3 min read•Last Updated on June 24, 2024
Integers are the building blocks of math, including whole numbers and their negative counterparts. They're plotted on a number line, with positive numbers to the right of zero and negative numbers to the left. Understanding integers is crucial for grasping more complex mathematical concepts.
Integers help us represent real-world situations involving gains, losses, temperatures, and more. We can compare, order, and find opposites of integers. Absolute value shows an integer's distance from zero, regardless of its sign. These concepts form the foundation for algebra and beyond.
Locating and Ordering Integers on the Number Line | Prealgebra | | Course Hero View original
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Notation and Definition of the Set of Integers | Prealgebra View original
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Locating and Ordering Integers on the Number Line | Prealgebra | | Course Hero View original
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Locating and Ordering Integers on the Number Line | Prealgebra | | Course Hero View original
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Notation and Definition of the Set of Integers | Prealgebra View original
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Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of the number's sign. It is a way to describe the magnitude or size of a number without considering its positive or negative direction.
Term 1 of 21
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of the number's sign. It is a way to describe the magnitude or size of a number without considering its positive or negative direction.
Term 1 of 21
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of the number's sign. It is a way to describe the magnitude or size of a number without considering its positive or negative direction.
Term 1 of 21
Integers are a set of positive and negative whole numbers, including zero. They are the foundation for many mathematical operations and concepts, and are essential in understanding and working with various topics in pre-algebra.
Whole Numbers: Whole numbers are a subset of integers, consisting of the non-negative integers (0, 1, 2, 3, and so on).
Absolute Value: The absolute value of an integer is the distance of that integer from zero on the number line, regardless of its sign.
Number Line: A number line is a visual representation of the set of integers, with positive integers to the right of zero and negative integers to the left.
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.
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.
Zero is a fundamental numerical concept that represents the absence of quantity or magnitude. It serves as a starting point and a reference for various mathematical operations and number systems, making it a crucial element in the understanding of whole numbers, integers, and the properties of identity, inverses, and zero.
Additive Identity: The property that any number added to zero results in the original number, with zero acting as the additive identity element.
Multiplicative Identity: The property that any number multiplied by one results in the original number, with one acting as the multiplicative identity element.
Additive Inverse: The property that a number and its additive inverse (opposite) sum to zero, with zero acting as the additive identity.
Opposites refer to two things or concepts that are completely different or contrary to each other. They represent the farthest ends of a spectrum or scale, with one being the exact inverse or negation of the other.
Positive and Negative: Positive and negative numbers are opposites, with positive numbers representing quantities above zero and negative numbers representing quantities below zero.
Additive Inverse: The additive inverse of a number is the opposite of that number, meaning when added together, they equal zero.
Multiplicative Inverse: The multiplicative inverse of a number is the reciprocal of that number, meaning when multiplied together, they equal one.
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of the number's sign. It is a way to describe the magnitude or size of a number without considering its positive or negative direction.
Integer: An integer is a whole number, including positive, negative, and zero values.
Number Line: A number line is a visual representation of the set of real numbers, where each point on the line corresponds to a unique real number.
Magnitude: Magnitude refers to the size or amount of a number, without regard to its positive or negative direction.
Positive integers are the set of all whole numbers greater than zero. They are an important concept in mathematics, particularly in the context of addition and other basic arithmetic operations.
Integers: Integers are the set of whole numbers, including both positive and negative numbers, as well as zero.
Natural Numbers: Natural numbers, also known as counting numbers, are the set of positive integers starting from 1.
Absolute Value: The absolute value of a number is the distance of that number from zero on the number line, regardless of its sign.
Negative integers are numbers that are less than zero on the number line. They represent quantities or values that are below the starting point of zero, such as debt, losses, or temperatures below freezing.
Integers: Integers are a set of positive and negative whole numbers, including zero.
Absolute Value: The absolute value of a number is its distance from zero on the number line, regardless of whether it is positive or negative.
Number Line: A visual representation of numbers, with positive numbers to the right of zero and negative numbers to the left.
The term 'greater than' is a mathematical comparison operator that indicates when one value exceeds another. It is a fundamental concept in both the study of integers and the addition and subtraction of fractions with common denominators.
Less Than: The opposite of 'greater than', this term indicates when one value is smaller than another.
Inequality: A mathematical statement that compares two expressions using comparison operators like 'greater than' or 'less than'.
Absolute Value: The distance of a number from zero on the number line, regardless of its sign, which can be used to determine if one value is greater than another.
The concept of ordering a set of numbers or values from the smallest or lowest value to the largest or highest value. This arrangement is often used to organize and compare numerical data in a logical and meaningful way.
Numerical Order: The arrangement of numbers in a specific sequence, typically from smallest to largest or vice versa.
