To find the quotient of
[tex]\[
\frac{1}{8} \div \frac{3}{4}
\][/tex]
we follow these steps:
1. Understand the operation: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore,
[tex]\[
\frac{1}{8} \div \frac{3}{4} = \frac{1}{8} \times \frac{4}{3}
\][/tex]
2. Multiply the fractions:
- Multiply the numerators: [tex]\(1 \times 4 = 4\)[/tex]
- Multiply the denominators: [tex]\(8 \times 3 = 24\)[/tex]
Thus, we get:
[tex]\[
\frac{1}{8} \times \frac{4}{3} = \frac{4}{24}
\][/tex]
3. Simplify the fraction:
- Find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 4 and 24 is 4.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{4}{24} = \frac{4 \div 4}{24 \div 4} = \frac{1}{6}
\][/tex]
So, the simplified quotient is:
[tex]\[
\frac{1}{6}
\][/tex]
Therefore,
[tex]\[
\frac{1}{8} \div \frac{3}{4} = \frac{1}{6}
\][/tex]
