Answer :

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]