The question asks which of the given equations uses the commutative property of addition to rewrite [tex]\(\frac{1}{4} + \frac{2}{5}\)[/tex].
The commutative property of addition states that [tex]\(a + b = b + a\)[/tex]. This means we can rewrite the sum of two fractions by simply switching the order of the addends.
Starting with the given expression:
[tex]\[
\frac{1}{4} + \frac{2}{5}
\][/tex]
Using the commutative property, we can write it as:
[tex]\[
\frac{2}{5} + \frac{1}{4}
\][/tex]
Now, let's examine the given options:
1. [tex]\(\frac{13}{20} - \frac{2}{5} = \frac{1}{4}\)[/tex] - This does not involve the commutative property and is an equation involving subtraction.
2. [tex]\(\frac{2}{4} + \frac{1}{5} = \frac{14}{20}\)[/tex] - This is an altered addition problem, not the original fractions.
3. [tex]\(\frac{2}{5} + \frac{1}{4} = \frac{13}{20}\)[/tex] - This is exactly the original expression [tex]\(\frac{1}{4} + \frac{2}{5}\)[/tex] rewritten using the commutative property.
4. [tex]\(\frac{1}{4} + \frac{1}{5} = \frac{5}{20} + \frac{8}{20}\)[/tex] - This is a different addition problem using different fractions.
Thus, the correct option is:
[tex]\[
\boxed{\frac{2}{5} + \frac{1}{4} = \frac{13}{20}}
\][/tex]
