Order of operations 🤔

See book section

Mathematical Order of Operations

Mathematical order of operations refers to the rules that dictate the sequence in which mathematical operations should be performed in an expression. These rules ensure that every mathematical expression is evaluated in a consistent and unambiguous manner. The order of operations is also known as “PEMDAS” which is an acronym representing the sequence of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Python, along with many other programming languages, follows the standard order of operations used in mathematics. The order of operations is essential to obtain accurate and meaningful results. Let’s break down each component of the order of operations and illustrate them with Python examples, including real-world scenarios.

1. Parentheses

Parentheses are used to indicate which parts of an expression should be evaluated first. Expressions within parentheses are calculated before anything else.

Example 1: Simple Parentheses

Code

result = (4 + 3) * 2
print(result)  # Output: 14 (since 4 + 3 = 7, and 7 * 2 = 14)

14

2. Exponents

Exponents are mathematical operations that raise a base to a certain power.

Example 2: Exponents

Code

result = 2 ** 3 + 4
print(result)  # Output: 12 (since 2 ** 3 = 8, and 8 + 4 = 12)

12

3. Multiplication and Division

These operations are performed from left to right, whichever comes first in the expression.

Example 3: Multiplication and Division

Code

result = 10 / 2 * 3
print(result)  # Output: 15 (since 10 / 2 = 5, and 5 * 3 = 15)

15.0

4. Addition and Subtraction

Similarly, addition and subtraction are performed from left to right, whichever comes first in the expression.

Example 4: Addition and Subtraction

Code

result = 8 - 3 + 2
print(result)  # Output: 7 (since 8 - 3 = 5, and 5 + 2 = 7)

7

Real-World Examples

Let’s consider some real-world examples where understanding the order of operations is crucial:

Example 5: Shopping Calculations

Code

price_per_item = 5
tax_rate = 0.08
quantity = 3

total_cost = price_per_item * quantity + (price_per_item * quantity) * tax_rate
print(total_cost)  # Output: 16.2 (5 * 3 = 15, 15 + 15 * 0.08 = 16.2)

16.2

Example 6: Engineering Calculation

Code

import math

base_length = 6.5 # a
height = 8.2 # b

hypotenuse = math.sqrt(base_length ** 2 + height ** 2)
print(hypotenuse)  # Output: 10.463...

10.463746938836012

In the second example, we use the Pythagorean theorem to find the length of the hypotenuse in a right-angled triangle. The order of operations ensures that the squares and addition are performed before the square root operation.

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Assignment

Basic: Make a short video explaining how to calculate distances between two coordinates. Do proper research and use code demos.

Stretch: Expand your video with an exploration of how to calculate the distance between geographical locations using their coordinates taking into account the curvature of the earth. Discuss and illustrate with code examples and maps. Provide a list of interesting resources on the matter.

Challenge: Share your content online (e.g. Linkedin or Medium), gather feedback and write a reflection on it.