Python Basic Arithmetic Operators – Comprehensive Guide with Examples
Arithmetic operators are fundamental in any programming language, including Python. They allow you to perform mathematical operations such as addition, subtraction, multiplication, division, and more. Understanding how these operators work and their subtle differences is key to writing effective and error-free code.
1. Addition (+
)
The addition operator +
adds two numbers together.
Example 1:
a = 10
b = 5
result = a + b
print(result) # Output: 15
Explanation: Here, a
and b
are added, resulting in 15.
2. Subtraction (-
)
The subtraction operator -
subtracts the right-hand number from the left-hand number.
Example 2:
a = 10
b = 5
result = a - b
print(result) # Output: 5
Explanation: The value of b
(5) is subtracted from a
(10), giving 5.
3. Multiplication (*
)
The multiplication operator *
multiplies two numbers.
Example 3:
a = 10
b = 5
result = a * b
print(result) # Output: 50
Explanation: The numbers 10 and 5 are multiplied, giving 50.
4. Division (/
)
The division operator /
divides the left-hand number by the right-hand number and returns a floating-point result.
Example 4:
a = 10
b = 3
result = a / b
print(result) # Output: 3.3333333333333335
Important Note: Division always returns a float
, even if the division is exact.
5. Floor Division (//
)
The floor division operator //
divides and returns the largest whole number less than or equal to the result (also called the quotient without the remainder).
Example 5:
a = 10
b = 3
result = a // b
print(result) # Output: 3
Explanation: 10 divided by 3 is 3.333..., but floor division truncates the decimal part and returns 3.
⚠️ Caution:
Floor division returns an integer result if both operands are integers, but if one operand is a float, the result will be a float rounded down.
a = 10.0
b = 3
result = a // b
print(result) # Output: 3.0
6. Modulus (%
)
The modulus operator %
returns the remainder after division of the left operand by the right operand.
Example 6:
a = 10
b = 3
result = a % b
print(result) # Output: 1
Explanation: When 10 is divided by 3, the quotient is 3 and the remainder is 1, which is what the modulus operator returns.
Use Case:
The modulus operator is often used to determine if a number is even or odd:
number = 7
if number % 2 == 0:
print("Even")
else:
print("Odd") # Output: Odd
7. Exponentiation (**
)
The exponentiation operator **
raises the left operand to the power of the right operand.
Example 7:
a = 2
b = 3
result = a ** b
print(result) # Output: 8
Explanation: 2 raised to the power of 3 means 2 × 2 × 2 = 8.
Summary Table
Operator | Description | Example | Output |
---|---|---|---|
+ | Addition | 10 + 5 | 15 |
- | Subtraction | 10 - 5 | 5 |
* | Multiplication | 10 * 5 | 50 |
/ | Division (float result) | 10 / 3 | 3.3333... |
// | Floor Division | 10 // 3 | 3 |
% | Modulus (Remainder) | 10 % 3 | 1 |
** | Exponentiation (Power) | 2 ** 3 | 8 |
Important Tips & Notes
- Division by zero: Be cautious! Dividing by zero causes a
ZeroDivisionError
in Python. Always validate divisor before division. - Order of operations: Python follows standard arithmetic precedence (PEMDAS/BODMAS). Use parentheses
()
to make order explicit. - Data types matter: Operators behave differently on integers, floats, and other numeric types. For example,
/
always returns float, floor division returns integer (or float if one operand is float). - Modulus with negative numbers: The sign of the result follows the divisor (right operand). This is important in some calculations.
Practice Example: Calculate the area and perimeter of a rectangle
length = 7
width = 4
# Area = length * width
area = length * width
# Perimeter = 2 * (length + width)
perimeter = 2 * (length + width)
print("Area:", area) # Output: Area: 28
print("Perimeter:", perimeter) # Output: Perimeter: 22
Explanation: Here, we use multiplication and addition operators to calculate the area and perimeter of a rectangle.
