Certainly! Let's analyze the given expression and understand the mathematical property it represents:
Given expression:
[tex]\[
\frac{2}{3} + \frac{3}{L_1} = \frac{3}{L_1} + \frac{2}{3}
\][/tex]
Step-by-Step Solution:
1. Observe the Expression:
We notice that the expression on the left-hand side (LHS):
[tex]\[
\frac{2}{3} + \frac{3}{L_1}
\][/tex]
is equal to the expression on the right-hand side (RHS):
[tex]\[
\frac{3}{L_1} + \frac{2}{3}
\][/tex]
2. Identify the Property:
Both sides of the equation contain the same terms [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{L_1}\)[/tex] but in different orders. The different order does not change the outcome of the addition. This is a key feature of a specific property in mathematics.
3. Commutative Property of Addition:
The property that states that changing the order of the terms in an addition operation does not change the sum is called the commutative property of addition. Formally, for any two rational numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
a + b = b + a
\][/tex]
In our case, we can see that:
[tex]\[
\frac{2}{3} + \frac{3}{L_1} = \frac{3}{L_1} + \frac{2}{3}
\][/tex]
This clearly illustrates that the order in which [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{L_1}\)[/tex] are added does not affect the result.
4. Conclusion:
Therefore, the expression [tex]\(\frac{2}{3} + \frac{3}{L_1} = \frac{3}{L_1} + \frac{2}{3}\)[/tex] exemplifies the commutative property of addition of rational numbers.
Hence, the property of addition represented in the given expression is the commutative property.
