This worksheet helps students practice solving complex fraction problems by breaking them down into three distinct steps.

Let's solve each problem step by step, following the order given in the image. We'll use the rules of operations involving fractions, including the order of operations (PEMDAS/BODMAS).

---

Problem 1:

\[
\frac{1}{5} + \frac{1}{5} \times \frac{1}{2}
\]

#### Step 1: Perform multiplication first (following PEMDAS/BODMAS)
\[
\frac{1}{5} \times \frac{1}{2} = \frac{1 \times 1}{5 \times 2} = \frac{1}{10}
\]

#### Step 2: Add the results
\[
\frac{1}{5} + \frac{1}{10}
\]
To add these fractions, find a common denominator. The least common denominator (LCD) of 5 and 10 is 10.
\[
\frac{1}{5} = \frac{2}{10}
\]
So,
\[
\frac{1}{5} + \frac{1}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10}
\]

#### Final Answer:
\[
\boxed{\frac{3}{10}}
\]

---

Problem 2:

\[
\frac{5}{12} - \frac{7}{13} \div \frac{3}{20}
\]

#### Step 1: Perform division first
Division of fractions involves multiplying by the reciprocal:
\[
\frac{7}{13} \div \frac{3}{20} = \frac{7}{13} \times \frac{20}{3} = \frac{7 \times 20}{13 \times 3} = \frac{140}{39}
\]

#### Step 2: Subtract the results
Now we need to subtract:
\[
\frac{5}{12} - \frac{140}{39}
\]
Find the least common denominator (LCD) of 12 and 39. The LCD is 156.
Convert each fraction:
\[
\frac{5}{12} = \frac{5 \times 13}{12 \times 13} = \frac{65}{156}
\]
\[
\frac{140}{39} = \frac{140 \times 4}{39 \times 4} = \frac{560}{156}
\]
So,
\[
\frac{5}{12} - \frac{140}{39} = \frac{65}{156} - \frac{560}{156} = \frac{65 - 560}{156} = \frac{-495}{156}
\]
Simplify the fraction:
\[
\frac{-495}{156} = \frac{-165}{52} \quad (\text{dividing numerator and denominator by 3})
\]

#### Final Answer:
\[
\boxed{\frac{-165}{52}}
\]

---

Problem 3:

\[
\left(1 - \frac{3}{4}\right) \times \frac{3}{7}
\]

#### Step 1: Simplify inside the parentheses
\[
1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}
\]

#### Step 2: Multiply the results
\[
\frac{1}{4} \times \frac{3}{7} = \frac{1 \times 3}{4 \times 7} = \frac{3}{28}
\]

#### Final Answer:
\[
\boxed{\frac{3}{28}}
\]

---

Problem 4:

\[
\left(3 \frac{7}{10} - \frac{11}{7}\right) \times \frac{8}{5} - 1 \frac{1}{7}
\]

#### Step 1: Convert mixed numbers to improper fractions
\[
3 \frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{37}{10}
\]
\[
1 \frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{8}{7}
\]

#### Step 2: Simplify inside the parentheses
\[
\frac{37}{10} - \frac{11}{7}
\]
Find the least common denominator (LCD) of 10 and 7, which is 70.
Convert each fraction:
\[
\frac{37}{10} = \frac{37 \times 7}{10 \times 7} = \frac{259}{70}
\]
\[
\frac{11}{7} = \frac{11 \times 10}{7 \times 10} = \frac{110}{70}
\]
So,
\[
\frac{37}{10} - \frac{11}{7} = \frac{259}{70} - \frac{110}{70} = \frac{259 - 110}{70} = \frac{149}{70}
\]

#### Step 3: Multiply the result by \(\frac{8}{5}\)
\[
\frac{149}{70} \times \frac{8}{5} = \frac{149 \times 8}{70 \times 5} = \frac{1192}{350}
\]
Simplify the fraction:
\[
\frac{1192}{350} = \frac{596}{175} \quad (\text{dividing numerator and denominator by 2})
\]

#### Step 4: Subtract \(1 \frac{1}{7}\)
Convert \(1 \frac{1}{7}\) to an improper fraction:
\[
1 \frac{1}{7} = \frac{8}{7}
\]
Now, subtract:
\[
\frac{596}{175} - \frac{8}{7}
\]
Find the least common denominator (LCD) of 175 and 7, which is 175.
Convert \(\frac{8}{7}\):
\[
\frac{8}{7} = \frac{8 \times 25}{7 \times 25} = \frac{200}{175}
\]
So,
\[
\frac{596}{175} - \frac{8}{7} = \frac{596}{175} - \frac{200}{175} = \frac{596 - 200}{175} = \frac{396}{175}
\]

#### Final Answer:
\[
\boxed{\frac{396}{175}}
\]

---

Problem 5:

\[
\left(\frac{3}{2} \times 3 \frac{1}{2}\right) \div \left(\frac{6}{5} - 1\right)
\]

#### Step 1: Convert mixed number to an improper fraction
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
\]

#### Step 2: Perform multiplication inside the first parentheses
\[
\frac{3}{2} \times \frac{7}{2} = \frac{3 \times 7}{2 \times 2} = \frac{21}{4}
\]

#### Step 3: Simplify inside the second parentheses
\[
\frac{6}{5} - 1 = \frac{6}{5} - \frac{5}{5} = \frac{6 - 5}{5} = \frac{1}{5}
\]

#### Step 4: Perform division
Division of fractions involves multiplying by the reciprocal:
\[
\frac{21}{4} \div \frac{1}{5} = \frac{21}{4} \times \frac{5}{1} = \frac{21 \times 5}{4 \times 1} = \frac{105}{4}
\]

#### Final Answer:
\[
\boxed{\frac{105}{4}}
\]

---

Final Answers:

1. \(\boxed{\frac{3}{10}}\)
2. \(\boxed{\frac{-165}{52}}\)
3. \(\boxed{\frac{3}{28}}\)
4. \(\boxed{\frac{396}{175}}\)
5. \(\boxed{\frac{105}{4}}\)