 3.14159: 180.00°.
  • Hours to seconds. Read a number of hours and print how many seconds that is. For 2 hours: 7200.
  • A character's code. Read a character and print its code. For A: 65. You get the first character of the text you read with in.nextLine().charAt(0). You will see what this means in the lesson on text.

Test

Check yourself

1. What is 17 / 5 if both numbers are int?
2. What is 17 % 5?
3. Which expression gives 2.5?
4. What does (int) 9.99 give?
5. What does System.out.println("Sum: " + 2 + 3) print?

Made by Ivo Gergov as part of Evo Tech's campaign for accessible programming education ·