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How To Read Number Lines.mov
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Placing Numbers on a Number Line
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Counting 1 - 10 on the Number Line With Froggy
Counting 1 - 10 on the Number Line With Froggy
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Pre-Algebra 4 - Whole Numbers, Integers, and the Number Line
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Number Line Song!
Number Line Song!
::2013/12/13::
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number line addition by Peter Weatherall
number line addition by Peter Weatherall
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Fractions on a number line
Fractions on a number line
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Comparing fractions visually and on number line
Comparing fractions visually and on number line
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Learn Grade 1 - Maths - Number line
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Number line subtraction by Peter Weatherall
Number line subtraction by Peter Weatherall
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How to Read a Number Line
How to Read a Number Line
::2011/12/27::
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Number Line - Numberphile
Number Line - Numberphile
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The Rappin
The Rappin' Mathematician: "The Number Line Dance"
::2009/02/02::
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Place fractions on a number line (1) - 3.NF.2
Place fractions on a number line (1) - 3.NF.2
::2011/11/22::
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Number Line
Number Line
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Learn Grade 1 - Maths - Subtraction Using Number line
Learn Grade 1 - Maths - Subtraction Using Number line
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Basic Math : How to Draw a Number Line
Basic Math : How to Draw a Number Line
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Numberline (little extra bit)
Numberline (little extra bit)
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Equivalent fractions visually and on number line
Equivalent fractions visually and on number line
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Division on a number line
Division on a number line
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Inequalities on a number line
Inequalities on a number line
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Lesson 12 From Ratio Tables to Double Number LIne Diagrams
Lesson 12 From Ratio Tables to Double Number LIne Diagrams
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Learn Multiplication Facts using Number Line
Learn Multiplication Facts using Number Line
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Open Number Line Basics
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Elapsed Time Number-Line
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Phish - Backwards Down the Number Line 8-31-13 Commerce City, CO live
Phish - Backwards Down the Number Line 8-31-13 Commerce City, CO live
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2.MD.6 - Addition Using the Number Line (Part 1 of 2)
2.MD.6 - Addition Using the Number Line (Part 1 of 2)
::2012/02/07::
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Learn Grade 1 - Maths - Addition Using Number line
Learn Grade 1 - Maths - Addition Using Number line
::2011/10/03::
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Fractions and Mixed Numbers on a Number Line
Fractions and Mixed Numbers on a Number Line
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Fractions and Decimals: Number Line
Fractions and Decimals: Number Line
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Locating decimals on number line
Locating decimals on number line
::2011/02/26::
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Place Value - Decimals on a Number Line (5-NBT-4 part 1)
Place Value - Decimals on a Number Line (5-NBT-4 part 1)
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Adding Integers Using a Number Line
Adding Integers Using a Number Line
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5th Grade Module 1 C   Rounding on Vertical Number Line
5th Grade Module 1 C Rounding on Vertical Number Line
::2014/07/21::
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6.NS.1 Dividing Fractions using a Number Line MaTh LAB 3.8
6.NS.1 Dividing Fractions using a Number Line MaTh LAB 3.8
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Multiplying With a Number Line
Multiplying With a Number Line
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How to Teach Fractions on a Number Line using Fraction Tower Cubes
How to Teach Fractions on a Number Line using Fraction Tower Cubes
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Representing Irrational numbers (√2, √3) on the number-line (Part-3)
Representing Irrational numbers (√2, √3) on the number-line (Part-3)
::2012/04/23::
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Using Double Number Line Diagrams
Using Double Number Line Diagrams
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YUNG BB NUMBER LINE FREESTYLE
YUNG BB NUMBER LINE FREESTYLE
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Adding and Subtracting Integers on a Number Line
Adding and Subtracting Integers on a Number Line
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Using a number line to help children learn to add up
Using a number line to help children learn to add up
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Place improper fractions on a number line - 5.NF.3
Place improper fractions on a number line - 5.NF.3
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Phish | 12.31.10 | Backwards Down the Number Line
Phish | 12.31.10 | Backwards Down the Number Line
::2011/01/02::
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Fractions on a Number Line
Fractions on a Number Line
::2010/12/26::
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Real numbers and the number line - N3
Real numbers and the number line - N3
::2010/08/06::
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Fractions on Number Lines - v1
Fractions on Number Lines - v1
::2012/09/18::
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Rounding with a Vertical Number Line - Engage NY Math - Common Core
Rounding with a Vertical Number Line - Engage NY Math - Common Core
::2013/09/21::
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Points on a number line
Points on a number line
::2011/01/19::
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Rational number on a number line
Rational number on a number line
::2011/06/01::
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From Wikipedia, the free encyclopedia
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This article is about the mathematical concept. For the printer's key, see Printer's key.
This article covers basic topics. For advanced topics, see Real line.

In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point.[1] Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers.

The number line

It is divided into two symmetric halves by the origin, that is the number zero.

In advanced mathematics, the expressions real number line, or real line are typically used to indicate the above-mentioned concept that every point on a straight line corresponds to a single real number, and vice versa.

Drawing the number line[edit]

The number line is usually represented as being horizontal. Positive numbers always lie on the right side of zero, and negative numbers always lie on the left side of zero. An arrowhead on either end of the drawing is meant to suggest that the line continues indefinitely in the positive and negative real numbers, denoted by \mathbb{R}. The real numbers consist of irrational numbers and rational numbers, the latter of which include the integers, which in turn include the natural numbers (also called the counting numbers or whole numbers).

Comparing numbers[edit]

If a particular number is farther to the right on the number line than is another number, then the first number is greater than the second (equivalently, the second is less than the first). The distance between them is the magnitude of their difference—that is, it measures the first number minus the second one, or equivalently the absolute value of the second number minus the first one.

Thus, for example, the length of a line segment between 0 and some other number represents the magnitude of the latter number.

Numbers can be added by "picking up" the length from 0 to one of the numbers, and putting it down again with the end that was 0 placed on top of the other number.

Portions of the number line[edit]

The section of the number line between two numbers is called an interval. If the section includes both numbers it is said to be a closed interval, while if it excludes both numbers it is called an open interval. If it includes one of the numbers but not the other one, it is called a half-open interval.

All the points extending forever in one direction from a particular point are together known as a ray. If the ray includes the particular point, it is a closed ray; otherwise it is an open ray.

Extensions of the concept[edit]

A line drawn through the origin at right angles to the real number line can be used to represent the imaginary numbers. This line, called imaginary line, extends the number line to a complex number plane, with points representing complex numbers.

Alternatively, one real number line can be drawn horizontally to denote potential values of one real number, commonly called x, and another real number line can be drawn vertically to denote potential values of another real number, commonly called y. Together these lines form what is known as the Cartesian coordinate system, and any point in the Cartesian plane denotes the values of a pair of real numbers.

See also[edit]

References[edit]

  1. ^ Stewart, James B.; Redlin, Lothar; Watson, Saleem (2008). College Algebra (5th ed.). Brooks Cole. pp. 13–19. ISBN 0-495-56521-0. 
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