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Chapter 1: Problem 13

Evaluate each of the following expressions, if possible. $$\frac{-30}{6}$$

Short Answer

Expert verified
-5

Step by step solution

01

Identify the Numerator and Denominator

The given expression is \(\frac{-30}{6}\). Here, the numerator is -30 and the denominator is 6.
02

Simplify the Fraction

To simplify the fraction \(\frac{-30}{6}\), divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 30 and 6 is 6.
03

Perform the Division

Divide the numerator and the denominator by their GCD: \(\frac{-30 \div 6}{6 \div 6} = \frac{-5}{1}\). Simplifying this gives -5.
04

Write the Final Answer

The simplified value of the expression is -5.

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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, you'll find two parts, the **numerator** and the **denominator**. The numerator is the number above the fraction bar, and it represents how many parts we are talking about. The denominator is the number below the fraction bar, and it shows how many equal parts the whole is divided into. For example, in \[\frac{-30}{6}\], -30 is the numerator, and 6 is the denominator. Understanding these terms is crucial as they are the basics of working with fractions.
Always identify these before performing any operations with fractions, as they dictate how the fraction behaves when simplified or manipulated.
Greatest Common Divisor
The **Greatest Common Divisor (GCD)** is the largest number that can evenly divide both the numerator and the denominator. Finding the GCD is essential when simplifying fractions. For instance, when given the fraction \[\frac{-30}{6}\], one must find the GCD of 30 (ignoring the sign for GCD calculations) and 6. The GCD of these numbers is 6.
Here's a quick way to find the GCD:
  • List out all the divisors of each number.
  • Identify the largest number that appears in both lists
Hence, knowing the GCD allows you to divide both parts of the fraction correctly and achieve the simplest form.
Division
Once you have the GCD, the process of division helps simplify the fraction. By dividing both the numerator and denominator by the GCD, you reduce the fraction to its simplest form. For example, in the fraction \[\frac{-30}{6}\], dividing both the numerator and the denominator by their GCD (which is 6) results in:

\[\frac{-30 \div 6}{6 \div 6} = \frac{-5}{1}\]
This simplification shows that the fraction \[\frac{-30}{6}\] is equivalent to -5. This process of division ensures you are representing the fraction in the most reduced terms possible. Always perform this division step correctly to avoid errors.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.831-0.746-0.294$$

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Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$2 \frac{1}{3}$$

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