Elementary arithmetic | Numbers

In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value. Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually (but not always) thought of as neither positive nor negative. The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign. Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as natural numbers (i.e., 0, 1, 2, 3...), while the positive and negative whole numbers (together with zero) are referred to as integers. (Some definitions of the natural numbers exclude zero.) In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. Negative numbers appeared for the first time in history in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han Dynasty (202 BC – AD 220), but may well contain much older material. Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd. Western mathematicians like Leibniz (1646–1716) held that negative numbers were invalid, but still used them in calculations. (Wikipedia).

"Order a mixture of negative and positive numbers."

From playlist Number: Negative Numbers

Why Does a Negative Times a Negative Equal a Positive

This tutorial uses basic math and logic to demonstrate that a negative times a negative equals a positive. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Basic Math

A look at why negative numbers multiply and divide to get positive products or quotients.

From playlist Core Standards - 7th Grade Math

Multiplying and Dividing Negative Numbers

"Multiply or divide a mixture of positive and negative numbers."

From playlist Number: Negative Numbers

Practice multiplying negatives

Quick examples dealing with the multiplication of positive and negative whole numbers, decimals and mixed numbers

From playlist Middle School - Worked Examples

Adding and Subtracting Negative Numbers

Add or subtract a mixture of positive and negative numbers.

From playlist Number: Negative Numbers

logarithm with negative base and negative input

What if we have both a negative base and a negative input in a logarithm! People often say we cannot have a negative number inside of a logarithm. Most of the time log(negative) gives us an imaginary number. But since (-2)^3=-8, so what do you think the answer to log base -2 of -8? Check

From playlist math for fun, complex world

How To Multiply Negative Numbers

Multiplying negatives is a very important part of algebra. This tutorial outlines how to go about multiplying negative numbers, and demonstrates the process with examples. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Basic Math

Grade 7: Module 3 Lesson 12 on Inequalities

From playlist Eureka Math Grade 7 Module 3

Complex Numbers - Basic Operations

This algebra 2 video tutorial explains how to perform operations using complex numbers such as simplifying radicals, adding and subtracting complex numbers, simplifying it in standard form, graphing complex numbers and calculating the absolute value of complex numbers. This video contains

From playlist New Precalculus Video Playlist

signed numbers, addition and subtraction (KristaKingMath)

► My Pre-Algebra course: https://www.kristakingmath.com/prealgebra-course In this video we'll learn how to add and subtract signed numbers, or negative numbers. If both numbers have the same sign, then the result will have the same sign as the original numbers. In other words, if we add t

From playlist Pre-Algebra

Factor Quadratic Trinomial x^2+bx+c | 10 Example Compilation

In this video I am going to work through 10 different examples of factoring quadratic trinomials so that you will gain more confidence on being able to factor on your own. ⭐ Solve by completing the square without fractions compilation - https://youtu.be/zYkV9GEHJIY ⭐ Factor Quadratic Trin

From playlist Compilations

Discrete Structures: Signed Integers

In this video we'll learn about signed integer representations, including 2's complement, sign-magnitude, and excess-n (or bias).

From playlist Discrete Structures, Spring 2022

Algebra Polynomial and Rational Inequalities

Algebra Polynomial and Rational Inequalities

From playlist Algebra

signed numbers, division (KristaKingMath)

► My Pre-Algebra course: https://www.kristakingmath.com/prealgebra-course In this video we'll learn about division of signed numbers, or negative numbers. When we divide two numbers with the same sign, whether both signs are positive or both signs are negative, the sign of the quotient wi

From playlist Pre-Algebra

signed numbers, multiplication (KristaKingMath)

► My Pre-Algebra course: https://www.kristakingmath.com/prealgebra-course In this video we'll learn about multiplication of signed numbers, or negative numbers. When we multiply together two numbers with the same sign, whether both signs are positive or both signs are negative, the sign o

From playlist Pre-Algebra

Prealgebra Lecture 2.1: Introduction to Integers

https://www.patreon.com/ProfessorLeonard Prealgebra Lecture 2.1: Introduction to Integers

From playlist Prealgebra (Full Length Videos)

Adding and Subtracting Fraction Integers Real Numbers

I introduce how to Add and Subtract Real Numbers, Adding and Subtracting Fractions, Adding and Subtracting Integers and Define Absolute Value. Adding Numbers with the Same signs Examples 3:40 5:35 8:41 Adding Numbers with Different signs Examples 14:04 16:40 Opposite Numbers defined 19:24

From playlist Algebra 1

Ex: Simplifying the Opposites of Negatives Integers

This video provides several examples of simplifying opposites of negative integers. Search Complete Video Library at http://www.mathispower4u.wordpress.com

From playlist Introduction to Integers