Problem 26 - Algebra A Combined Function

Question

Subtract. \(-6.1-(-5.3)\)

Step-by-Step Solution

Answer

The result is \(-0.8\).

Step 1: Identify the Operation

The expression given is \(-6.1 - (-5.3)\). We need to perform a subtraction operation, but notice that the number we are subtracting is negative.

Step 2: Simplify the Expression

Subtracting a negative number is the same as adding its positive counterpart. Therefore, \(-6.1 - (-5.3)\) is equivalent to \(-6.1 + 5.3\).

Step 3: Perform the Addition

Now we need to add \(5.3\) to \(-6.1\). Start by subtracting the smaller absolute value from the larger one. \(|-6.1| = 6.1\) and \(|5.3| = 5.3\). So, \(6.1 - 5.3 = 0.8\). Since \(|-6.1|\) is larger, the result will be negative. Thus, \(-6.1 + 5.3 = -0.8\).

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation. It involves taking one number away from another, to find the difference between them. When looking at an expression like \(-6.1 - (-5.3)\), the key to solving it is understanding how subtraction interacts with the numbers involved.

• Standard subtraction: Involves directly subtracting one number from another. Example: \(7 - 3 = 4\).
• Subtracting a negative number: Changes this to an addition operation. For example: \(7 - (-3)\) becomes \(7 + 3\).

Subtraction becomes especially interesting when combined with negative numbers, requiring deeper understanding of negative values in mathematics.

Negative Numbers

Negative numbers are numbers less than zero and are represented with a minus sign. Understanding them is crucial when dealing with subtraction situations like in our problem.

• Identifying negative numbers: They always have a \'-\' sign, such as \(-6.1\).
• Behavior in operations: When a negative number is subtracted, it turns into an addition. For example,\(-(-5.3)\) becomes \(+5.3\).
• Comparison: Negative numbers are always less than any positive number. \(-6.1\) is less than \(-5.3\), even though 6.1 is larger in absolute terms.

Handling negative numbers correctly can simplify otherwise challenging arithmetic operations.

Absolute Value

The absolute value of a number refers to its distance from zero on a number line, disregarding any negative sign. It helps us measure the size or magnitude of numbers, which is useful when combining or comparing numbers.

• Definition: Absolute value is denoted by vertical bars, like \(|-6.1|\) which equals 6.1.
• Use in subtraction: Understand which number has a larger absolute value to determine the direction of the result. With \(-6.1 + 5.3\), the absolute value of \(6.1\) is greater than \(5.3\), hence the negative result.
• Simplifying Calculations: For \(-6.1 + 5.3\), subtract \(5.3\) from \(6.1\) using absolute values and maintain the sign of the number with the largest absolute value.

This approach makes it easier to solve subtraction problems, especially with negative numbers involved.

Arithmetic Operations

Arithmetic operations form the basics of mathematics and include addition, subtraction, multiplication, and division. Each operation has its role and rules:

• Addition: Combining two numbers. For positive and negative numbers, add their absolute values but keep the sign of the larger original number.
• Subtraction: Taking away one number from another, which sometimes can turn into addition when negative numbers are involved.
• Multiplication & Division: Beyond our current focus, used to scale numbers up or down but obeying the sign rules.

Understanding these basic operations is crucial for mastering more complex mathematical concepts and successfully solving various problems, like the one presented. With consistent practice, these operations become second nature, allowing for efficient problem-solving.