what is the deference between mathematics and arithmetic

 Arithmetic is like a toolbox, while mathematics is the entire workshop. Here's how they differ:

Mathematics (the workshop):

• A vast field studying relationships among numbers, shapes, quantities using symbols and logic.
• Includes arithmetic, algebra, geometry, calculus, trigonometry, statistics and more.
• Deals with concepts, theories, proofs, and applications in various fields.

Arithmetic (the toolbox):

• A fundamental branch of mathematics focusing on basic operations with numbers.
• Covers addition, subtraction, multiplication, division and their properties.
• Lays the groundwork for more advanced math concepts.

Here's an analogy:

Imagine building a house (solving a complex problem). Math provides the blueprints (theoretical framework), tools (arithmetic, algebra, etc.), and construction techniques (applying the knowledge). Arithmetic itself is just a set of tools like the hammer and saw, but you need the entire workshop (mathematics) to build the house.

Here are some key differences to remember:

• Scope: Math is broader, encompassing arithmetic and many other areas.
• Complexity: Math deals with more complex concepts and problems.
• Applications: Math has applications in various fields, while arithmetic is primarily used for basic calculations.

I hope this clarifies the difference between mathematics and arithmetic!