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Chapter 2: Problem 71

Divide the real numbers, if possible. $$\frac{204}{-6}$$

Short Answer

Expert verified
The result is \(-34\).

Step by step solution

01

Identify the Numerator and Denominator

The given problem is a fraction \(\frac{204}{-6}\). Here, 204 is the numerator, and -6 is the denominator.
02

Perform the Division

Divide the numerator by the denominator: \[ \frac{204}{-6} = 204 \div -6 \]
03

Calculate the Result

Performing the division, \(\frac{204}{-6} = -34\).

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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 top number is called the numerator and the bottom number is the denominator. For example, in the fraction \(\frac{204}{-6}\), the numerator is 204, and the denominator is -6. The numerator represents the number of parts we have, while the denominator indicates how many parts make up a whole. Understanding the roles of the numerator and denominator is crucial for performing arithmetic operations on fractions.
negative numbers
Negative numbers are numbers less than zero. They are written with a minus sign (-) in front. In our example, -6 is a negative number. When working with negative numbers, they follow specific rules of arithmetic. For instance, when dividing a positive number by a negative number, the result is a negative number. This property is essential for accurate calculations and understanding the result of a division involving negative numbers.
fraction division
Dividing fractions involves performing division with the numerator and the denominator. In our example, we want to divide 204 by -6. To do this, we rewrite the fraction: \(\frac{204}{-6} = 204 \div -6\). By performing the division, this yields -34. Remember, when you divide two numbers and one of them is negative, the outcome will be negative. This rule helps simplify the process of dividing fractions, especially when dealing with negative numbers.
real numbers arithmetic
Real numbers include both positive and negative numbers, as well as zero. Arithmetic operations such as addition, subtraction, multiplication, and division can be performed with real numbers. In our division example, 204 and -6 are both real numbers. We follow the standard division rules to find that 204 divided by -6 equals -34. Understanding real numbers and their properties allow us to handle complex arithmetic operations efficiently.

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Most popular questions from this chapter

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$|a|+|b|$$

a. What number must be multiplied by \(-4\) to obtain \(-36 ?\) b. What number must be multiplied by \(-4\) to obtain \(36 ?\)

Perform the indicated operation. $$(-9)(-12)$$

Translate each English phrase to a mathematical expression. Then simplify. Subtract 10 from 16

Translate the English phrase to a mathematical expression. Then simplify. \(-108\) divided by \(-4\)
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