Pre-Algebra

Pre-Algebra introduces foundational concepts in mathematics, including integers, fractions, and basic equations, essential for higher-level math courses.

Basic Concepts

Understanding Integers

What Are Integers?

Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. Think of them as the numbers you can count on your fingers (including negatives, if you could count below zero!).

Why Do We Use Integers?

Integers are used to represent quantities that can go above or below zero, such as temperatures, money owed, or levels in a video game.

Working with Integers

  • Adding integers: \( 3 + (-5) = -2 \)
  • Subtracting integers: \( -4 - (-7) = 3 \)
  • Multiplying integers: \( -3 \times 2 = -6 \)
  • Dividing integers: \( 8 \div -2 = -4 \)

Real-World Connections

  • Temperatures can drop below zero in winter.
  • Credits and debts in a bank account can be positive or negative.

Tips

  • Adding a negative is the same as subtracting.
  • Subtracting a negative is the same as adding.

Examples

  • If the temperature is -5°C and rises by 7 degrees, the new temperature is \( -5 + 7 = 2 \)°C.

  • A diver starts at sea level (0 meters) and dives down 10 meters, ending at -10 meters.

In a Nutshell

Integers are whole numbers that can be positive, negative, or zero and help us describe real-life situations that go above and below zero.

Key Terms

Integer
A whole number, positive, negative, or zero.
Negative Number
A number less than zero, shown with a minus sign.
Positive Number
A number greater than zero.