Problem 23 - Prealgebra

Question

Name the property shown by each statement. $$7 k+0=7 k$$

Step-by-Step Solution

Answer

Identity Property of Addition.

Step 1: Examine the Equation

The given equation is \(7k + 0 = 7k\). Look at what is being added to \(7k\) and how the equation simplifies.

Step 2: Identify the Added Element

In the equation \(7k + 0\), a zero is being added to the term \(7k\). This operation does not change the value of \(7k\).

Step 3: Recognize the Mathematical Property

When adding zero to any number or expression does not change its value, it demonstrates the Identity Property of Addition.

Key Concepts

addition properties

Addition can be understood through various properties which make mathematical tasks easier and more intuitive. One of the primary properties is the **Identity Property of Addition**. This property states that for any number or expression, adding zero will not alter its value. For example, given the expression \(7k + 0 = 7k\), the \(+0\) part demonstrates this property clearly. No matter how large or small the initial number or expression is, zero acts as a neutral element in addition. Other key properties of addition include:

• **Commutative Property:** Order does not matter; \(a + b = b + a\).
• **Associative Property:** Grouping does not matter; \((a + b) + c = a + (b + c)\).

Understanding these properties helps simplify and solve equations, provides a deeper insight into mathematical structures, and aids in grasping more complex algebraic concepts.

zero in arithmetic

Zero serves as a unique number in arithmetic, with distinct properties that differentiate it from other numbers. In terms of addition, zero acts as the **identity element**, meaning adding zero to any number leaves the original number unchanged. It does practically nothing to a number. In a broader sense, zero plays several roles:

• **In Multiplication:** Any number multiplied by zero equals zero.
• **In Subtraction:** Subtracting zero leaves a number unchanged: \(a - 0 = a\).
• **Division:** Zero divided by any non-zero number is zero, but dividing by zero is undefined.

Zero is essential in positional numeral systems like the decimal system and acts as a placeholder, helping to distinguish between numbers like 50 and 500.

basic algebra concepts

Algebra is a branch of mathematics that uses symbols to represent numbers and express mathematical relationships. At its core, basic algebra involves understanding expressions, equations, and various operations. A fundamental concept is recognizing and applying properties of operations, such as the **Identity Property**, to manipulate and solve equations effectively.
Variables are common in algebra, representing unknown values that help solve for specific quantities. Equations like \(7k + 0 = 7k\) illustrate how simple operations, such as addition, can be analyzed using algebraic principles. Understanding these basics provides the foundation for tackling more complex algebraic problems and exploring advanced topics in mathematics.