# Lab 3: Experiment 3

## Arithmetic Expressions

C++ provides several arithmetic operators:

 `+` addition, computes the sum of two (integer or real) operands `-` subtraction, computes the difference of two (integer or real) operands `*` multiplication, computes the product of two (integer or real) operands `/` division, computes the quotient of the division of two (integer or real) operands `%` modulus, computes the remainder of the division of two integer operands

Question #3.3.1: The current version of our program outputs the sum of `i` and `j`. Modify it (or add more output statements) to output their difference and product. What changes did you make? Test your changes to make sure they are correct.

These arithmetic operators should be familiar to you, except for the last one. Let's spend some time looking at it and the corresponding division operator.

## Integer and Real Division

There is an important difference between the division of two integers and two real numbers. You will now explore these differences now by making some changes to our programs.

Make sure that your program still has an input statement to get values for `i` and `j` and that it is between the declarations and the output statement(s). With this input statement you can compile the program once but execute it many times for different values for `i` and `j`.

Now modify your output statement(s) or add a new one so that it will compute `i/j` and `i%j`. Be sure to change the string labels so that you can read your output easily.

Once you have these changes made, compile and execute the program to make sure it's correct.

Then, using this code as a basis, add similar lines of code for `double` variables `x` and `y`. For these real-number variables, you shouldn't compute `x%y` because `%` is only defined for integers..

Question #3.3.2: Use your program to fill in the following table with the values exactly as produced by your program:
` ` `i` `j` `i / j` `i % j` `x` `y` `x / y`
a. 4 1     4.0 1.0
b. 4 2     4.0 2.0
c. 4 3     4.0 3.0
d. 4 4     4.0 4.0
e. 4 5     4.0 5.0
f. 4 6     4.0 6.0
g. 5 4     5.0 4.0
h. 6 4     6.0 4.0
i. 7 4     7.0 4.0

Integers are whole numbers without any fractional part. So when you divide the integer 9 by the integer 10 (i.e, `9/10`), you will get 0, not 0.9. But with real numbers, you can compute fractional amounts. So `9.0/10.0` is `0.9` as a real number.

## Splitting Apart Integers

Now, more about the modulus operation. "Modulus " is basically just another name for "remainder". When you first learned about division, you probably learned to talk about your result in terms of quotient and remainder:

"28 divided by 3 is 9 with a remainder of 1."

Division and modulus by 10 allow us to split up integers into their decimal digits.

Question #3.3.3: Use your program to fill in the following table with the values exactly as produced by your program:
` ` `i` `j` `i / j` `i % j`
a. 1234 1
b. 1234 10
c. 1234 100
d. 1234 1000

Can you see a pattern? How significant is the number of 0s in `j`?

Question #3.3.4: Use your observations from the preceding question to fill in the following table:
` ` `i` `j` `i / j` `i % j`
a. 5678 1
b. 5678 10
c. 5678 100
d. 5678 1000

## Multiples

The multiples of 2 are 0, 2, 4, 6, 8, 10, 12, ... The multiples of 3 are 0, 3, 6, 9, 12, ...

What do the multiples of 2 have in common? Two evenly divides each multiple of two; that is, two divides each multiple without any remainder. So if `m % 2` is 0, then `m` must be a multiple of two.

Using this same thinking, use `%` to develop the tests in the following questions.

Question #3.3.5: Write a boolean expression that can be used to check if an integer`number` is a multiple of 3.

Question #3.3.6: Write a boolean expression that can be used to check if an integer `number` is a multiple of 4.

The multiples of 2 are also known as the even numbers.

Question #3.3.7: Write a boolean expression that can be used to check if an integer `number` is an even number.

The odd numbers are all the integers that aren't even.

Question #3.3.8: Write a boolean expression that can be used to check if an integer `number` is an odd number.

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