Conclusion
Mastering Python's arithmetic operators is essential for all kinds of programming tasks, from simple calculations to complex algorithms. Remember to understand the subtle differences between division types, modulus, and exponentiation to write efficient and bug-free code. Practice with examples and experiment with different numeric types to gain confidence.
π Related Topics:
- ➤ Python Arithmetic Operators
- ➤ Basic String Functions
- ➤ Advanced String Functions
- ➤ Basic List Functions
- ➤ Advanced List Functions : Part-1
- ➤ Advanced List Functions : Part-2
- ➤ Basic Tuple Functions
- ➤ Advanced Tuple Functions
- ➤ Basic Dictionary Functions
- ➤ Advanced Dictionary Functions
- ➤ Conditional Statements : if-elif-else
- ➤ Python 'for' Loop
- ➤ Python 'while' Loop
- ➤ Difference between 'for' loop and 'while' loop
- ➤ Introducing Python Functions
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Stage 1: Python & Programming Fundamentals
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1. Python & Programming Fundamentals
----------------------------------------
1.1 Environment Setup
• Install Python 3.x, VS Code / PyCharm
• Configure linting, formatters (e.g., Pylint, Black)
• Jupyter Notebook / Google Colab basics
1.2 Core Python Syntax
• Variables, Data Types (int, float, str, bool)
• Operators: arithmetic, comparison, logical, bitwise
• Control Flow: if / else / elif
• Loops: for, while, break/continue
1.3 Functions & Modules
• Defining functions, return values
• Parameters: positional, keyword, default args
• *args, **kwargs
• Organizing code: modules and packages
• Standard library exploration (os, sys, datetime, random, math)
1.4 Data Structures
• Lists, Tuples, Sets, Dictionaries
• List/dict comprehensions
• Built-in functions: map, filter, zip, enumerate
• When to use which structure
1.5 File Handling & Exceptions
• Reading/Writing text and binary files
• Context managers (`with` statement)
• Exception handling: try/except/finally
• Custom exceptions
1.6 Object-Oriented Programming (OOP)
• Classes, Instances, Attributes, Methods
• __init__, self, class vs instance attributes
• Inheritance, Polymorphism, Encapsulation
• Magic methods: __str__, __repr__, __add__, etc.
• Use-cases in structuring larger projects
1.7 Virtual Environments & Package Management
• venv / pipenv / poetry basics
• Installing and managing dependencies
• requirements.txt and environment.yml
π Tools: VS Code, Git for version control, Jupyter/Colab
Stage 2: Mathematics for Machine Learning
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2. Mathematics for Machine Learning
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2.1 Linear Algebra
• Scalars, Vectors, Matrices, Tensors
• Operations: addition, multiplication, dot product
• Matrix properties: transpose, inverse, rank
• Eigenvalues & Eigenvectors (intuition)
• Applications: data transformations, PCA
2.2 Calculus
• Functions and limits (intuitive overview)
• Derivatives: gradient of single-variable and multi-variable functions
• Chain rule (key for backpropagation in neural networks)
• Partial derivatives
• Basic integration (overview; less often used directly)
2.3 Probability & Statistics
• Basic probability theory: events, conditional probability, Bayes’ theorem
• Random variables, distributions (normal, binomial, Poisson, etc.)
