To divide the fractions [tex]\(\frac{1}{3} \div 15\)[/tex], follow these steps:
1. Express 15 as a fraction:
Any whole number can be written as a fraction with a denominator of 1. So, we can write 15 as [tex]\(\frac{15}{1}\)[/tex].
2. Rewrite the division as multiplication by the reciprocal:
The division of fractions can be translated into multiplication by taking the reciprocal (or multiplicative inverse) of the divisor. Thus, we need to take the reciprocal of [tex]\(\frac{15}{1}\)[/tex], which is [tex]\(\frac{1}{15}\)[/tex].
Hence, [tex]\(\frac{1}{3} \div 15 = \frac{1}{3} \times \frac{1}{15}\)[/tex].
3. Multiply the fractions:
To multiply two fractions, multiply the numerators together and the denominators together.
So,
[tex]\[
\frac{1}{3} \times \frac{1}{15} = \frac{1 \times 1}{3 \times 15} = \frac{1}{45}
\][/tex]
4. Simplify the fraction:
In this case, [tex]\(\frac{1}{45}\)[/tex] is already in its simplest form because 1 is the greatest common divisor (GCD) of 1 and 45.
Thus, the result of [tex]\(\frac{1}{3} \div 15\)[/tex] is [tex]\(\frac{1}{45}\)[/tex].
