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When subtracting fractions, it's important to have a common denominator. The denominator is the bottom number in a fraction, such as the 5 in \(-\frac{2}{5}\) or the 6 in \(-\frac{7}{6}\). To make it easier to subtract, we rewrite the fractions so they have the same denominator. This is called finding a common denominator.

First, determine the least common multiple (LCM) of the denominators. For our example, the denominators are 5 and 6. The LCM of 5 and 6 is 30. By converting each fraction so they share this common denominator, we make subtraction straightforward.

Converting fractions involves multiplying both the numerator and the denominator by a number that changes the denominator to the LCM without changing the fraction's value.

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For fractions, finding the LCM of the denominators helps in getting a common base to simplify operations like addition or subtraction.

In our example, we found the LCM of the denominators 5 and 6 to be 30. Here’s how:

• Write down the multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40...
• Write down the multiples of 6: 6, 12, 18, 24, 30, 36...
• The smallest number that appears in both lists is 30, so the LCM is 30.

Once we have the LCM, we can convert the fractions to have the same denominators, setting the stage for easy subtraction.

After converting fractions to have a common denominator and performing subtraction, the final step is to simplify the result if possible. Simplifying means reducing the fraction to its simplest form. However, not all fractions can be simplified further.

For instance, after subtracting in our example, we get \(-\frac{47}{30}\). To check if it can be simplified, we look for any common factors between the numerator and the denominator. Since 47 is a prime number (its only factors are 1 and 47), and 30 has no common factors with 47, \(-\frac{47}{30}\) is already in its simplest form.

Understanding and applying these steps—finding common denominators, identifying the least common multiple, and simplifying fractions—can make solving fraction problems clear and straightforward.