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Chapter 4: Problem 628

In the following exercises, subtract. $$\frac{4}{5}-\frac{y}{5}$$

Short Answer

Expert verified
\(\frac{4-y}{5}\)

Step by step solution

01

Identify the Common Denominator

Notice that both fractions, \(\frac{4}{5}\) and \(\frac{y}{5}\), have the same denominator (5). This means you can directly subtract the numerators.
02

Subtract the Numerators

Subtract the numerators of the fractions while keeping the common denominator: \(\frac{4-y}{5}\).
03

Simplify the Expression

There is no further simplification needed since the expression \(\frac{4-y}{5}\) is already in its simplest form.

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Key Concepts

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

Common Denominator
When subtracting fractions, having a common denominator is essential. The common denominator allows us to combine or subtract the fractions easily.
The denominator is the bottom part of a fraction that shows the total number of equal parts. In the exercise \( \frac{4}{5} - \frac{y}{5} \), both fractions already have the same denominator, which is 5.
Since they have the same denominator, you can directly move on to subtracting the numerators.
Remember: If the denominators are different, you would need to find a common denominator first before subtracting. You can do this by finding the Least Common Multiple (LCM) of the two denominators.
Subtracting Fractions
Once you have a common denominator, the next step is subtracting fractions. To subtract fractions, you only need to work with the numerators (the top parts of the fractions). The common denominator stays the same.
In the given exercise, you subtract the numerators 4 and y, and keep the common denominator 5:
\(\frac{4}{5} - \frac{y}{5} = \frac{4 - y}{5}\).
This step is straightforward since you simply combine the numerators over the shared denominator.
Make sure to place the new numerator in parentheses if needed, especially when it involves multiple terms.
Simplifying Expressions
Finally, after subtracting the fractions, you should always check if the resulting expression can be simplified. Simplifying means reducing it to its simplest form.
In this exercise, the expression \( \frac{4 - y}{5} \) is already in its simplest form.
To simplify larger expressions, look for common factors or terms that can cancel out.
Additionally, remember that a fraction is in simplest form when the numerator and denominator have no common factors other than 1.
In our exercise's context, no further simplification is needed as \( 4 - y \) and 5 share no common factors.

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Most popular questions from this chapter

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