Problem 52 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(-4.95-96.89\)

Step-by-Step Solution

Answer

The result is \(-101.84\).

Step 1: Identify the Operation

The given expression is \(-4.95 - 96.89\). This tells us that we need to subtract two decimal numbers with like signs, meaning both numbers are negative.

Step 2: Add the Absolute Values

When subtracting two negative numbers, we are essentially adding their absolute values and keeping the sign negative. Calculate the absolute values: \(4.95 + 96.89 = 101.84\).

Step 3: Apply the Sign

Since both original numbers were negative, the result will also be negative. So, we apply the negative sign to the sum: \(-101.84\).

Key Concepts

Absolute Values

Absolute value is a foundational concept in mathematics, essential for correctly performing operations with negative numbers. Think of absolute value as a number's distance from zero on a number line, ignoring any negative signs. For example, the absolute value of

• -5 is 5, because it is 5 units away from zero.
• Similarly, the absolute value of 4.95 is simply 4.95.

Understanding absolute values is crucial when dealing with negative numbers, especially in subtraction problems. This is because when you subtract a negative number, you actually add the absolute values of both numbers together. In our problem, although we have -4.95 and -96.89, the operation calls for the sum of their absolute values. This makes the addition of 4.95 and 96.89 straightforward, as these numbers are simply distances away from zero.

Negative Numbers

Negative numbers are numbers that are less than zero, often represented with a minus sign (-). They appear commonly in real-world situations, such as temperatures below freezing or financial debts. Working with negative numbers can sometimes be tricky, especially when it comes to arithmetic operations.

When subtracting with negative numbers, remember these key points:

• Subtracting a negative number is akin to adding its absolute value.
• Combining two negative numbers as in -4.95 -96.89 involves adding their absolute values.

It is important to maintain the negative sign in your final result when adding negatives. This is because two negative numbers together become a larger negative number, evidenced in the solution to our problem, where -4.95 - 96.89 equals -101.84.

Decimal Arithmetic

Decimal arithmetic deals with numbers that have decimal points. These numbers, also known as decimals, are simply fractions written in a different format. Managing decimal arithmetic requires careful alignment of the decimal points to ensure correct addition or subtraction.

Here are a few tips when working with decimal numbers:

• Always align the decimal points vertically.
• Fill in any empty spaces with zeros if necessary to keep the calculation neat.
• Perform calculations on the right of the decimal point first, moving to the left.
• Keep the decimal point in line in the final result.

When faced with an expression such as -4.95 - 96.89, ensure that you align decimal points and add the numbers accurately. The correct alignment allows you to find the absolute sum, 101.84 in this case, and then apply the appropriate negative sign based on the original signs of the numbers.