To simplify the expression [tex]\(\frac{1}{5} + \frac{3}{4} + \frac{4}{5}\)[/tex] using the commutative property, follow these steps:
1. Reorder the terms using the commutative property:
The commutative property of addition states that you can add numbers in any order. So, we can reorder the terms as:
[tex]\[
\frac{1}{5} + \frac{4}{5} + \frac{3}{4}
\][/tex]
2. Combine like terms:
Now, let's combine the fractions with the same denominator:
[tex]\[
\frac{1}{5} + \frac{4}{5} = \frac{1 + 4}{5} = \frac{5}{5} = 1
\][/tex]
3. Add the remaining fraction:
Next, add the remaining fraction to the result:
[tex]\[
1 + \frac{3}{4}
\][/tex]
4. Convert to a mixed number:
The addition of a whole number and a fraction can be written as:
[tex]\[
1 + \frac{3}{4} = 1 \frac{3}{4}
\][/tex]
Therefore, the correct answer is choice:
D. [tex]\(\frac{1}{5} + \frac{4}{5} + \frac{3}{4} = 1 + \frac{3}{4} = 1 \frac{3}{4}\)[/tex]