• Descriptive statistics: mean, median, mode, variance, standard deviation
• Inferential statistics: hypothesis testing, p-values, confidence intervals
• Sampling methods, bias, variance concepts
2.4 Optimization Basics
• Concept of optimization in ML (finding minima of loss functions)
• Gradient descent: batch, stochastic, mini-batch
• Learning rate intuition
π Tools / References:
• Interactive calculators: Desmos, GeoGebra
• Python libraries: NumPy for experimentation
Stage 3: Data Handling & Preprocessing
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3. Data Handling & Preprocessing
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3.1 NumPy Essentials
• ndarrays: creation, indexing, slicing
• Vectorized operations vs Python loops
• Broadcasting rules
• Random number generation
3.2 Pandas for Tabular Data
• Series & DataFrame: creation and basic ops
• Reading data: CSV, Excel, JSON
• Indexing, selection (loc/iloc), filtering rows
• Handling missing values: dropna, fillna
• Detecting/removing duplicates
• Combining datasets: merge, join, concat
• GroupBy operations, aggregation, pivot tables
3.3 Feature Engineering
• Feature scaling: normalization (Min-Max), standardization (Z-score)
• Encoding categorical variables: one-hot, ordinal encoding
• Date/time feature extraction (if applicable)
• Creating new features via domain knowledge
• Feature selection: variance threshold, correlation analysis
3.4 Data Visualization
• Matplotlib basics: line plot, scatter plot, histograms, bar charts
• Seaborn overview: higher-level plots (heatmap, pairplot)
• Visualizing distributions, relationships, outliers
• Plot customization: titles, labels, legends
3.5 Handling Real-World Data Challenges
• Imbalanced datasets: oversampling (SMOTE), undersampling, class weights
• Outlier detection and treatment
• Data leakage awareness
• Pipeline creation in scikit-learn
π Tools: NumPy, Pandas, Matplotlib, Seaborn, scikit-learn utilities
Stage 4: Core Machine Learning
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4. Core Machine Learning
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4.1 ML Concepts & Workflow
• What is ML? Supervised vs Unsupervised vs Semi-supervised vs Reinforcement
• Training, Validation, Testing splits
• Overfitting vs Underfitting, bias-variance trade-off
• Cross-validation techniques: k-fold, stratified
4.2 Supervised Learning: Regression
• Linear Regression: assumptions, cost function, normal equation
• Regularized Regression: Ridge, Lasso, Elastic Net
• Polynomial Regression
• Evaluation metrics: MSE, RMSE, MAE, R²
4.3 Supervised Learning: Classification
• Logistic Regression: sigmoid, decision boundary, loss
• k-Nearest Neighbors (KNN)
• Decision Trees: entropy/gini, pruning
• Ensemble Methods:
- Bagging: Random Forest
- Boosting: AdaBoost, Gradient Boosting, XGBoost (intro)
• Support Vector Machines (SVM): kernel trick overview
• Naive Bayes: Gaussian, Multinomial
• Evaluation: accuracy, precision, recall, F1-score, ROC-AUC
• Confusion matrix analysis
4.4 Unsupervised Learning
• Clustering:
- K-Means: elbow method, silhouette score
- Hierarchical clustering: dendrograms
- DBSCAN
• Dimensionality Reduction:
- PCA: variance explained
- t-SNE / UMAP (visualization-focused)
• Anomaly Detection overview
4.5 Model Selection & Tuning
• Hyperparameter tuning: grid search, random search, Bayesian optimization (overview)
• Automated tuning libraries (e.g., scikit-learn’s GridSearchCV, RandomizedSearchCV)
• Pipeline building to avoid leakage
• Feature importance and model interpretability basics
π Tools: scikit-learn, pandas, NumPy
Stage 5: Deep Learning Foundations
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5. Deep Learning Foundations
----------------------------------------
5.1 Neural Network Basics
• Artificial neuron model, activation functions (ReLU, Sigmoid, Tanh)
• Architecture: input, hidden, output layers
• Forward propagation, loss functions (Cross-entropy, MSE)
• Backpropagation: gradient computation, chain rule
5.2 Deep Learning Frameworks
• TensorFlow & Keras: Sequential and Functional APIs
