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When working with negative numbers, the key is to understand how they behave in operations like multiplication. A negative number is a number less than zero.
For example, \(-5\) is a negative number. When you multiply a positive number by a negative number, the result is always negative.
So, in the exercise, \(\frac{1}{3} \times (-123)\), we expect a negative result. Multiplying 1 by \(-123)\) gives us \(-123\). When this result is divided by 3, it remains negative, therefore the final fraction is \(\frac{-123}{3} = -41\).
Always remember, \(-\times += -\) and \(-\times - = +\).

Simplifying fractions is the process of making the fraction as simple as possible. This involves turning it into its lowest terms.
You can simplify a fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
In our example, \(\frac{-123}{3}\), we check if the numerator \(-123\) and the denominator \(3\) have any common factors. Since 3 is itself a factor of -123, we can simplify further by dividing both the numerator and the denominator by 3.
Thus, \(\frac{-123 \div 3}{3 \div 3} = \frac{-41}{1} = -41\).
Simplifying fractions makes calculations easier and helps in understanding the result better.

Basic arithmetic involves adding, subtracting, multiplying, and dividing numbers. Understanding these operations is essential for solving any math problem.
In this exercise, we focus on multiplication and division. Multiplication of fractions involves multiplying the numerators together and the denominators together. For example, \(\frac{a}{b} \times c = \frac{a \times c}{b} \).
Here, \(\frac{1}{3} \times (-123)\) simplifies to \(\frac{1 \times (-123)}{3} = \frac{-123}{3} = -41\) through straightforward multiplication followed by division.
Practicing arithmetic operations like this ensures better understanding and quicker problem-solving.
Breaking down each step and verifying them ensures accuracy and clarity in solutions.
Besides, being familiar with these basics lays a strong foundation for more complex mathematical concepts.