Section 1.7 Mathematical Expressions

In the last lesson, we assigned values to variables like score = 0, but the right side of an assignment statement can be more than just a simple value like 0. We can use expressions which combine numbers, variables, and operators to calculate a value and assign it to the variable in an assignment statement like below.

This looks like a mathematical formula, but in coding, an assignment statement always has a single variable on the left side and an expression on the right side. The expression is evaluated and then assigned to the variable.

If you use a variable to keep score, you would probably increment the score (add one to the current value) as the game progresses. You can do this by setting the variable to the current value of the variable plus one (score = score + 1) as shown below. The formula would look strange in math class, but it makes sense in coding because it is assigning a new value to the variable on the left that comes from evaluating the arithmetic expression on the right. So, the score variable is set to the previous value of score plus 1.

In Python, you do not need to indicate the data type of a variable, but variable that are assigned whole number values like score = 5 are automatically type int for integer.

Python uses the following basic arithmetic operators:

Python also has the following non-standard operators:

The modulo (mod) or remainder operator is very useful in coding. For example, it can be used to check if a number is even (divisible by 2) if it has no remainders when divided by 2. The expression 5 % 2 is equal to 1, because 5 divided by 2 is equal to 2 with a remainder of 1 (since 2 * 2 = 4).

If you have a smaller number divided by a larger number the remainder is always the smaller number.

When compound expressions are evaluated, operator precedence rules are used, just like when we do math, so that multiplication *, division /, and remainder % are done before addition + and subtraction -. However, anything in parentheses is done first. The PEMDAS acronym can help you remember the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (from left to right). It doesn’t hurt to put in extra parentheses if you are unsure as to what will be done first or just to make it more clear.

Compound assignment operators +=, -=, *=, /=, and %= are shortcuts that do a math operation and assignment in one step. For example, x += 1 adds 1 to the current value of x and assigns the result back to x. It is the same as x = x + 1. This pattern is possible with any operator put in front of the = sign.

When tracing through code with expressions, always remember to evaluate the right-hand side of the assignment first, then assign the result to the variable on the left-hand side. You can practice and check your answers by adding print statements to show the variables or click on the "Show CodeLens" button on any Active Code exercise to turn on the interactive tracing tool called CodeLens as seen below. This is a tool called Python Tutor that is built into Runestone.

a = 2
b = 10
a = b
a = a + 1
b = b * 3

When you use the input() command to get input from a user, the value is always treated as a string, even if the user types in a number. If you want to use that input in a mathematical expression, you need to convert it to a number first using the int() command for integers or float() command for decimal numbers. For example:

ageStr = input("How old are you? ")
age = int(ageStr)
# Now we can do math with the age variable since it is an int instead of a string
print("Next year you will be", age + 1, "years old.")

minutes = 150
---
hours = minutes // 60
---
hours = minutes / 60 #paired
---
remainingMinutes = minutes % 60
---
remainingMinutes = minutes / 60 #paired

Games would be boring if the same thing happened each time you played the game. Random numbers can be used in games to generate different actions or outcomes each time the game is played. Try a game app on your phone or computer and try to identify where random numbers are used. If you roll dice or flip a coin or if the enemies in the game do not always act the same way, then random numbers are likely being used.

In Python, there is a library called random that can be imported and used to generate random values. Use random.randint(start, end) to generate a random integer from start to end, including both endpoints. For example:

import random
# pick a random number from 0 to 10
r = random.randint(0, 10)

Try running the program below a few times to see that it generates different random numbers each time it runs.

Computers can’t usually generate truly random numbers without measuring something that is random (like static noise on radio frequencies or lava lamps). If they don’t have access to something like that, they must rely on generating pseudorandom numbers that look random even though they are created using a mathematical formula. Python takes the system time as the seed or starting point (since it is always changing) and then uses a mathematical formula to generate the next random number each time we ask for one.

Let’s practice with turtles drawing with random colors and random movements. Colors on computers and on the web can be set using RGB (red, green, blue) values that range from 0 to 255 (which can be saved in 8 bits). Try the Color Picker and look at the RGB values for different colors below the selected color box. Any color can be made by mixing different amounts of red, green, and blue light. Mixing light is different than mixing paint, so when you mix red, green, and blue light, you get white light.

If your class started the Paint Pot app using MIT’s App Inventor, you can now finish the Paint Pot Tutorial part 2, enhancements, and reflections.