Ascending Order: The arrangement of numbers or values from the smallest to the largest, with the lowest value first.
Comparative Relationships: The ability to determine the relative size, quantity, or magnitude of one number or value in comparison to another.
The term 'less than' is a mathematical comparison that indicates a value or quantity is smaller or lower in magnitude than another. This concept is crucial in understanding integers and performing operations with fractions.
Greater Than: The opposite of 'less than,' this term indicates a value or quantity is larger or higher in magnitude than another.
Inequality: A mathematical statement that compares two values using symbols like '<' (less than) or '>' (greater than).
Absolute Value: The distance of a number from zero on the number line, regardless of its sign (positive or negative).
Equidistant refers to the property of being an equal distance from two or more points or objects. It describes a relationship where the distance between a specific point and multiple other points is the same.
Midpoint: The midpoint is the point that is equidistant between two other points on a line segment.
Parallel Lines: Parallel lines are lines in a plane that are equidistant from each other along their entire length.
Perpendicular Bisector: A perpendicular bisector is a line segment that intersects another line segment at its midpoint and forms right angles with it, making the two segments equidistant.
The additive inverse of a number is the opposite value that, when added to the original number, results in a sum of zero. It is a fundamental concept in the context of integers and other number systems.
Integers: The set of whole numbers, including positive, negative, and zero, that can be expressed without a fractional component.
Opposites: Two numbers that, when added together, result in a sum of zero. The additive inverse is the opposite of a given number.
Additive Identity: The number zero, which when added to any other number, leaves that number unchanged.
The sum is the result of adding two or more numbers or quantities together. It represents the total or combined value of the addends. The sum is a fundamental concept in mathematics that is essential for understanding addition and its applications in various mathematical topics.
Addend: An addend is any of the numbers or quantities that are being added together to find the sum.
Addition: Addition is the mathematical operation of combining two or more numbers or quantities to find their total or sum.
Commutative Property: The commutative property of addition states that the order of the addends does not affect the sum, i.e., a + b = b + a.
The difference between two numbers is the amount by which one number exceeds the other. It is the result of subtracting one number from another and represents the magnitude of the separation between the two values.
Subtraction: The mathematical operation of removing one number from another to find the difference between them.
Negative Number: A number less than zero, representing a value that is less than the reference point.
Absolute Value: The distance of a number from zero on the number line, regardless of its sign.
The product is the result of multiplying two or more numbers or quantities together. It represents the combined or cumulative effect of the factors involved in the multiplication operation.
Factor: A factor is a number or quantity that is multiplied with another to find the product.
Multiplication: Multiplication is the mathematical operation of finding the product by repeatedly adding one of the factors.
Prime Factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
Signed numbers are a set of numbers that include both positive and negative values, represented by a sign (+ or -) in front of the number. They are used to describe quantities that have direction or can be above or below a reference point.
Integers: The set of whole numbers, both positive and negative, including zero.
Absolute Value: The distance of a number from zero on the number line, regardless of its sign.
Number Line: A visual representation of the set of real numbers, with positive numbers to the right of zero and negative numbers to the left.
The coordinate plane is a two-dimensional grid used to represent and analyze the position and relationships of points, lines, and other geometric shapes. It consists of a horizontal x-axis and a vertical y-axis that intersect at a central point known as the origin.
Quadrants: The coordinate plane is divided into four quadrants, labeled I, II, III, and IV, based on the positive or negative values of the x and y coordinates.
Ordered Pair: A set of two numbers that represent the position of a point on the coordinate plane, written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.
Cartesian Coordinate System: The coordinate plane is also known as the Cartesian coordinate system, named after the mathematician and philosopher René Descartes, who developed this system for representing and analyzing spatial relationships.
Integer operations refer to the basic mathematical operations that can be performed on integers, which are whole numbers that can be positive, negative, or zero. These operations form the foundation for working with integers in various mathematical contexts.
Addition: The process of combining two or more integers to find their sum.
Subtraction: The operation of finding the difference between two integers.
Multiplication: The repeated addition of an integer with itself, resulting in a product.
Real numbers are a comprehensive collection of numerical values that encompass all rational and irrational numbers. They represent the complete set of numbers that can be used to describe and quantify the physical world around us, including measurements, quantities, and mathematical relationships.
Integers: Integers are a subset of real numbers that include all positive and negative whole numbers, as well as zero.
Rational Numbers: Rational numbers are real numbers that can be expressed as a ratio of two integers, such as fractions and terminating or repeating decimals.
Irrational Numbers: Irrational numbers are real numbers that cannot be expressed as a ratio of two integers, such as pi (\pi) and the square root of 2 (\sqrt{2}).