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Chapter 1: Problem 96

Divide. $$ \frac{-18}{-6} $$

Short Answer

Expert verified
The quotient is 3.

Step by step solution

01

- Identify the numerator and denominator

The numerator is the number on top of the fraction, which in this case is -18. The denominator is the number on the bottom of the fraction, which is -6.
02

- Divide the absolute values

Divide the absolute value of the numerator by the absolute value of the denominator: \[ \frac{18}{6} = 3 \]
03

- Determine the sign of the quotient

Since both the numerator and the denominator are negative, their quotient will be positive. The product or quotient of two numbers with the same sign (both positive or both negative) is always positive.
04

- Combine the results

Combine the results from steps 2 and 3 to get the final answer. Thus, \[ \frac{-18}{-6} = 3 \]

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Key Concepts

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

Understanding Numerator and Denominator
When dealing with fractions, it's important to understand the roles of the numerator and the denominator. The numerator is the top number in a fraction. It represents how many parts of the whole are being considered. In our exercise, the numerator is -18.
On the other hand, the denominator is the bottom number in a fraction. It shows the total number of equal parts the whole is divided into. For our problem, the denominator is -6.

By clearly identifying these two components, we can move on to solving the fraction problem.
Absolute Value and Its Importance
The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute value of -18 is 18, and the absolute value of -6 is 6.
Absolute value is crucial when dividing fractions because it allows us to simplify division without worrying about the signs. We just focus on the magnitude of the numbers.

So, in our exercise, we convert \(-18\) and \(-6\) into their absolute values, getting 18 and 6. Then, we divide these values: \(\frac{18}{6} = 3\).
Determining the Signs of Results
After working with absolute values, we must determine the sign of our answer. Remember, the product or quotient of two numbers is:
  • Positive if both numbers are either positive or both are negative.
  • Negative if one number is positive and the other is negative.
In our case, since both the numerator (-18) and the denominator (-6) are negative, the quotient will be positive.

Therefore, \(\frac{-18}{-6} = 3\). Combining all steps, we get the final result as 3.

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Most popular questions from this chapter

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ (-4)^{2} $$

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