Problem 57 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(-8-(-3.686)\)

Step-by-Step Solution

Answer

The result of the operation is -4.314.

Step 1: Identify the Operation

The expression given is \(-8-(-3.686)\), which involves subtraction of a negative decimal. According to the rules of arithmetic, subtracting a negative number is the same as adding its positive counterpart.

Step 2: Convert Subtraction to Addition

Change the expression by removing the subtraction of a negative sign. The expression becomes:\(-8 + 3.686\).

Step 3: Perform the Addition

Align the decimal points and add the numbers as follows:\[-8.000 + 3.686 = -4.314\]Perform the addition while keeping in mind that one number is negative, so you are essentially taking 3.686 away from 8.

Step 4: Determine the Sign

Since -8 is larger in magnitude than 3.686, the result will follow the sign of -8. Therefore, the result will be a negative number.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of the number. These numbers are positioned to the left of zero on a number line. When you deal with negative numbers, it's important to remember:

• They are used to represent things like temperatures below freezing, depths below sea level, or debts.
• Negative numbers can be added, subtracted, multiplied, and divided just like positive numbers but with special rules for addition and subtraction.

When approaching calculations involving negative numbers, keep in mind how they interact with positive numbers, especially in operations like subtraction.

Subtraction Rules with Decimals

Subtraction can sometimes be tricky, especially with negative numbers involved. Let's break down the subtraction of decimals with a focus on important rules:

• To subtract a negative number, you effectively turn the operation into addition. For example, \(-8-(-3.686)\), becomes \(-8+3.686\).
• Always align the decimal points of the numbers in the expression. This helps to ensure accuracy when adding or subtracting decimals.
• Subtracting involves identifying which number is larger in magnitude and using its sign as the result's sign. If the larger number is negative, the final result will be negative.

These rules are crucial for ensuring that you not only execute the arithmetic correctly but also understand why every step is necessary.

Addition of Decimals

Adding decimals is a fundamental arithmetic skill that can be very straightforward if approached correctly:

• Ensure all numbers are aligned by their decimal points. This helps to maintain the place values properly during addition.
• Add the numbers column by column, starting from the rightmost digit, which is the smallest unit, just like whole number addition.
• Remember to bring down the decimal point straight into the answer.

In the given problem, after converting \(-8-(-3.686)\) to \(-8+3.686\), you add \(3.686\) to \(-8\). When handling mixed signs, find the difference between the absolute values and give the sum the sign of the number with the larger absolute value, ensuring you arrive at the correct result of \(-4.314\).