To determine which of the two expressions [tex]$\frac{1}{20} \div \frac{1}{5}$[/tex] or [tex]$\frac{1}{5} \div \frac{1}{20}$[/tex] is smaller, let's evaluate each one step-by-step.
1. Evaluate [tex]\(\frac{1}{20} \div \frac{1}{5}\)[/tex]:
- When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction.
- The reciprocal of [tex]\(\frac{1}{5}\)[/tex] is [tex]\(\frac{5}{1}\)[/tex].
- So, we have:
[tex]\[
\frac{1}{20} \div \frac{1}{5} = \frac{1}{20} \times \frac{5}{1} = \frac{1 \cdot 5}{20 \cdot 1} = \frac{5}{20} = \frac{1}{4} = 0.25
\][/tex]
2. Evaluate [tex]\(\frac{1}{5} \div \frac{1}{20}\)[/tex]:
- Again, we multiply the first fraction by the reciprocal of the second fraction.
- The reciprocal of [tex]\(\frac{1}{20}\)[/tex] is [tex]\(\frac{20}{1}\)[/tex].
- So, we have:
[tex]\[
\frac{1}{5} \div \frac{1}{20} = \frac{1}{5} \times \frac{20}{1} = \frac{1 \cdot 20}{5 \cdot 1} = \frac{20}{5} = 4
\][/tex]
Now we have the results of our evaluations:
- [tex]\(\frac{1}{20} \div \frac{1}{5} = 0.25\)[/tex]
- [tex]\(\frac{1}{5} \div \frac{1}{20} = 4\)[/tex]
Comparing the two results:
- [tex]\(0.25\)[/tex] is smaller than [tex]\(4\)[/tex].
Thus, [tex]\(\frac{1}{20} \div \frac{1}{5}\)[/tex] is the smaller value.
