Arithmetic Expressions

Learning Goals

• Trace Resolution of Variables to Scalar Values to Return Value
• Recognize + as the symbol for addition
• Demonstrate the addition operator
• Recognize - as the symbol for subtraction
• Demonstrate the subtraction operator
• Recognize * as the symbol for multiplication
• Demonstrate the multiplication operator
• Recognize / as the symbol for division
• Demonstrate the division operator
• Identify how division in Python differs from normal division

Introduction

When we first introduced expressions, we presented a series of operators and their corresponding operations that were familiar from basic arithmetic:

Operator	Operation	Note
+	Addition
-	Subtraction
*	Multiplication	We use * instead of × because it looks like x-the-letter
/	Division	We use / instead of ÷ because that's not on a keyboard
**	Exponentiation	We use ** instead of ^ because that means something else in programming languages
()	Association	Expressions inside of () get evaluated earlier

When we learned about these operators and their part in expressions, we didn't know how to use the variable assignment and variable lookup expressions yet. We knew how operators worked with constant expressions: 5 + 1. How do these expressions work with variables?

Trace Resolution of Variables to Scalar Values to Return Value

In this section we're going to trace this expression of "variables" until we get a return value. Consider:

x = 5
y = 1
x + y #=> ???

Our mission is to calculate the value of adding x and y.

We know how to handle the first two lines: these are simple uses of the assignment expression which assigns two scalar values, Integer values to the variables x and y:

x = 5
y = 1

Let's consider what happens in the last expression, step-by-step

x + y #=> ???

Expression	Action
x + y	Variable lookup: x, resolves to 5
5 + y	Variable lookup: y, resolves to 1
5 + 1	Two constant, scalar, Integers; apply + operation
6	Addition produces 6, no operators to apply, constant expression

Similar logic follows for all of the basic arithmetic operators. While our examples will use simple expressions with operators and values you should try setting the numbers to variables and enjoy experimenting in your conversation with Python.

Recognize + as the Symbol for Addition

Addition's symbol should look familiar. The symbol that is used to perform this operation is (+).

Demonstrate the Addition Operator

To get a feel for performing addition operations in Python, let's experiment. Open up the Python interpreter by opening your terminal; type the Python interpreter and hit enter and type the commands below:

10 + 1 #=> 11

5 + -1 #=> 4

Recognize - as the Symbol for Subtraction

Like addition, the symbol for subtraction (-) is also the same as in common arithmetic.

Demonstrate the Subtraction Operator

Let's experiment again. Open the Python interpreter and type these commands below:

4 - 13 #=> -9

And don't forget that losing negative things is a positive!

11 - -11 #=> 22

Recognize * as the Symbol For Multiplication

The symbol for the multiplication is (*) so that we don't confuse it with the letter x.

Demonstrate the Multiplication Operator

Use the Python interpreter and try typing the following the multiplication commands:

10 * 10 #=> 100

11 * -11 #=> -121

If everything was typed correctly, your results should be 100 and -121. Nothing out of the ordinary, right?

Recognize / as the Symbol For Division

The symbol for the division (/) is a forward slash. There's no handy ÷ character on most keyboards, so programmers adopted /.

Demonstrate the Division Operator

Open up the Python interpreter and try typing the following the division commands:

20 / 2 #=> 10.0

8 / 3 #=> 2.6666666666666665

4.0 / 13  #=> 0.3076923076923077

Notice that we're using Integers for division here, but we will always get back a Float.

Conclusion

Wow that was amazing! We took three lessons to learn three expressions, but in this lesson we added 4 more! We can now use the Python interpreter as a calculator — many programmers keep the Python interpreter open when doing some mathematics...or when splitting the bill for a lunch order.

Amazingly, our ability to "converse" with Python is on or about 2nd grade in the US education system (7 years of age). We went from conversational "babies" to basic school-children in 2 lessons! We're about to take another multi-year leap by learning to be formal about logic: something that most humans don't get skilled at until around 5th grade according to most psychologists (or 25 years of age, according to most parents).