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Chapter 1: Problem 451

Simplify. $$ \frac{n}{5}-\frac{4}{5} $$

Short Answer

Expert verified
\frac{n - 4}{5}

Step by step solution

01

Identify common denominators

Observe that the fractions \(\frac{n}{5}\) and \(\frac{4}{5}\) already have a common denominator, which is 5.
02

Combine the fractions

Since the denominators are the same, combine the fractions by subtracting the numerators: \(\frac{n}{5} - \frac{4}{5} = \frac{n - 4}{5}\).
03

Final answer

The simplified form of the expression is \(\frac{n - 4}{5}\).

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Key Concepts

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

Common Denominator
Before you can combine or subtract fractions, you need to have the same denominator for each fraction. The denominator is the bottom number of each fraction. If the denominators are already the same, like in the exercise \(\frac{n}{5} - \frac{4}{5}\), you don't need to do any extra steps to find a common denominator.

This is important because fractions must refer to the same size parts to be compared, subtracted, or added accurately. Just think of it like comparing pieces of a pizza; the pieces must be of the same size to directly compare them.
Combining Fractions
Once you have established a common denominator, you can combine the fractions. Adding and subtracting fractions is straightforward when the denominators match. In our given exercise, since both fractions have the same denominator (5), we can directly combine them by focusing on their numerators.

For example, to combine \(\frac{n}{5}\) and \(\frac{4}{5}\):
  • Keep the common denominator the same.
  • Combine the numerators through addition or subtraction.

In our case, subtracting the numerators gives us \(n - 4\). Therefore, our combined fraction becomes \(\frac{n - 4}{5}\).
Subtracting Fractions
Subtracting fractions with the same denominator is made simple: you only need to subtract the numerators and keep the denominator constant. Using the exercise as an example, \(\frac{n}{5} - \frac{4}{5}\):
  • Identify the fractions have a common denominator of 5.
  • Subtract the numerators: \(n - 4\).
  • Place the result over the common denominator: \(\frac{n - 4}{5}\).

So, subtracting fractions when they share the same denominator simplifies to dealing with only the numerators and placing the result back over the shared denominator.

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