Let's solve each problem step by step, showing all the working and reducing the final answers where necessary.
---
Problem 1:
$$
\frac{3}{11} + \frac{7}{11}
$$
Step 1: Since the denominators are the same, we can add the numerators directly.
$$
\frac{3}{11} + \frac{7}{11} = \frac{3 + 7}{11} = \frac{10}{11}
$$
Step 2: The fraction $\frac{10}{11}$ is already in its simplest form.
Final Answer:
$$
\boxed{\frac{10}{11}}
$$
---
Problem 2:
$$
\frac{7}{18} + \frac{2}{18}
$$
Step 1: Since the denominators are the same, we can add the numerators directly.
$$
\frac{7}{18} + \frac{2}{18} = \frac{7 + 2}{18} = \frac{9}{18}
$$
Step 2: Simplify the fraction $\frac{9}{18}$ by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9.
$$
\frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2}
$$
Final Answer:
$$
\boxed{\frac{1}{2}}
$$
---
Problem 3:
$$
\frac{6}{15} - \frac{3}{15}
$$
Step 1: Since the denominators are the same, we can subtract the numerators directly.
$$
\frac{6}{15} - \frac{3}{15} = \frac{6 - 3}{15} = \frac{3}{15}
$$
Step 2: Simplify the fraction $\frac{3}{15}$ by dividing both the numerator and the denominator by their GCD, which is 3.
$$
\frac{3}{15} = \frac{3 \div 3}{15 \div 3} = \frac{1}{5}
$$
Final Answer:
$$
\boxed{\frac{1}{5}}
$$
---
Problem 4:
$$
\frac{16}{19} - \frac{14}{19}
$$
Step 1: Since the denominators are the same, we can subtract the numerators directly.
$$
\frac{16}{19} - \frac{14}{19} = \frac{16 - 14}{19} = \frac{2}{19}
$$
Step 2: The fraction $\frac{2}{19}$ is already in its simplest form.
Final Answer:
$$
\boxed{\frac{2}{19}}
$$
---
Problem 5:
$$
\frac{6}{10} \times \frac{5}{12}
$$
Step 1: Multiply the numerators together and the denominators together.
$$
\frac{6}{10} \times \frac{5}{12} = \frac{6 \times 5}{10 \times 12} = \frac{30}{120}
$$
Step 2: Simplify the fraction $\frac{30}{120}$ by dividing both the numerator and the denominator by their GCD, which is 30.
$$
\frac{30}{120} = \frac{30 \div 30}{120 \div 30} = \frac{1}{4}
$$
Final Answer:
$$
\boxed{\frac{1}{4}}
$$
---
Problem 6:
$$
\frac{12}{14} \times \frac{4}{9}
$$
Step 1: Multiply the numerators together and the denominators together.
$$
\frac{12}{14} \times \frac{4}{9} = \frac{12 \times 4}{14 \times 9} = \frac{48}{126}
$$
Step 2: Simplify the fraction $\frac{48}{126}$ by dividing both the numerator and the denominator by their GCD, which is 6.
$$
\frac{48}{126} = \frac{48 \div 6}{126 \div 6} = \frac{8}{21}
$$
Final Answer:
$$
\boxed{\frac{8}{21}}
$$
---
Final Answers:
1. $\boxed{\frac{10}{11}}$
2. $\boxed{\frac{1}{2}}$
3. $\boxed{\frac{1}{5}}$
4. $\boxed{\frac{2}{19}}$
5. $\boxed{\frac{1}{4}}$
6. $\boxed{\frac{8}{21}}$
Parent Tip: Review the logic above to help your child master the concept of fraction operation worksheet.
