# Lesson 01-02: Python Operators¶

Learning Target: I can write mathematical expressions in python.

## Basic Operators¶

Let’s first review the four common math operators:
Operator Symbol Example
Addition + 3+7 (result: 10)
Subtraction - 5-8 (result: -3)
Multiplication * 3*5 (result: 15)
Division / 6/2 (result: 3)

## New Operators¶

In Python, there are two other operators we need to know.

Power is simply an exponent. 3**2 can be described as 3 raised to the 2nd power. In math classes you’ve probably seen it as $$3^2$$

Note: You can do square roots by using a power of one-half. For example, the square root of 16 is the same as 16 raised to the 1/2th power, or 16**(1/2)

Modulo represents remainder after division. 10%3 can be described as the extra parts when 10 divided by 3, or how much of 10 is not divisible by 3. In this case, 10 divided by 3 is 3 remainder 1 (or 3 fits into 10, 3 times, with 1 left over), so 10 mod 3 = 1.

Operator Symbol Example
Power ** 3**2 (result: 9)
Modulo (mod) % 10%3 (result: 1)
Three more examples of modulo:
• 20 % 6

6 fits into 20 three (3) times. 3 * 6 = 18, which means that there is 20 (total) - 18 (result) = 2 (remainder) left over. The remainder of this expression is 2, so 20 % 6 = 2.

Another way of saying it is: 20 divided by 6 is 3.333, rounded down is 3, and 20 - (6 * 3) = 2.

• 27 % 9

9 fits into 27 three (3) times. 9 * 3 = 27, which means that there is 27 (total) - 27 (result) = 0 (remainder) left over. Since 9 divides 27 evenly, there is no remainder, so 27 % 9 = 0.

Another way of saying it is: 27 divided by 9 is exactly 3, so there is no remainder, so it is 0.

• 4 % 7

7 fits into 4 zero (0) times. 7 * 0 = 0, which we can follow with 4 (total) - 0 (result) = 4 (remainder). Since 7 doesn’t fit into 4 at all, the remainder is just 0.

Another way of saying it is: 4 divided by 7 is .571, rounded down is 0, and 4 - (7 * 0) = 4.

We can develop a general rule for this case, which is this: Given the expression a % b , where a and b are positive integers, if a < b , the result is always a.

## Order of Operations¶

Order of operations determines which operator is done first. These order of operations are followed by most programming languages, where the order of operations are:

• P - Parentheses first, then
• E - Exponents, then
• M/D - Multiplication/Division/Modulo, then
• A/S - Addition/Subtraction last

Note that Modulo is on the same level as multiplication and division.

## Practice: Check Your Understanding¶

### Q#1¶

Evaluate the following expression: 3 ** 2 + 3 Don't forget your order of operations!!

### Q#2¶

Evaluate the following expression: 3 ** (2 % 3) Make sure you do the parentheses first!

### Q#3¶

        ch0102-1: Order the groups of operations in the order that they should be evaluated.  Top is evaluated first, while bottom is evaluated last.  Make sure that all the blocks are the same size! (keep them all the way to the left)parentheses
exponents
mult/div/mod
add/sub

### Q#4¶

Evaluate the following expression (answer will be an integer): (3 * 2) % 5 + 3

### Q#5¶

Evaluate the following expression (answer will be an integer): ((10 / 2) + 5 % 2 ) * 2

### Q#6¶

Evaluate the following expression (answer will be an integer): 2 * 3 - 6 / 2 % 8

### Q#7¶

Evaluate the following expression (answer will be an integer): 100 - (24 % 5) * 3 / 4

### Q#8¶

Evaluate the following expression (answer will be an integer): 2 * ((4 * 2) + 3 / 6) % 10 - 5

Next Section - Lesson 01-03: Operators on Strings