To solve the division of two fractions, [tex]\(\frac{1}{36} \div \frac{18}{4}\)[/tex], we can follow these steps:
1. Understand Division of Fractions:
To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction.
2. Identify the Reciprocal:
The reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is [tex]\(\frac{b}{a}\)[/tex]. So, the reciprocal of [tex]\(\frac{18}{4}\)[/tex] is [tex]\(\frac{4}{18}\)[/tex].
3. Rewrite the Division as Multiplication:
Replace the division with multiplication by the reciprocal:
[tex]\[
\frac{1}{36} \div \frac{18}{4} = \frac{1}{36} \times \frac{4}{18}
\][/tex]
4. Simplify Before Multiplying:
Before performing the multiplication, simplify the fractions if possible. Both 4 and 36 can be simplified by dividing by 4:
[tex]\[
\frac{1}{36} = \frac{1}{4 \times 9} = \frac{1}{4 \cdot 9}
\][/tex]
[tex]\[
\frac{4}{18} = \frac{2 \cdot 2}{2 \cdot 9} = \frac{2}{9}
\][/tex]
Therefore, the problem becomes:
[tex]\[
\frac{1}{36} \times \frac{4}{18} = \frac{1}{36} \times \frac{2}{9}
\][/tex]
5. Multiply the Numerators and the Denominators:
Now multiply the numerators together and the denominators together:
[tex]\[
\frac{1 \times 2}{36 \times 9}
\][/tex]
6. Simplify the Result:
Multiply the denominators:
[tex]\[
\frac{2}{324}
\][/tex]
Simplify [tex]\(\frac{2}{324}\)[/tex]:
[tex]\[
\frac{2}{324} = \frac{2}{2 \times 162} = \frac{1}{162}
\][/tex]
Therefore, the final simplified result of the division [tex]\(\frac{1}{36} \div \frac{18}{4}\)[/tex] is [tex]\(0.006172839506172839\)[/tex].
