Problem 26 - Beginning and Intermediate Algebra

Question

Subtract. See Examples 1 through 5 $$ -6.1-(-5.3) $$

Step-by-Step Solution

Answer

-0.8

Step 1: Understand the Expression

The given expression is \(-6.1 - (-5.3)\).It involves the subtraction of a negative number. Recall that subtracting a negative number is equivalent to adding its positive counterpart.

Step 2: Remove Parentheses

Rewrite the expression by removing parentheses, applying the rule that subtracting a negative is the same as adding the positive:\(-6.1 - (-5.3)\) becomes \(-6.1 + 5.3\).

Step 3: Perform the Addition

Now, simply add \(-6.1 + 5.3\) as you would with any numbers. Think of this as \(-6.1 + 5.3\) equals \(-6.1 + 5.3\) which results in \(-0.8\).

Step 4: Interpret the Result

The result of the subtraction problem is \(-0.8\). This makes sense, as starting at \(-6.1\) and moving 5.3 units toward the positive direction lands you at \(-0.8\).

Key Concepts

Negative Numbers

Negative numbers can sometimes be confusing, especially if you're new to them. Simply put, negative numbers are those that are less than zero. They are typically shown with a minus sign in front, like - (-1, -2, -3, etc.), and they represent values that are below zero. These numbers are often used to denote losses, temperatures below freezing, or even debts.

• Definition: Any number less than zero.
• Notation: Represented with a minus sign (-) before the number.
• Concept: Think of these numbers as what you owe or have spent.

Remember, moving left on the number line heads into the negative territory, which is critical when solving math problems involving these numbers.

Addition of Numbers

Addition of numbers is one of the four fundamental arithmetic operations. It involves adding one number to another, which is straightforward with positive numbers. However, it becomes interesting with negative numbers. When you add a positive number, you move to the right on the number line. But when adding a negative number, you move to the left.

• Positive + Positive: Simple addition.
• Negative + Negative: Like adding two positive numbers but results in a bigger negative number.
• Negative + Positive / Positive + Negative: Subtract the smaller absolute value from the bigger one, and the result takes the sign of the number with the larger absolute value.

Mastering the addition of negatives and positives is crucial for understanding more complex math operations.

Parentheses in Math Expressions

Parentheses in math expressions are used to indicate which operations should be completed first. They are essential for clarifying expressions and ensuring accurate calculations. In our problem, we saw how the subtraction of a negative number - \(-(-5.3)\) - was turned into an addition by removing the parentheses.

• Order of Operations: Parentheses alter the order in which operations are performed. Always solve expressions inside parentheses first.
• Subtraction: Changing subtraction to addition can simplify problems, such as changing \(-a - (-b)\) to \(-a + b\).
• Clarity: Use parentheses to make clear which parts of expressions should be handled together.

Effectively using parentheses allows for clearer and more easily solvable expressions.

Interpreting Results in Math

After solving a mathematical expression, understanding the result is critical. Interpreting results helps in verifying the solution and connects mathematical operations to real-life scenarios. In our exercise, we determined the expression \(-6.1 + 5.3 = -0.8\) and interpreted it as moving from - \(-6.1\) - towards positive by \(5.3\) units.

• Verification: Always double-check your calculations to ensure the result makes logical sense.
• Contextual Understanding: Relate the result to a real-life scenario for better comprehension.
• Result Accuracy: Ensure accuracy, especially with negative numbers, to avoid errors in interpretations.

Understanding and interpreting results bridges your problem-solving skills with practical applications.