• PyTorch basics: tensors, autograd, nn.Module
• Comparing TF/Keras vs PyTorch (choose one to start)
5.3 Training Deep Models
• Optimizers: SGD, Adam, RMSprop
• Learning rate scheduling
• Regularization: Dropout, Batch Normalization, Weight Decay
• Handling overfitting: early stopping, data augmentation
5.4 Basic DL Projects
• MNIST digit classification
• CIFAR-10 image classification (small CNN)
• Simple feedforward network on tabular data
π Tools: TensorFlow/Keras or PyTorch, GPU if available (Colab/GPU runtime)
Stage 6: Advanced Deep Learning & Architectures
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6. Advanced Deep Learning & Architectures
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6.1 Convolutional Neural Networks (CNNs)
• Convolution operations, filters, feature maps
• Pooling layers, padding, stride
• Famous architectures overview: LeNet, AlexNet, VGG, ResNet (intuition)
• Transfer Learning: fine-tuning pre-trained models
6.2 Recurrent Neural Networks (RNNs) & Sequence Models
• RNN basics: hidden states, vanishing gradients
• LSTM, GRU: gating mechanisms
• Sequence-to-sequence models (intro)
• Attention mechanism: intuition
6.3 Transformers & Attention
• Self-attention mechanism
• Transformer architecture: encoder, decoder overview
• Pre-trained transformer models: BERT, GPT family (conceptual)
• Fine-tuning transformers for tasks
6.4 Generative Models
• Autoencoders: basic, variational autoencoders (VAE) overview
• Generative Adversarial Networks (GANs): generator/discriminator intuition
• Applications and basic experiments
6.5 Advanced Techniques
• Multi-task learning, meta-learning (intro)
• Few-shot learning, transfer learning deeper dive
• Neural architecture search (overview)
• Model compression, pruning, quantization (deployment considerations)
π Tools: TensorFlow / PyTorch, Hugging Face Transformers library
Stage 7: Natural Language Processing (NLP) Advanced
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7. Natural Language Processing (NLP)
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7.1 Text Preprocessing & Representation
• Tokenization (word, subword/BPE)
• Stopwords removal, lemmatization vs stemming
• Word embeddings: Word2Vec, GloVe, FastText
• Contextual embeddings: ELMo, BERT embeddings
7.2 Transformer-based NLP
• Pre-trained models: BERT, RoBERTa, GPT, T5
• Fine-tuning for classification, QA, summarization
• Sequence generation tasks using GPT-like models
7.3 Specialized NLP Tasks
• Named Entity Recognition (NER)
• Machine Translation overview
• Question Answering pipelines
• Text Summarization (extractive vs abstractive)
• Sentiment Analysis deep dive
7.4 Evaluation Metrics in NLP
• BLEU, ROUGE, METEOR (for generation)
• Accuracy, F1 for classification tasks
π Tools: Hugging Face Transformers, spaCy, NLTK
Stage 8: Computer Vision Advanced
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8. Computer Vision (CV)
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8.1 Image Preprocessing & Augmentation
• OpenCV basics: reading, resizing, color conversions
• Data augmentation techniques: flips, rotations, crops, color jitter
8.2 Advanced CNN Architectures
• Inception, ResNet, DenseNet, EfficientNet (conceptual)
• Transfer learning and fine-tuning advanced models
• Object detection frameworks: YOLOvX, SSD, Faster R-CNN (overview)
• Semantic segmentation: U-Net, Mask R-CNN
• Instance segmentation concepts
8.3 Vision Transformers (ViT)
• Applying transformer concepts to images
• Fine-tuning ViT for classification
8.4 Specialized CV Tasks
• Face recognition pipelines
• Video analysis basics: action recognition, object tracking
• 3D vision intro (depth estimation)
π Tools: OpenCV, TensorFlow/PyTorch, libraries like Detectron2 or YOLO implementations
Stage 9: Reinforcement Learning & Advanced Topics
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9. Reinforcement Learning & Advanced Topics
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9.1 Reinforcement Learning Foundations
• Markov Decision Process (MDP)
• Value functions, policy functions
• Q-Learning, SARSA (tabular methods)
