To solve the division of the given fractions [tex]\(\frac{1}{36} \div \frac{18}{4}\)[/tex], follow these steps:
1. Understand the operation: Division of fractions is equivalent to multiplying by the reciprocal of the divisor.
2. Identify the fractions:
- First fraction: [tex]\(\frac{1}{36}\)[/tex]
- Second fraction: [tex]\(\frac{18}{4}\)[/tex]
3. Find the reciprocal of the second fraction:
- The reciprocal of [tex]\(\frac{18}{4}\)[/tex] is [tex]\(\frac{4}{18}\)[/tex].
4. Rewrite the original operation using multiplication by the reciprocal:
[tex]\[
\frac{1}{36} \div \frac{18}{4} = \frac{1}{36} \times \frac{4}{18}
\][/tex]
5. Multiply the numerators:
[tex]\[
1 \times 4 = 4
\][/tex]
6. Multiply the denominators:
[tex]\[
36 \times 18 = 648
\][/tex]
7. Form the new fraction from the results of the multiplication:
[tex]\[
\frac{4}{648}
\][/tex]
8. Simplify the fraction:
- Identify the greatest common divisor (GCD) of 4 and 648, which is 4.
- Divide both the numerator and the denominator by 4:
[tex]\[
\frac{4 \div 4}{648 \div 4} = \frac{1}{162}
\][/tex]
9. Convert the simplified fraction to a decimal:
- Perform the division [tex]\( \frac{1}{162} \)[/tex] to get the decimal form.
- [tex]\(\frac{1}{162} \approx 0.006172839506172839\)[/tex].
Therefore, the result of [tex]\(\frac{1}{36} \div \frac{18}{4}\)[/tex] is approximately [tex]\(0.006172839506172839\)[/tex].
