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Chapter 1: Problem 20

Evaluate each of the following expressions, if possible. $$\frac{-10}{0}$$

Short Answer

Expert verified
The expression \frac{-10}{0}\ is undefined because division by zero is not possible.

Step by step solution

01

Understand Division by Zero

The denominator of the fraction is zero. Any number divided by zero is undefined in mathematics.
02

Conclusion

Since the expression involves division by zero, it cannot be evaluated.

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Key Concepts

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

undefined expressions
In mathematics, some expressions cannot be given a definitive value. One common type is an undefined expression. This usually occurs when there's a division by zero.
Let's break it down: Imagine you have an expression like \(\frac{-10}{0}\). The fraction \(\frac{a}{b}\) is only valid when \(b \eq 0\). If the denominator is zero, the expression doesn't make sense and is considered undefined.
Why? Because division by zero defies the basic properties of numbers and arithmetic operations.
For example, if we try to divide 10 by 0, asking how many times 0 fits into 10 is impossible since multiplying 0 by any number still yields 0.
Thus, dividing by zero produces an undefined expression.
fractions
A fraction represents a part of a whole or, more simply, division between two numbers.
It is written as \(\frac{a}{b}\), where \(a\) is the numerator (top number) and \(b\) is the denominator (bottom number).
Fractions show how many parts we have and how many such parts make up one whole.
If the numerator is zero, the fraction equals zero.For instance, \(\frac{0}{5} = 0\).
If the denominator is zero, the fraction is undefined, as seen in \(\frac{5}{0}\).
This is because you can't have a whole divided into zero parts. It doesn't make sense mathematically or practically.
elementary algebra
Elementary algebra deals with the basic properties of numbers and the rules governing the operations performed on them.
It introduces variables to represent unknown values and uses algebraic expressions and equations to solve problems.
One fundamental aspect is understanding the constraints of operations, such as division.
In algebra, dividing by zero is not allowed. It's a rule that's part of the foundational properties of numbers.
This ensures that expressions and equations remain consistent and meaningful.
So, when working with algebraic expressions like \(\frac{a}{b}\), always check if the denominator \(b\) is non-zero to avoid undefined results.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.8-9.2(3.4-1.6)$$

Evaluate the given expression. Remember to follow the order of operations. $$6+4(3+2)$$

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. $$0.24$$

Sketch the given set on a number line. $$\\{x |-3 \leq x \leq 2\\}$$

Graph the given set on a number line. $$\\{0,3,7\\}$$
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