Problem 62 - Elementary and Intermediate Algebra

Question

Add. $$ 0+(-2.14) $$

Step-by-Step Solution

Answer

The sum is -2.14.

Step 1: Understanding the Problem

We need to find the sum of 0 and -2.14. This is a straightforward addition problem involving zero and a negative number.

Step 2: Identifying the Rule

Recall that adding zero to any number results in the number itself. Thus, adding 0 to -2.14 will not change the value of -2.14.

Step 3: Executing the Addition

Apply the rule: \(0 + (-2.14) = -2.14\). The sum remains the same as the negative number because zero does not alter the sum.

Key Concepts

Addition Properties

Addition is one of the basic arithmetic operations that combines two numbers to produce a sum. The properties of addition help us understand how different numbers interact when summed. The two most pertinent properties of addition in our context are the **Commutative Property** and the **Associative Property**.

• **Commutative Property:** This property states that the order of numbers does not affect the sum. In mathematical terms, if you have two numbers, say 'a' and 'b', then \(a + b = b + a\).
• **Associative Property:** This allows us to group numbers in an addition operation in any manner. Mathematically, for any three numbers, 'a', 'b', and 'c', we have \((a + b) + c = a + (b + c)\).

These properties simplify calculations and provide flexibility when solving problems. While our given problem involves zero, these properties become more relevant when handling larger sets of numbers.

Zero Property of Addition

One crucial aspect of addition is the zero property. Imagine zero as a gentle friend who politely joins the party but never overshadows anyone else. Whenever you add zero to any number, that number maintains its identity, unchanged. Mathematically, if you have any number 'a', then \(a + 0 = a\).
The zero property is especially useful in simplifying problems. It quickly informs us that the sum of zero and any number remains the same as that number.
In our exercise involving \(0 + (-2.14)\), applying the zero property tells us immediately that the result is \(-2.14\). This property saves time and ensures accuracy in arithmetic operations.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics, involving addition, subtraction, multiplication, and division. Each operation has its own rules and properties to make calculations easier. In this context, the focus is on addition, specifically when involving negative numbers.
Adding a negative number is actually similar to subtracting its absolute value. For instance, adding \(-2.14\) is the same as subtracting 2.14 from zero. In practice, when a number is summed with zero, addition doesn't alter its value, thanks to the zero property.
Understanding each arithmetic operation's role and effect becomes essential in solving operations involving different types of numbers, ensuring we can navigate through more complex problems efficiently.