Problem 75 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -6.4-3.5 $$

Step-by-Step Solution

Answer

-9.9

Step 1: Understand the Problem

The exercise requires finding the difference between the two decimals -6.4 and 3.5.

Step 2: Rewrite the Equation

Write the expression as i.e. -6.4 - 3.5.

Step 3: Combine Like Terms

Combine the two numbers. Since both numbers are negative, add their absolute values: 6.4 + 3.5 = 9.9.

Step 4: Include the Negative Sign

Since both numbers are negative, the result is also negative. Thus, the final answer is -9.9.

Key Concepts

Negative Numbers

Negative numbers represent values less than zero and are often used to describe deficits, losses, and other situations where values are below a baseline. When dealing with negative numbers:

• If you add a negative number, you move left on a number line.
• Subtracting a negative number is like adding its positive counterpart.

For example, subtracting 3.5 from -6.4 means moving further left into the negative side because you're adding to a deficit. So, -6.4 - 3.5 is the same as \(-6.4 + (-3.5)\).

Absolute Values

Absolute values measure how far a number is from zero on a number line, without considering direction. It is always a positive value or zero. For instance:
\(|-6.4| = 6.4\)
\(|3.5| = 3.5\)
In the given problem, we take the absolute values of both \(-6.4\) and \(3.5\) to calculate \(|-6.4| + |3.5| = 6.4 + 3.5 = 9.9\). However, since we were dealing with negative numbers, the final answer retains the negative sign, resulting in \(-9.9\).

Combining Like Terms

Combining like terms is essential for simplifying expressions. It means adding or subtracting numbers or variables that are of the same type. For negative decimals:

• Combine the absolute values if both numbers are negative or positive.
• Apply the common sign to the result.

In the exercise \(-6.4 - 3.5\), both terms are negative:

• Combine: \(6.4 + 3.5 = 9.9\)
• Apply the negative sign: \(-9.9\)

By understanding and applying these rules, you can correctly solve problems with negative numbers and decimals.