Number lines

key notes :

Introduction to Number Lines:

  • Definition: A number line is a visual representation of numbers on a straight line, where each point on the line corresponds to a number.
  • Purpose: Helps visualize the relationships between numbers, perform arithmetic operations, and understand concepts of magnitude and direction.

Basic Structure of a Number Line:

  • Zero Point: The center of the number line is typically zero.
  • Positive and Negative Numbers: Numbers increase to the right of zero and decrease to the left.
  • Equal Intervals: The distance between consecutive points (numbers) is equal.

Plotting Points:

  • Positive Numbers: Plot points to the right of zero.
  • Negative Numbers: Plot points to the left of zero.
  • Examples: Plot points like -3, 0, and 5 on a number line.

Operations with Number Lines:

  • Addition: Move to the right to add. For example, to add 3 + 2, start at 3 and move 2 units to the right to reach 5.
  • Subtraction: Move to the left to subtract. For example, to subtract 4 – 2, start at 4 and move 2 units to the left to reach 2.
  • Adding and Subtracting Negative Numbers: Moving left or right depending on the operation’s sign.

Understanding Fractions and Decimals:

  • Fractions: Plot fractions between whole numbers. For example, 1/2 is halfway between 0 and 1.
  • Decimals: Plot decimals in the same manner. For example, 0.75 is between 0.7 and 0.8.

Comparing and Ordering Numbers:

  • Comparison: Determine which numbers are greater or smaller by their position on the number line.
  • Ordering: Arrange numbers from smallest to largest by their relative positions.

Absolute Value:

  • Definition: The absolute value of a number is its distance from zero on the number line, regardless of direction.
  • Notation: Denoted as ∣x∣.
  • Example: ∣−7∣=7 because -7 is 7 units away from zero.

Learn with an example

🎯 Type the missing number.

Each interval represents 1, so find the missing number by adding or subtracting 1.

The missing number is smaller than –10, so subtract 1. Since –10 − 1 = –11, the missing number is –11.

🎯 Type the missing number.

Each interval represents 1, so find the missing number by adding or subtracting 1.

The missing number is smaller than –4, so subtract 1. Since –4 − 1 = –5, the missing number is –5.

🎯 Type the missing number.

Each interval represents 1, so find the missing number by adding or subtracting 1.

The missing number is larger than –58, so add 1. Since –58 + 1 = –57, the missing number is –57.

Let’s Practice!