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When we subtract fractions, they must share the same denominator. A common denominator helps us align the fractions for easy subtraction. Imagine trying to compare slices of cakes of different sizes; converting both cakes to have the same number of slices makes it simpler to understand. In our example problem, we have \(\frac{7}{8}-\frac{1}{16}\). To subtract these fractions, we first need to identify a number that both 8 and 16 can divide into without leaving a remainder. This number is called the least common multiple (LCM). Once we find this common denominator, we can convert each fraction to have the same denominator and proceed with the subtraction.

The least common multiple (LCM) is the smallest number that two or more denominators share. It's essential for adding or subtracting fractions because it allows us to convert each fraction so they share the same denominator. For our exercise, we need the LCM of 8 and 16. Since 16 is a multiple of 8, the LCM is 16. Let's look at why:

• Multiples of 8: 8, 16, 24, 32, ...
• Multiples of 16: 16, 32, 48, ...

As you can see, 16 is the smallest number that appears in both lists. By knowing the LCM, we can change \(\frac{7}{8}\) so that it has a denominator of 16, making our subtraction possible. We do this by multiplying both the numerator and denominator of \(\frac{7}{8}\) by 2, resulting in \(\frac{14}{16}\).

After performing arithmetic with fractions, the last step is to simplify the result. Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. In our example, after converting and subtracting the fractions, we get \(\frac{13}{16}\). To check for simplification, we look to see if both 13 and 16 can be divided by the same number. Since 13 is a prime number and doesn't divide evenly into 16, \(\frac{13}{16}\) is already in its simplest form. Simplifying fractions makes your answers neat and easy to understand. Remember, always check if both the numerator and denominator have common factors, and reduce as much as possible.