Sure, let's solve each part of the question step-by-step:
### Part (a)
[tex]\[
\frac{1}{4} \div \frac{1}{8}
\][/tex]
When dividing fractions, we multiply by the reciprocal of the second fraction:
[tex]\[
\frac{1}{4} \div \frac{1}{8} = \frac{1}{4} \times \frac{8}{1} = \frac{1 \times 8}{4 \times 1} = \frac{8}{4} = 2
\][/tex]
Therefore,
[tex]\[
\frac{1}{4} \div \frac{1}{8} = 2.0
\][/tex]
### Part (b)
[tex]\[
\frac{5}{16} \div \frac{2}{7}
\][/tex]
Again, we divide by multiplying by the reciprocal of the second fraction:
[tex]\[
\frac{5}{16} \div \frac{2}{7} = \frac{5}{16} \times \frac{7}{2} = \frac{5 \times 7}{16 \times 2} = \frac{35}{32} = 1.09375
\][/tex]
Therefore,
[tex]\[
\frac{5}{16} \div \frac{2}{7} = 1.09375
\][/tex]
### Part (c)
Convert the mixed numbers to improper fractions first.
For [tex]\(1 \frac{2}{5}\)[/tex]:
[tex]\[
1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{5 + 2}{5} = \frac{7}{5}
\][/tex]
For [tex]\(3 \frac{1}{4}\)[/tex]:
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
\][/tex]
Now, we perform the division:
[tex]\[
\frac{7}{5} \div \frac{13}{4} = \frac{7}{5} \times \frac{4}{13} = \frac{7 \times 4}{5 \times 13} = \frac{28}{65} \approx 0.43076923076923074
\][/tex]
Therefore,
[tex]\[
1 \frac{2}{5} \div 3 \frac{1}{4} = 0.43076923076923074
\][/tex]
Summarizing all parts:
[tex]\[
(a) \ \frac{1}{4} \div \frac{1}{8} = 2.0
\][/tex]
[tex]\[
(b) \ \frac{5}{16} \div \frac{2}{7} = 1.09375
\][/tex]
[tex]\[
(c) \ 1 \frac{2}{5} \div 3 \frac{1}{4} = 0.43076923076923074
\][/tex]
