To evaluate the expression [tex]\(\frac{1}{5} \div \frac{3}{4}\)[/tex], let's follow these steps:
1. Understand the division of fractions rule: Dividing by a fraction is the same as multiplying by its reciprocal. So, we need to convert the division operation into a multiplication by taking the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex].
2. Rewrite the expression:
[tex]\[
\frac{1}{5} \div \frac{3}{4} = \frac{1}{5} \times \frac{4}{3}
\][/tex]
3. Multiply the fractions: To multiply two fractions, multiply their numerators together and their denominators together:
[tex]\[
\frac{1 \times 4}{5 \times 3} = \frac{4}{15}
\][/tex]
4. Simplify the fraction: The fraction [tex]\(\frac{4}{15}\)[/tex] is already in its simplest form because the greatest common divisor (GCD) of 4 and 15 is 1. Hence, it cannot be reduced any further.
Therefore, the evaluated expression in its lowest terms is:
[tex]\[
\frac{4}{15}
\][/tex]
