https://r2.erweima.ai/mathbot/image/1724848912083tuveqmwo.jpg

Let's go through each of the fraction questions from the image one by one.

### Solving Each Fraction Problem

1. **\( \frac{12}{5} \times 2 = \)**
   \[
   \frac{12 \times 2}{5} = \frac{24}{5} = 4 \frac{4}{5}
   \]

2. **\( \frac{7}{12} + \frac{5}{14} = \)**
   \[
   \text{LCD of 12 and 14 is 84.} \\
   \frac{7 \times 7}{84} + \frac{5 \times 6}{84} = \frac{49}{84} + \frac{30}{84} = \frac{79}{84}
   \]

3. **\( \frac{4}{9} + \frac{4}{7} = \)**
   \[
   \text{LCD of 9 and 7 is 63.} \\
   \frac{4 \times 7}{63} + \frac{4 \times 9}{63} = \frac{28}{63} + \frac{36}{63} = \frac{64}{63} = 1 \frac{1}{63}
   \]

4. **\( \frac{15}{4} - \frac{2}{11} = \)**
   \[
   \text{LCD of 4 and 11 is 44.} \\
   \frac{15 \times 11}{44} - \frac{2 \times 4}{44} = \frac{165}{44} - \frac{8}{44} = \frac{157}{44} = 3 \frac{25}{44}
   \]

5. **\( \frac{30}{22} - \frac{9}{11} = \)**
   \[
   \frac{30}{22} - \frac{18}{22} = \frac{12}{22} = \frac{6}{11}
   \]

6. **\( \frac{1}{3} + \frac{7}{8} = \)**
   \[
   \text{LCD of 3 and 8 is 24.} \\
   \frac{1 \times 8}{24} + \frac{7 \times 3}{24} = \frac{8}{24} + \frac{21}{24} = \frac{29}{24} = 1 \frac{5}{24}
   \]

7. **\( \frac{2}{11} + \frac{7}{8} = \)**
   \[
   \text{LCD of 11 and 8 is 88.} \\
   \frac{2 \times 8}{88} + \frac{7 \times 11}{88} = \frac{16}{88} + \frac{77}{88} = \frac{93}{88} = 1 \frac{5}{88}
   \]

8. **\( \frac{1}{4} + \frac{1}{8} = \)**
   \[
   \frac{2}{8} + \frac{1}{8} = \frac{3}{8}
   \]

9. **\( \frac{15}{18} + \frac{1}{6} = \)**
   \[
   \frac{5}{6} + \frac{1}{6} = \frac{6}{6} = 1
   \]

10. **\( \frac{3}{4} \times \frac{5}{8} = \)**
    \[
    \frac{3 \times 5}{4 \times 8} = \frac{15}{32}
    \]

11. **\( \frac{7}{12} + \frac{11}{16} = \)**
    \[
    \text{LCD of 12 and 16 is 48.} \\
    \frac{7 \times 4}{48} + \frac{11 \times 3}{48} = \frac{28}{48} + \frac{33}{48} = \frac{61}{48} = 1 \frac{13}{48}
    \]

12. **\( \frac{13}{6} \times 6 = \)**
    \[
    \frac{13 \times 6}{6} = 13
    \]

13. **\( \frac{12}{21} + \frac{14}{21} = \)**
    \[
    \frac{12 + 14}{21} = \frac{26}{21} = 1 \frac{5}{21}
    \]

14. **\( \frac{21}{14} \div \frac{14}{21} = \)**
    \[
    \frac{21}{14} \times \frac{21}{14} = \frac{441}{196} = \frac{9}{4} = 2 \frac{1}{4}
    \]

15. **\( \frac{12}{21} \div \frac{56}{12} = \)**
    \[
    \frac{12}{21} \times \frac{12}{56} = \frac{12 \times 12}{21 \times 56} = \frac{144}{1176} = \frac{1}{8}
    \]

### Summary of Answers:

1. \( \frac{24}{5} \) or \( 4 \frac{4}{5} \)
2. \( \frac{79}{84} \)
3. \( \frac{64}{63} \) or \( 1 \frac{1}{63} \)
4. \( \frac{157}{44} \) or \( 3 \frac{25}{44} \)
5. \( \frac{6}{11} \)
6. \( \frac{29}{24} \) or \( 1 \frac{5}{24} \)
7. \( \frac{93}{88} \) or \( 1 \frac{5}{88} \)
8. \( \frac{3}{8} \)
9. \( 1 \)
10. \( \frac{15}{32} \)
11. \( \frac{61}{48} \) or \( 1 \frac{13}{48} \)
12. \( 13 \)
13. \( \frac{26}{21} \) or \( 1 \frac{5}{21} \)
14. \( \frac{9}{4} \) or \( 2 \frac{1}{4} \)
15. \( \frac{1}{8} \)

Would you like more details on any specific problem, or do you have any questions?

### Relative Questions to Explore:

1. How do you find the least common denominator for adding fractions?
2. What are the steps to simplify a fraction?
3. How do you convert an improper fraction to a mixed number?
4. What is the process for multiplying two fractions together?
5. How can you divide fractions, and what does it mean to multiply by the reciprocal?

**Tip:** Always simplify your fractions to their lowest terms to make them easier to interpret and use.

Explore detailed solutions to various fraction problems involving addition, subtraction, multiplication, and division. Topics include finding the least common denominator (LCD) and simplifying fractions. Suitable for Grades 5-8 students.

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