Basic Concepts
In a nutshell: Learn how numbers work and how to use their properties to solve problems quickly and accurately.
## Understanding Numbers
Numbers are the foundation of all math! You'll work with whole numbers, decimals, fractions, and even negative numbers. It's important to know how to add, subtract, multiply, and divide these different kinds of numbers confidently.
## Order of Operations
To solve expressions correctly, use the order of operations: Parentheses, Exponents, Multiplication & Division (left to right), Addition & Subtraction (left to right)—often remembered as PEMDAS.
## Properties of Numbers
Numbers have special properties that can help you simplify problems. For example:
- **Commutative Property:** Changing the order doesn't change the answer (\( a + b = b + a \)).
- **Associative Property:** Grouping doesn't change the answer (\( (a + b) + c = a + (b + c) \)).
- **Distributive Property:** Multiply a number by a sum (\( a(b + c) = ab + ac \)).
## Why It Matters
Mastering these basics helps you solve more complex problems and understand patterns in math and real-life situations!
a(b + c) = ab + ac
Examples
- Calculate \( 3 \times (4 + 5) \) using the distributive property.
- Add \( 2/5 + 3/5 \) and explain why the denominators stay the same.
Key terms
- Commutative
- A property where the order of numbers does not affect the result.
- PEMDAS
- An acronym to remember the order of operations.