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Chapter 0: Problem 93

$$ -0.4-0.9 $$

Short Answer

Expert verified
-1.3

Step by step solution

01

Understand the Operation

This question requires you to perform a subtraction operation between two decimal numbers: $$-0.4 - 0.9$$
02

Rewrite the Operation

Subtraction of a positive number can be thought of as adding a negative number. Rewrite the equation with this understanding: $$-0.4 - 0.9 = -0.4 + (-0.9)$$
03

Combine Negative Numbers

When adding two negative numbers, the result is also negative. Add the absolute values and then apply the negative sign: Absolute values: $$| -0.4 | = 0.4$$ and $$| -0.9 | = 0.9$$ Combine them: $$0.4 + 0.9 = 1.3$$ Apply the negative sign: $$-1.3$$

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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. They are often used to show losses, temperatures below zero, or depths below sea level. In mathematical operations:

- When adding two negative numbers, the result is negative. For example: \(-2 + (-3) = -5\).
- When subtracting a negative number from another, it鈥檚 like adding its positive counterpart. So, \(-4 - (-2)\) becomes \(-4 + 2\) = \(-2\).

Understanding these simple rules can aid in grasping more complex arithmetic involving negative numbers and help in solving problems effectively.
Absolute Value
The absolute value of a number is its distance from zero on a number line without considering the direction. It鈥檚 always positive or zero. Symbolically, it is denoted as \(| x |\).

- For instance, \( | -5 | = 5\) and \( | 3 | = 3 \).
- In our exercise, \( | -0.4 | = 0.4 \) and \( | -0.9 | = 0.9 \).

When adding or subtracting negative numbers with absolute values, first consider the absolute values, perform the operation, and then apply the correct sign based on the original context. This concept is especially useful when combining negative numbers or working with subtraction of decimals.
Decimal Addition
Adding decimals follows the same principles as adding whole numbers, but it is crucial to line up the decimal points to ensure accuracy.

Here鈥檚 a step-by-step approach for our exercise:

1. Align the decimals: Place the numbers one below the other with decimal points aligned: \(0.4\) and \(0.9\).
2. Add normally: Start by adding the digits from right to left, just like whole numbers: \(0.4 \ + \ 0.9 = 1.3\).
3. Apply the sign: Since we originally combined negative numbers, the result remains negative: \(-1.3\).

By mastering decimal addition, students can effectively handle operations involving both positive and negative decimals.

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