Problem 46 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$-3.47-(-3.47)$$

Step-by-Step Solution

Answer

The result of the indicated subtraction is 0.

Step 1: Identify the subtraction operation

The problem requires us to subtract \( -3.47 \) from \( -3.47 \). Thus our equation is \( -3.47 - (-3.47) \).

Step 2: Change subtraction of a negative to addition

We know mathematically subtracting a negative is the same as adding. Therefore, the equation changes to \( -3.47 + 3.47 \).

Step 3: Perform the addition

Now adding these two values gives us 0. Therefore, \( -3.47 + 3.47 = 0 \).

Key Concepts

Negative Numbers

Negative numbers can often be a bit tricky to understand, especially when dealing with subtraction. A negative number is a number less than zero, and it is represented with a minus sign (-). Understanding how negative numbers interact with each other is essential in algebra.
When you have two negative numbers, like -3.47 and -3.47, interacting through subtraction, it might seem confusing at first. Subtracting a negative number means you effectively move in the opposite direction on the number line. Hence, subtracting -3.47 is like adding its positive counterpart, 3.47.
Here are a few helpful pointers to remember when dealing with negative numbers:

• Think of negative numbers as 'owing' an amount, while positive is 'having' an amount.
• Subtracting a negative number is equivalent to adding the positive equivalent.
• Negative times negative always results in a positive result, while negative times positive results in a negative.

Understanding these basic operations can greatly ease your journey through algebra.

Mathematical Operations

Mathematical operations such as addition, subtraction, multiplication, and division form the building blocks of many algebraic equations. They are the basics you need to confidently tackle complex problems.
Subtraction might seem straightforward, but when it involves negative numbers or variables, it becomes more interesting. For instance, the expression \(-3.47 - (-3.47)\) involves two operations: subtraction and the handling of negative numbers.
In algebra, it's crucial to recognize that:

• Subtraction of a negative number changes to addition.
• Order of operations matters, often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• Simplifying expressions helps in understanding the core problem.

Math operations form the language of equations and instantly become simpler once you practice regularly.

Equality in Equations

Equations are a central aspect of algebra and often involve understanding equality. Equality means that two expressions represent the same value. It’s like saying the left side of the equation balances perfectly with the right side.
When you solve an equation, you aim to maintain equality until you reduce it to a solution. In our example, converting \(-3.47 - (-3.47) = 0\) illustrates maintaining balance by recognizing the equivalence of subtracting a negative and adding a positive.
Keep these in mind when dealing with equations:

• Always perform the same operation on both sides of an equation to maintain equality.
• Recognize that zero acts as the neutral element in addition/subtraction.
• Subtracting a value and then adding the same value maintains a zero balance.

By practicing these principles, equations become less of a challenge and more of an exploration.