To address the question of which is smaller between [tex]\(\frac{1}{20} + \frac{1}{5}\)[/tex] and [tex]\(\frac{1}{5} + \frac{1}{20}\)[/tex], let's analyze both expressions step-by-step.
First, let's simplify each fraction independently:
1. [tex]\(\frac{1}{20} + \frac{1}{5}\)[/tex]:
When adding fractions, a common denominator is needed. The least common denominator for 20 and 5 is 20.
Rewrite [tex]\(\frac{1}{5}\)[/tex] with a denominator of 20:
[tex]\[
\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
\][/tex]
Now add the fractions:
[tex]\[
\frac{1}{20} + \frac{4}{20} = \frac{1 + 4}{20} = \frac{5}{20}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{5}{20} = \frac{1}{4} = 0.25
\][/tex]
2. [tex]\(\frac{1}{5} + \frac{1}{20}\)[/tex]:
Similarly, use the common denominator of 20. We have already converted [tex]\(\frac{1}{5}\)[/tex] to [tex]\(\frac{4}{20}\)[/tex]:
[tex]\[
\frac{1}{5} = \frac{4}{20}
\][/tex]
Now add the fractions:
[tex]\[
\frac{4}{20} + \frac{1}{20} = \frac{4 + 1}{20} = \frac{5}{20}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{5}{20} = \frac{1}{4} = 0.25
\][/tex]
Thus, we see that:
[tex]\[
\frac{1}{20} + \frac{1}{5} = \frac{1}{5} + \frac{1}{20} = 0.25
\][/tex]
So, both [tex]\(\frac{1}{20} + \frac{1}{5}\)[/tex] and [tex]\(\frac{1}{5} + \frac{1}{20}\)[/tex] are equal to 0.25. Neither is smaller; they are exactly the same.
