1. Arithmetic Expressions
Chapter 2
Arithmetic Expressions
2/19 & 2/23
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 1 1

2. Chapter Topics Arithmetic Operators Standard Mathematical Methods
The Order of Operations
The Division Operator /
The Remainder Operator %
The Data Type of an Arithmetic Expression
Standard Mathematical Methods
Casting
A Problem Solved: Wind Chill
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 2 2

3. Objectives After studying this chapter, you should be able to:
Write Java arithmetic expressions representing algebraic expressions
Identify type of an arithmetic expression
Write a type cast, identify when it is necessary
Use class Math to evaluate mathematical functions such as square root, power
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 3 3

4. Arithmetic Operations and the Math Class4 4

5. Addition and Subtraction Operators
As binary operators
As used in algebraic expressions
int y = ;
As unary operators
Equivalent to binary operation with 0 as first operand
int sum = +5; // sum is +5
int negSum = -sum //negSum is -5
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 5 5

6. Multiplication Operator *
Always used as a binary operator
When consecutive operations occur
Multiplied from left to right in order of appearance
When real numbers are being multiplied the order of operations can be significant
No implied multiplication: 3(x + y)
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 6 6

7. The Division Operator /
Always a binary operator
Type of result (the quotient) depends on types of operands
When both are integers, result is the integer portion of the quotient
When either or both are doubles, the result is double
To force a decimal answer, divide by a double
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 7 7

8. The Remainder Operator %
Results in the remainder after a division
Note it is not the decimal portion of a division expression
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 8 8

9. Order of Operations
Operators in an arithmetic expression execute in the following order:
Operators within parentheses
The unary operators + and -
The operators *, /, and %
The binary operators + and –
Operators at the same level execute from left to right
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 9 9

10. What is the Value of? 9.2 + -2.5 * 2.0 1 + 5 % 2 4 + 2 / 5 + 1
( ) / 4.0
( ) / 4 10 10

11. Participation What is the Value of?
4.2 / / 2.0
11 % % 2
/ 5 + 6
(6 + 16) / (5 + 6)
(9 + 6) / 5.0 11 11

12. Lab Participation(Skip)
E = mc2 is a formula to find energy, E, in newtons, that is derived from mass, m,in grams. C is the speed of light.
Write a program in input the mass then find E. Make the speed of light a named constant. You can use 300,000,000 m/s for the speed of light. 12 12

13. Programming Example
The formula for finding the nth term in an arithmetic sequence is:
xn = a + d(n-1)
Where a is the first term, d is the difference. Write a program to input a, d and n the find the nth term of the series. 13 13

14. Look at Exam Review
On my website. 14

15. Standard Mathematical Methods
Java provides a collection of methods to do mathematical tasks
Math is the name of the class
Call to methods is Math.method_name( … )
Examples
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 15 15

16. Standard Mathematical Methods
Args and return type are double:
Math.sqrt(x) -- square root of x
Math.pow(x,y) – x to the y power
Math.log(x) – ln x
Math.log10(x) – log10x
Math.exp(x) – ex
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17. Standard Mathematical Methods
These return same type as argument:
Math.abs(x) -- |x|
Math.max(x,y) – maximum of x & y
Math.min(x,y) – minimum of x & y
Math.round(x) – Returns the nearest whole number to x.
If x is double it returns a long.
If x is float it returns an int
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 17 17

18. Standard Mathematical Methods
Figure 3-2 Call to method Math.sqrt
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 18 18

19. Example-Quarterback Ages
Write a program to ask for the ages of two quarterbacks. Output the difference their ages as a positive number.
Input qbAge1 qbAge2
diff = | qbAge1 –qbAge2 |
Output diff 19 19

20. Write a program to find the 4th root of a number input by the user.20 20

21. Participation What is wrong with the following?
a.) y = (1/2) * Math.sqrt(x);
b.) y = sqrt(38.0);
c.) y = Math.exp(2,3);
d.) y = math.sqrt( b*b – 4*a*c)/ (2*a)

22. Participation Example
(Skip/Already Did)
Write a program to find the 4th root of a number input by the user.
fourthRoot.c

23. Problem (Skip/Already Did)
Write a program to find the length of side C of a right triangle, given the lengths of sides A and B.
Write the program. It is started for you on the next slide. 23 23

24. 24 24

25. Casting 25 25

26. Conversion between Numeric Types
Conversion in expressions may happen implicitly or be required explicitly
Consider
Variable is a double
Literal is an int
The int is coerced implicitly, converted to a double
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27. Conversion between Numeric Types
However, this does not work in the opposite direction
In expressions
If all values are of same type, result is of that type
If one of the values is a floating-point, the result is floating-point
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28. Casting Conversion can be forced with type casting What was illegal
Can be made legal by preceding the desired type in parentheses
This is considered a unary operator
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 28 28

29. Program Example
Write a program that asks for the number of cars in a neighborhood and the number of households. It should output the average number of cars per household.
Let's write an algorithm first.
Can use casting to get an accurate double answer. 29 29

30. Solved Problem: Wind-Chill
(Skip)
Consider the formula for wind chill where
T = current temp in deg F
V = velocity of wind in mph
c1 = 35.74, c2 = , c3 = 35.75, c4 =
Imagine! Java: Programming Concepts in Context by Frank M. Carrano, (c) Pearson Education - Prentice Hall, 2010 30 30

31. Solved Problem: Wind-Chill
(Skip)
View listing of wind chill calculation program
Listing 3-1 and output.(p of text)
Note the sections of the program
Describe the program
Get input data
Compute wind-chill
Display results
Also notice the comments in the program.
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32. Questions What does the % operator do in Java?
What is a unary operator?
What is wrong with this statement? How could it be made legal?
int i = 1.5;
How can I find x2.5 in Java? 32 32

33. Using mobaxterm to Transfer Your Program to onyx
Make a directory on onyx to put you program in
mkdir myProg4
Open the directory in the left area of mobaxterm
Drag the file from the PC’s folder to myProg4 mobaxterm 33 33