• Exploration vs Exploitation
9.2 Deep Reinforcement Learning
• Deep Q-Networks (DQN)
• Policy Gradient Methods: REINFORCE, Actor-Critic
• Advanced: A3C, PPO, DDPG overview
9.3 Other Advanced AI Topics
• Graph Neural Networks (GNNs): node/graph embeddings (overview)
• Time Series Forecasting with ML/DL: RNN/LSTM, Prophet intro
• Bayesian Methods overview
• AutoML and neural architecture search concepts
• Federated Learning basics (privacy-aware training)
• MLOps fundamentals:
- Model versioning
- Continuous integration/continuous deployment (CI/CD) for ML
- Monitoring models in production
- Tools: MLflow, Kubeflow (intro)
• Edge AI / TinyML overview (deploying models on devices)
π Tools: RL libraries (Stable Baselines3), MLflow, Kubernetes intro, Docker
Stage 10: Deployment, Production & MLOps
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10. Deployment, Production & MLOps
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10.1 Model Serving & APIs
• REST API with Flask / FastAPI
• gRPC basics (overview)
• Dockerizing ML applications
• Serving with TensorFlow Serving or TorchServe
10.2 Cloud Deployment
• Deploy on AWS Sagemaker / GCP AI Platform / Azure ML (basic workflow)
• Serverless deployments (AWS Lambda, Cloud Functions) for small models
• CI/CD pipelines for ML: GitHub Actions or Jenkins integration
10.3 Monitoring & Maintenance
• Logging model inputs/outputs
• Drift detection (data/model drift)
• Retraining pipelines (automated or scheduled)
• Scaling considerations
10.4 MLOps Tools & Practices
• Experiment tracking (MLflow, Weights & Biases)
• Data versioning (DVC)
• Model registry concepts
• Infrastructure as Code (Terraform intro)
π Tools: Docker, Kubernetes basics, CI/CD tools, cloud consoles
Stage 11: Real-World Projects & Portfolio
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11. Real-World Projects & Portfolio
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11.1 Project Ideas by Domain
• Tabular Data: Predictive analytics (e.g., churn prediction)
• NLP: Chatbot, summarizer, translation prototype
• CV: Image classifier, object detector, image segmentation app
• Time Series: Forecasting stock or weather data
• RL: Simple game-playing agent
• Generative: GAN art generation or style transfer demo
11.2 End-to-End Pipeline
• Data collection & preprocessing
• Model training & validation
• Deployment as API or web app (Streamlit/Flask)
• Monitoring & iteration
• Documentation & README
11.3 Collaboration & Open Source
• Participate in Kaggle competitions (beginner → intermediate)
• Contribute to open-source ML projects
• Write blog posts/tutorials documenting your projects
11.4 Soft Skills & Communication
• Clear README, code comments
• Presentation slides or videos of project demos
• Networking: sharing work on LinkedIn, GitHub
π Tools: GitHub Pages, Streamlit, Heroku/Netlify, Docker
Stage 12: Ethics, Explainability & Continuous Learning
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12. Ethics, Explainability & Continuous Learning
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12.1 AI Ethics & Responsible AI
• Bias & Fairness: identifying and mitigating bias
• Privacy concerns: GDPR, data protection best practices
• Transparency: documenting data sources and model decisions
12.2 Explainable AI (XAI)
• Model interpretability: SHAP, LIME (basic usage)
• Interpreting black-box models vs inherently interpretable models
• Communicating explanations to stakeholders
12.3 Continuous Learning & Staying Updated
• Following research: arXiv alerts, ML conferences (NeurIPS, ICML, CVPR summaries)
• Blogs, podcasts, newsletters (e.g., “The Batch” by deeplearning.ai)
• Reading codebases of popular libraries, exploring new architectures
• Community involvement: forums, study groups
12.4 Advanced Research Topics (Optional/For Aspirants)
• Research paper reading workflow
• Experimentation frameworks
• Contributing to academic research or advanced industrial research
π Tools: arXiv, Google Scholar alerts, RSS readers, community forums
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