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Fractions are a way to represent parts of a whole. They consist of two parts: a numerator and a denominator. Think of fractions as a pizza. The numerator is how many slices you have, whereas the denominator is how many slices make up a whole pizza.

In mathematical notation, a fraction is expressed as \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator. In our exercise, we work with \(-\frac{1}{15}\) and \( \frac{1}{90}\), which means 1 part out of 15 and 1 part out of 90, respectively. It's important to remember that a negative sign in a fraction means you are considering a negative portion of the whole.

When working with fractions, particularly adding or comparing them, it's crucial they have a common denominator. That's where finding the least common denominator (LCD) is so useful. Let's dive deeper into what this means.

The least common multiple (LCM) is a fundamental concept in understanding how to find the least common denominator. It's the smallest number that is a multiple of two or more numbers.

To find the LCM, you need to list the multiples of the numbers in the denominators. Let’s take 15 and 90 as examples. Multiples of 15 are 15, 30, 45, 60, 75, 90, etc., and multiples of 90 are 90, 180, 270, etc. The smallest or 'least' number common in both lists is 90. Therefore, 90 is the LCM of 15 and 90.

Finding the LCM is a crucial step since the LCM of the denominators gives us the least common denominator needed to simplify or compare fractions.

The denominator of a fraction indicates into how many equal parts the whole is divided. It's located below the line in a fraction and is crucial in determining the size of each fractional part. For instance, in the fraction \(\frac{1}{15}\), the whole is divided into 15 parts. Similarly, in \(\frac{1}{90}\), it’s divided into 90 parts.

When dealing with operations involving fractions, like addition or comparison, it's vital to have the same denominators. Why? Because it makes the fractions easy to combine. The simplest way to achieve this is to convert each fraction to an equivalent fraction with the least common denominator (LCD), which ensures consistency.

In finding the LCD, you effectively make the denominators of all fractions within an equation compatible. In our example, we found 90 as the LCD, meaning we can easily perform operations on these fractions without further conversion. Understand this concept simplifies many aspects of working with fractions.