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Chapter 1: Problem 16

Evaluate each of the following expressions, if possible. $$\frac{-24}{-8}$$

Short Answer

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Step by step solution

01

Identify the Numbers

The given expression is \( \frac{-24}{-8} \). Identify the numerator (-24) and the denominator (-8).
02

Simplify the Negative Signs

Both the numerator and the denominator have negative signs. Dividing a negative number by another negative number results in a positive number: \( \frac{-24}{-8} = \frac{24}{8} \).
03

Perform the Division

Now perform the division \( \frac{24}{8} = 3 \). This is the simplified form of the expression.

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Key Concepts

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

Numerator and Denominator
In any fraction, the numerator and denominator are two critical components. These terms refer to the top and bottom parts of a fraction, respectively. For example, in the fraction \(\frac{-24}{-8}\),
  • The numerator is -24, which is the number above the fraction line.
  • The denominator is -8, which represents the number below the fraction line.

The concept of numerator and denominator is foundational in algebra and arithmetic, where we frequently encounter fractions. Always remember:
  • The numerator signifies how many parts we have.
  • The denominator indicates into how many equal parts the whole is divided.

When evaluating expressions, correctly identifying these parts helps in applying various mathematical operations such as division and simplification.
Simplifying Negative Signs
Simplifying negative signs is an important skill in algebra. When both the numerator and the denominator of a fraction are negative, the negatives cancel each other out, resulting in a positive number. This is because dividing two negative numbers yields a positive result.
Consider the fraction \(\frac{-24}{-8}\): Both the numerator (-24) and the denominator (-8) come with negative signs.

According to the rule of signs in mathematics:
  • When dividing two numbers with the same sign, the result is positive.
  • This applies to both negative and positive numbers.

So, \(\frac{-24}{-8} = \frac{24}{8}\). By removing the negative signs, the expression simplifies to \(\frac{24}{8}\). This simplification step makes the actual division easier to handle.
Division in Algebra
Division is a fundamental operation in algebra. When dealing with fractions or expressions that involve division, following a structured approach simplifies the process. For example, after simplifying \(\frac{-24}{-8}\) to \(\frac{24}{8}\), we perform the division:
  • First, recognize how many times the denominator fits into the numerator.
  • The expression \(\frac{24}{8}\) asks how many times 8 goes into 24.

Performing the division gives:
\(\frac{24}{8} = 3\)
When you simplify fractions, you make calculations more manageable and easier to understand. Practice dividing both positive and negative numbers to become more comfortable with these operations.
Remember, when it comes to division in algebra:
  • Always simplify negative signs first.
  • Divide the numbers as you would with whole numbers.
  • Clearly identify the numerator and denominator.

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Most popular questions from this chapter

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