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Sagot :
चला, या प्रश्नांचे उत्तर एक एक करुन बघू.
### Step-by-step Solutions:
1. Fraction Multiplication
[tex]\[ \frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4} = \frac{1}{12} \][/tex]
2. Fraction Multiplication
[tex]\[ \frac{3}{2} \times \frac{1}{4} = \frac{3 \times 1}{2 \times 4} = \frac{3}{8} \][/tex]
3. Fraction Multiplication
[tex]\[ \frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12} \][/tex]
4. Fraction Multiplication
[tex]\[ \frac{7}{4} \times \frac{2}{5} = \frac{7 \times 2}{4 \times 5} = \frac{14}{20} \][/tex]
5. Fraction Multiplication
[tex]\[ \frac{2}{5} \times \frac{2}{4} = \frac{2 \times 2}{5 \times 4} = \frac{4}{20} \][/tex]
6. Fraction Multiplication
[tex]\[ \frac{1}{6} \times \frac{3}{5} = \frac{1 \times 3}{6 \times 5} = \frac{3}{30} \][/tex]
7. Fraction Multiplication
[tex]\[ \frac{1}{5} \times \frac{1}{6} = \frac{1 \times 1}{5 \times 6} = \frac{1}{30} \][/tex]
8. Fraction Multiplication
[tex]\[ \frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1 \][/tex]
9. Fraction Multiplication
[tex]\[ \frac{8}{7} \times \frac{5}{2} = \frac{8 \times 5}{7 \times 2} = \frac{40}{14} \][/tex]
10. Fraction Multiplication
[tex]\[ \frac{2}{5} \times \frac{3}{2} = \frac{2 \times 3}{5 \times 2} = \frac{6}{10} \][/tex]
11. Fraction Multiplication
[tex]\[ \frac{1}{5} \times \frac{15}{7} = \frac{1 \times 15}{5 \times 7} = \frac{15}{35} \][/tex]
12. Fraction Multiplication
[tex]\[ \frac{22}{7} \times \frac{7}{11} = \frac{22 \times 7}{7 \times 11} = \frac{154}{77} \][/tex]
Summarized Solutions:
[tex]\[ \begin{aligned} 1) & \quad \frac{1}{3} \times \frac{1}{4} = \frac{1}{12},\\ 2) & \quad \frac{3}{2} \times \frac{1}{4} = \frac{3}{8},\\ 3) & \quad \frac{1}{4} \times \frac{4}{3} = \frac{4}{12},\\ 4) & \quad \frac{7}{4} \times \frac{2}{5} = \frac{14}{20},\\ 5) & \quad \frac{2}{5} \times \frac{2}{4} = \frac{4}{20},\\ 6) & \quad \frac{1}{6} \times \frac{3}{5} = \frac{3}{30},\\ 7) & \quad \frac{1}{5} \times \frac{1}{6} = \frac{1}{30},\\ 8) & \quad \frac{2}{3} \times \frac{3}{2} = \frac{6}{6},\\ 9) & \quad \frac{8}{7} \times \frac{5}{2} = \frac{40}{14},\\ 10) \quad \qquad & \frac{2}{5} \times \frac{3}{2} = \frac{6}{10},\\ 11) \quad \qquad & \frac{1}{5} \times \frac{15}{7} = \frac{15}{35},\\ 12) \quad \qquad & \frac{22}{7} \times \frac{7}{11} = \frac{154}{77}. \end{aligned} \][/tex]
### Step-by-step Solutions:
1. Fraction Multiplication
[tex]\[ \frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4} = \frac{1}{12} \][/tex]
2. Fraction Multiplication
[tex]\[ \frac{3}{2} \times \frac{1}{4} = \frac{3 \times 1}{2 \times 4} = \frac{3}{8} \][/tex]
3. Fraction Multiplication
[tex]\[ \frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12} \][/tex]
4. Fraction Multiplication
[tex]\[ \frac{7}{4} \times \frac{2}{5} = \frac{7 \times 2}{4 \times 5} = \frac{14}{20} \][/tex]
5. Fraction Multiplication
[tex]\[ \frac{2}{5} \times \frac{2}{4} = \frac{2 \times 2}{5 \times 4} = \frac{4}{20} \][/tex]
6. Fraction Multiplication
[tex]\[ \frac{1}{6} \times \frac{3}{5} = \frac{1 \times 3}{6 \times 5} = \frac{3}{30} \][/tex]
7. Fraction Multiplication
[tex]\[ \frac{1}{5} \times \frac{1}{6} = \frac{1 \times 1}{5 \times 6} = \frac{1}{30} \][/tex]
8. Fraction Multiplication
[tex]\[ \frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1 \][/tex]
9. Fraction Multiplication
[tex]\[ \frac{8}{7} \times \frac{5}{2} = \frac{8 \times 5}{7 \times 2} = \frac{40}{14} \][/tex]
10. Fraction Multiplication
[tex]\[ \frac{2}{5} \times \frac{3}{2} = \frac{2 \times 3}{5 \times 2} = \frac{6}{10} \][/tex]
11. Fraction Multiplication
[tex]\[ \frac{1}{5} \times \frac{15}{7} = \frac{1 \times 15}{5 \times 7} = \frac{15}{35} \][/tex]
12. Fraction Multiplication
[tex]\[ \frac{22}{7} \times \frac{7}{11} = \frac{22 \times 7}{7 \times 11} = \frac{154}{77} \][/tex]
Summarized Solutions:
[tex]\[ \begin{aligned} 1) & \quad \frac{1}{3} \times \frac{1}{4} = \frac{1}{12},\\ 2) & \quad \frac{3}{2} \times \frac{1}{4} = \frac{3}{8},\\ 3) & \quad \frac{1}{4} \times \frac{4}{3} = \frac{4}{12},\\ 4) & \quad \frac{7}{4} \times \frac{2}{5} = \frac{14}{20},\\ 5) & \quad \frac{2}{5} \times \frac{2}{4} = \frac{4}{20},\\ 6) & \quad \frac{1}{6} \times \frac{3}{5} = \frac{3}{30},\\ 7) & \quad \frac{1}{5} \times \frac{1}{6} = \frac{1}{30},\\ 8) & \quad \frac{2}{3} \times \frac{3}{2} = \frac{6}{6},\\ 9) & \quad \frac{8}{7} \times \frac{5}{2} = \frac{40}{14},\\ 10) \quad \qquad & \frac{2}{5} \times \frac{3}{2} = \frac{6}{10},\\ 11) \quad \qquad & \frac{1}{5} \times \frac{15}{7} = \frac{15}{35},\\ 12) \quad \qquad & \frac{22}{7} \times \frac{7}{11} = \frac{154}{77}. \end{aligned} \][/tex]
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