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Chapter 1: Problem 75

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

Short Answer

Expert verified
-9.9

Step by step solution

01

Understand the Problem

The exercise requires finding the difference between the two decimals -6.4 and 3.5.
02

Rewrite the Equation

Write the expression as i.e. -6.4 - 3.5.
03

Combine Like Terms

Combine the two numbers. Since both numbers are negative, add their absolute values: 6.4 + 3.5 = 9.9.
04

Include the Negative Sign

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

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