Solve the multiplication and division problems presented in the image.

Okay, let's break down each problem step by step. The key here is to remember how to multiply and divide fractions. When you have a problem like $\frac{a}{b} \cdot \frac{c}{d}$, you multiply the numerators (the top numbers) and the denominators (the bottom numbers) to get $\frac{a \cdot c}{b \cdot d}$. For division, $\frac{a}{b} : \frac{c}{d}$, you flip the second fraction and multiply: $\frac{a}{b} \cdot \frac{d}{c} = \frac{a \cdot d}{b \cdot c}$. Let's solve each one: 1. $\frac{8}{15} \cdot \frac{12}{120} \cdot \frac{30}{40}$ First, simplify before multiplying. Notice that 12/120 = 1/10, and 30/40 = 3/4. So the problem becomes $\frac{8}{15} \cdot \frac{1}{10} \cdot \frac{3}{4} = \frac{8 \cdot 1 \cdot 3}{15 \cdot 10 \cdot 4} = \frac{24}{600}$ Now simplify the result: $\frac{24}{600} = \frac{1}{25}$ 2. $\frac{4}{3} : \frac{12}{20} \cdot \frac{1}{5}$ Division first. $\frac{4}{3} : \frac{12}{20} = \frac{4}{3} \cdot \frac{20}{12} = \frac{80}{36}$ Simplify this to $\frac{20}{9}$ Now multiply by $\frac{1}{5}$ : $\frac{20}{9} \cdot \frac{1}{5} = \frac{20}{45} = \frac{4}{9}$ 3. $\frac{6}{10} \cdot \frac{5}{44} : \frac{2}{11}$ First, multiplication: $\frac{6}{10} \cdot \frac{5}{44} = \frac{30}{440} = \frac{3}{44}$ Now divide: $\frac{3}{44} : \frac{2}{11} = \frac{3}{44} \cdot \frac{11}{2} = \frac{33}{88} = \frac{3}{8}$ 4. $\frac{13}{50} : \frac{26}{12} : \frac{52}{13}$ First division: $\frac{13}{50} : \frac{26}{12} = \frac{13}{50} \cdot \frac{12}{26} = \frac{156}{1300} = \frac{3}{25}$ Second division: $\frac{3}{25} : \frac{52}{13} = \frac{3}{25} \cdot \frac{13}{52} = \frac{39}{1300} = \frac{3}{100}$ 5. $\frac{3}{9} \cdot \frac{1}{6} \cdot \frac{18}{72}$ Simplify first: $\frac{3}{9} = \frac{1}{3}$ and $\frac{18}{72} = \frac{1}{4}$ So, $\frac{1}{3} \cdot \frac{1}{6} \cdot \frac{1}{4} = \frac{1}{72}$ 6. $\frac{25}{10} : \frac{65}{90} : \frac{13}{45}$ First division: $\frac{25}{10} : \frac{65}{90} = \frac{25}{10} \cdot \frac{90}{65} = \frac{2250}{650} = \frac{45}{13}$ Second division: $\frac{45}{13} : \frac{13}{45} = \frac{45}{13} \cdot \frac{45}{13} = \frac{2025}{169}$ 7. $\frac{4}{7} \cdot \frac{2}{16} : \frac{2}{21}$ Multiplication: $\frac{4}{7} \cdot \frac{2}{16} = \frac{8}{112} = \frac{1}{14}$ Division: $\frac{1}{14} : \frac{2}{21} = \frac{1}{14} \cdot \frac{21}{2} = \frac{21}{28} = \frac{3}{4}$ 8. $\frac{54}{8} : \frac{27}{16} : \frac{2}{3}$ First division: $\frac{54}{8} : \frac{27}{16} = \frac{54}{8} \cdot \frac{16}{27} = \frac{864}{216} = 4$ Second division: $4 : \frac{2}{3} = 4 \cdot \frac{3}{2} = \frac{12}{2} = 6$ 9. $\frac{11}{99} \cdot \frac{9}{88} : \frac{8}{10}$ Multiplication: $\frac{11}{99} \cdot \frac{9}{88} = \frac{99}{8712} = \frac{1}{88}$ Division: $\frac{1}{88} : \frac{8}{10} = \frac{1}{88} \cdot \frac{10}{8} = \frac{10}{704} = \frac{5}{352}$ 10. $\frac{12}{18} : \frac{24}{9} : \frac{9}{48}$ First division: $\frac{12}{18} : \frac{24}{9} = \frac{12}{18} \cdot \frac{9}{24} = \frac{108}{432} = \frac{1}{4}$ Second division: $\frac{1}{4} : \frac{9}{48} = \frac{1}{4} \cdot \frac{48}{9} = \frac{48}{36} = \frac{4}{3}$ Now, let's solve the other side: 1. $\frac{17}{33} \cdot \frac{11}{34} = \frac{17 \cdot 11}{33 \cdot 34} = \frac{187}{1122} = \frac{1}{6}$ 2. $\frac{7}{30} \cdot \frac{6}{21} = \frac{7 \cdot 6}{30 \cdot 21} = \frac{42}{630} = \frac{1}{15}$ 3. $\frac{4}{12} \cdot \frac{18}{20} = \frac{4 \cdot 18}{12 \cdot 20} = \frac{72}{240} = \frac{3}{10}$ 4. $\frac{21}{25} \cdot \frac{15}{42} = \frac{21 \cdot 15}{25 \cdot 42} = \frac{315}{1050} = \frac{3}{10}$ 5. $\frac{14}{24} \cdot \frac{16}{21} = \frac{14 \cdot 16}{24 \cdot 21} = \frac{224}{504} = \frac{4}{9}$ 6. $\frac{50}{70} \cdot \frac{77}{150} = \frac{50 \cdot 77}{70 \cdot 150} = \frac{3850}{10500} = \frac{11}{30}$ 7. $\frac{23}{45} \cdot \frac{9}{46} = \frac{23 \cdot 9}{45 \cdot 46} = \frac{207}{2070} = \frac{1}{10}$ 8. $\frac{30}{66} \cdot \frac{77}{90} = \frac{30 \cdot 77}{66 \cdot 90} = \frac{2310}{5940} = \frac{7}{18}$ 9. $\frac{26}{32} \cdot \frac{12}{13} = \frac{26 \cdot 12}{32 \cdot 13} = \frac{312}{416} = \frac{3}{4}$ 10. $\frac{8}{19} \cdot \frac{38}{40} = \frac{8 \cdot 38}{19 \cdot 40} = \frac{304}{760} = \frac{2}{5}$