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Chapter 1: Problem 97

Divide. $$ \frac{-100}{25} $$

Short Answer

Expert verified
-4

Step by step solution

01

Identify the Numerator and Denominator

The given fraction is \( \frac{-100}{25} \). In this case, the numerator is -100 and the denominator is 25.
02

Simplify the Signs

Since the numerator is -100 (a negative number) and the denominator is 25 (a positive number), the result of the division will be negative.
03

Perform the Division

Divide the absolute value of the numerator by the denominator: \( \frac{100}{25} = 4 \). Since the answer has a negative sign, the result is -4.

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Key Concepts

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

Simplifying Signs
When working with fractions, particularly during division, understanding the signs (positive and negative) is crucial. One of the first steps is to identify the sign of the not only the numbers involved but also the resulting quotient.

To simplify the signs, examine both the numerator and the denominator:
  • If both are positive, the result is positive.
  • If both are negative, their division result is also positive.
  • If one is positive and the other is negative, the result will be negative.
In this exercise, \(\frac{-100}{25}\), we see that -100 is negative and 25 is positive. So, the end result must be negative. Recognizing this at the start helps set the right expectations for the remainder of the steps.
Absolute Value
Absolute value is a fundamental concept in mathematics. It represents the magnitude of a number without considering its sign.

The symbol for absolute value is two vertical bars around the number, such as \(|-100|\). The absolute value tells us how far a number is from zero on a number line without worrying about whether it is positive or negative. For example, both -3 and 3 have an absolute value of 3.

In the given exercise, \(\frac{-100}{25}\), we take the absolute value of the numerator -100, which becomes 100. This allows us to focus on the quantitative aspect of division before reapplying the necessary sign.
Division of Integers
Dividing integers involves a few specific rules that help simplify calculations. It's essential to manage both magnitude and signs correctly. Here's a step-by-step approach:
  • Identify the absolute values: As we did with \(\frac{-100}{25}\), changing -100 to its absolute value, 100.
  • Perform the division: Simply divide the absolute values. Here, dividing 100 by 25 yields 4.
  • Update the sign: Based on step 1, decide if the result should be positive or negative. Since our numerator and denominator had opposite signs, the result is negative.
Thus, the complete solution gives us -4 as the final result.

Handling division in this manner ensures a systematic, accurate approach, minimizing errors especially when dealing with negative numbers.

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