key term - Number Line

Definition

A number line is a visual representation of the number system, where numbers are arranged in a linear fashion along a horizontal or vertical axis. It serves as a fundamental tool in understanding and working with various numerical concepts, including whole numbers, integers, fractions, and rational and irrational numbers.

5 Must Know Facts For Your Next Test

1. The number line is used to represent and compare whole numbers, with the leftmost point representing zero and the positive integers increasing to the right.
2. Subtracting whole numbers on the number line involves finding the distance between two points, with the direction of the subtraction determining the sign of the result.
3. Integers, including positive and negative numbers, are represented on the number line, with the origin (0) as the center point and the positive and negative numbers extending in opposite directions.
4. Addition and subtraction of integers on the number line involve moving in the appropriate direction, with the sign of the integer determining the direction of movement.
5. Fractions are represented on the number line by identifying the location of the numerator in relation to the denominator, allowing for the visualization and comparison of different fractions.

Review Questions

• Explain how the number line is used to represent and compare whole numbers.
  • The number line is a visual representation of the number system, where whole numbers are arranged in a linear fashion from left to right. The leftmost point on the number line represents zero, and the positive integers increase in value as you move to the right. This allows for the easy comparison of whole numbers, as larger numbers are positioned to the right of smaller numbers on the number line. The number line is a fundamental tool for understanding and working with whole numbers, as it provides a concrete way to visualize and manipulate these numerical concepts.
• Describe how the number line is used to perform subtraction of whole numbers.
  • Subtracting whole numbers on the number line involves finding the distance between two points. The direction of the subtraction determines the sign of the result. For example, to subtract 5 from 10, you would start at 10 on the number line and move 5 units to the left, arriving at 5. This shows that 10 - 5 = 5. The number line provides a visual representation of the subtraction process, allowing students to better understand the relationship between the minuend, subtrahend, and difference.
• Analyze how the number line is used to represent and perform operations with integers.
  • The number line is essential for understanding and working with integers, which include both positive and negative numbers. The origin (0) is the center point on the number line, with positive integers extending to the right and negative integers extending to the left. Addition and subtraction of integers on the number line involve moving in the appropriate direction, with the sign of the integer determining the direction of movement. For example, to add -3 and 7, you would start at 0 and move 3 units to the left, then 7 units to the right, arriving at 4. This visual representation helps students grasp the concept of integer operations and their relationship to the number line.

Related terms

Coordinate Plane:

A two-dimensional grid system that uses a horizontal x-axis and a vertical y-axis to locate and represent points, lines, and other geometric figures.

Absolute Value:

The distance of a number from zero on the number line, regardless of its sign (positive or negative).

Ordering Numbers: The process of arranging numbers in a specific order, such as from smallest to largest or largest to smallest, using the number line as a reference.