In mathematics, mastering the basic operations of addition, subtraction, multiplication, and division is crucial. These operations are the building blocks for more complex mathematical concepts. This section delves into each operation with a focus on integers, fractions, and decimals, emphasizing the correct ordering of operations and the use of brackets.
![Basic operations in Mathematics](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F50bea1f4-11a8-4726-9ce3-8d422666ee4d-file.png&w=1080&q=75)
Addition
Addition combines two or more numbers into their total or sum.
![Addition](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F88a8c52d-fc16-4abb-8e4e-5da0324e33f6-file.png&w=1080&q=75)
- Properties:
- Commutative: Order doesn't affect the sum, e.g., .
- Associative: Grouping doesn't affect the sum, e.g., .
Example: Calculating a Sum
Question: What is the sum of , , and ?
Solution:
Subtraction
Subtraction finds the difference between two numbers, essentially reversing addition.
![Subtraction](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fe1402c70-db32-4dfd-8c59-96e87b920ecc-file.png&w=1080&q=75)
- Symbols and Terms: The - symbol denotes subtraction. The number being subtracted is the subtrahend, from the minuend, to get the difference.
- Properties:
- Non-Commutative: The order in subtraction matters, e.g., .
Example: Finding a Difference
Question: What is the difference between and ?
Solution:
Multiplication
Multiplication adds a number to itself a specified number of times, streamlining addition.
![Multiplication](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fbb829f43-21e9-4198-a91b-de4d3f05c102-file.png&w=1080&q=75)
- Symbols and Terms: The × or * symbol is for multiplication. The numbers being multiplied are factors, with the result called the product.
- Properties:
- Commutative: The order of factors doesn't affect the product, e.g., .
- Associative: Grouping of factors doesn't affect the product, e.g., .
Example: Multiplying Numbers
Question: Multiply by .
Solution:
Division
Division splits a number into equal parts, the inverse of multiplication.
![Division](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F5cbe3449-2c87-45f6-b746-8b6d22db8914-file.png&w=1080&q=75)
- Symbols and Terms: The ÷ or / symbol represents division. The number being divided is the dividend, by the divisor, to get the quotient.
- Properties:
- Non-Commutative: Order matters significantly in division.
- Division by Zero: Undefined.
Example: Dividing Numbers
Question: Divide by .
Solution:
Order of Operations and Bracket Usage
Correct operation ordering and bracket usage are pivotal for solving problems accurately. PEMDAS guides the order: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
- Brackets: Operations within are prioritized; nested ones are solved inside out.
Example: