Identity Property

The identity property, also known as the identity element, is a property that states that a specific mathematical operation leaves a number unchanged when it is combined with a certain value. The identity property differs based on the operation being performed (addition or multiplication).

Addition Identity Property

The identity property of addition states that the sum of any number and zero is the original number. In other words, when you add zero to any number, the result is that original number.

For example:
5 + 0 = 5
-3 + 0 = -3

Multiplication Identity Property

The identity property of multiplication states that the product of any number and one is the original number. In other words, when you multiply any number by one, the result is that original number.

For example:
7 * 1 = 7
-4 * 1 = -4

Study Guide

Here are some key points to remember about the identity property:

Identity property of addition: a + 0 = a
Identity property of multiplication: a * 1 = a
The identity element for addition is 0, and for multiplication is 1.
These properties are fundamental in understanding how numbers behave under addition and multiplication.

When working with problems involving addition or multiplication, always keep the identity properties in mind to simplify calculations and understand the behavior of the numbers involved.

Remember to apply the correct identity property based on the operation being performed, whether it's addition or multiplication.

Understanding the identity property is essential for building a strong foundation in arithmetic and algebraic concepts.

Practice problems:

Calculate the following using the identity property of addition: 12 + 0 = ?
Calculate the following using the identity property of multiplication: 5 * 1 = ?

By mastering the identity property and practicing related problems, you'll gain a solid understanding of this fundamental concept in mathematics.

◂Math Worksheets and Study Guides Eighth Grade. Linear equations

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Geometry: Given a line in a coordinate plane, students understand that all 'slope triangles' - triangles created by a vertical 'rise' line segment (showing the change in y), a horizontal 'run' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line.