Problem 46 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(-95.23-(-71.7)\)

Step-by-Step Solution

Answer

The result is -23.53.

Step 1: Identify the Operation

The expression given is \(-95.23 - (-71.7)\). We identify that this is a subtraction problem where a negative number is subtracted.

Step 2: Change Subtraction to Addition

Subtracting a negative number is equivalent to adding the positive equivalent of that number. So, \(-95.23 - (-71.7) = -95.23 + 71.7\).

Step 3: Align Decimals

When adding or subtracting decimals, align their decimal points. So, align \(-95.23\) and \(71.70\).

Step 4: Perform the Addition

Starting from the right, add \(71.70\) to \(-95.23\). Calculate:1. In the hundredths place: \(0 + 3 = 3\).2. In the tenths place: \(7 + 2 = 9\).3. Subtract the whole numbers (since \(95.23\) is negative):\(-95 + 71 = -24\). Put these numbers together to get \(-24.30\).

Step 5: Write the Answer

After performing the operation, we find the result is \(-23.53\). This means \(-95.23 - (-71.7) = -23.53\).

Key Concepts

Understanding Negative Numbers

Negative numbers can sometimes feel confusing, especially when you see them in subtraction problems. Let's break it down a bit. A negative number is any number less than zero. You typically see them with a minus sign (-) in front. These are often used to represent values below zero, such as temperatures in winter or bank overdrafts.

• A negative number subtracted from another number turns into addition. For instance, a negative sign followed by another negative becomes a positive.
• In the expression e \(-95.23 - (-71.7)\), the subtraction of (-71.7) is changed to addition: \(-95.23 + 71.7\). This is because two minus signs become a plus.

To think of it simply, subtracting a negative is the same as moving in a positive direction. Keep practicing this concept, and soon it will become second nature!

The Importance of Decimal Alignment

When working with decimals in operations like subtraction or addition, perfect alignment is key. This means lining up the numbers so that each digit falls perfectly in its respective place value column.

• Arrange numbers so the decimal points are directly above each other.
• It's a bit like stacking boxes neatly so none falls over.
• If necessary, add extra zeros to ensure each number has the same length after the decimal, like turning \(71.7\) into \(71.70\) for easy handling.

This clear alignment avoids any mix-up in columns and ensures accurate calculations. Think of decimal points as anchors, holding the numbers steady in place!

Carrying Out Arithmetic Operations

Arithmetic operations are fundamental to solving mathematical problems. They include addition, subtraction, multiplication, and division. In this exercise, we're focusing on adding after converting from a subtraction problem.
Let's explore this further:

• First, turn subtraction into addition when you deal with negative figures, which transforms \(-95.23 - (-71.7)\) into \(-95.23 + 71.7\).
• Proceed by aligning your decimals carefully and calculate step by step from the rightmost digit (hundredths place) to the left (whole number place).
• Adjust for carrying if necessary, similar to when you have more than 10 in a column.

This entire process ensures precision and helps avoid errors. Remember, practice makes perfect, and these operations will become effortless with time!