Common Core: High School - Number and Quantity

This subject covers the foundational concepts of number and quantity, focusing on real numbers, complex numbers, and their applications in various mathematical contexts.

Basic Concepts

The Properties of Numbers

Essential Properties

Numbers follow certain rules that make math work reliably! These are called properties.

Key Properties

  • Commutative Property: Order doesn't matter for addition or multiplication. \(a + b = b + a\)
  • Associative Property: Grouping doesn't matter for addition or multiplication. \((a + b) + c = a + (b + c)\)
  • Distributive Property: Multiplying across addition. \(a(b + c) = ab + ac\)
  • Identity Property: Adding 0 or multiplying by 1 keeps the number the same.
  • Inverse Property: Adding a number and its opposite or multiplying by its reciprocal gives you the identity.

Why Are Properties Useful?

They help you simplify and solve equations and make mental math easier.

Applying These Properties

These properties work for real numbers, and many also work for complex numbers.

Examples

  • \(4 + 5 = 5 + 4\) because of the commutative property.

  • \(2(3 + 7) = 2 \times 3 + 2 \times 7 = 6 + 14 = 20\), using the distributive property.

In a Nutshell

Properties of numbers make calculations predictable and simplify math.