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Chapter 4: Problem 25

Simplify if possible. $$\frac{-3}{0}$$

Short Answer

Expert verified
The expression \( \frac{-3}{0} \) is undefined.

Step by step solution

01

Identify the Problem

The given problem is to simplify \( \frac{-3}{0} \) if possible. This requires understanding division by zero.
02

Division by Zero

Any number divided by zero is undefined in mathematics. Dividing by zero does not produce a finite or meaningful value.
03

Conclusion

Since \( \frac{-3}{0} \) involves division by zero, the expression is undefined and cannot be simplified to a meaningful numerical result.

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Key Concepts

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

simplifying expressions
Simplifying expressions often involves making them easier to understand or solve. It could mean combining like terms, factoring, or reducing fractions. In some cases, expressions can be simplified to a single number or a more compact form. However, the basic rules of arithmetic apply. When given an expression, one always has to check if any rules or special cases impact the ability to simplify it.
undefined expressions
Undefined expressions occur when an expression cannot produce a meaningful or finite result. A common instance is division by zero. For example, in the provided problem, simplifying \( \frac{-3}{0} \) results in an undefined expression. Since dividing any number by zero does not result in a defined value, such expressions don't have a solution in the realm of real numbers. Thus, \( \frac{-3}{0} \) is classified as undefined.
basic arithmetic rules
Understanding basic arithmetic rules is crucial for solving mathematical problems correctly. Some fundamental rules include:
  • Addition: Combining numbers.
  • Subtraction: Finding the difference between numbers.
  • Multiplication: Repeated addition of a number.
  • Division: Splitting a number into equal parts.
One critical rule of division is that you cannot divide by zero. Dividing by zero disrupts the arithmetic balance, causing the result to be undefined. This is why, when simplfying expressions, division by zero is flagged and deemed unsolvable.

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Most popular questions from this chapter

How many fifths are in \(2 \frac{3}{5} ?\)

Divide. Write the quotient as a mixed number. $$5281 \div 5$$

Simplify the expression. $$\frac{18 p q r}{6 q}$$

For a recent year, the population of the United States was reported to be \(296,000,000\). During the same year, the population of California was \(36,458,000\). a. Round the U.S. population to the nearest hundred million. b. Round the population of California to the nearest million. c. Using the results from parts (a) and (b), write a simplified fraction showing the portion of the U.S. population represented by California.

Divide. Write the quotient as a mixed number. $$7213 \div 8$$
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