Answer :
Let's work through the division of fractions step by step. Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number is just flipping the numerator and the denominator.
[tex]\frac{1}{2} \div 3[/tex]
First, write 3 as a fraction: [tex]\frac{3}{1}[/tex]. Then, find the reciprocal of [tex]\frac{3}{1}[/tex], which is [tex]\frac{1}{3}[/tex]. Now multiply:
[tex]\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}[/tex][tex]\frac{2}{5} \div 4[/tex]
Write 4 as a fraction: [tex]\frac{4}{1}[/tex]. The reciprocal is [tex]\frac{1}{4}[/tex]. Multiply:
[tex]\frac{2}{5} \times \frac{1}{4} = \frac{2 \times 1}{5 \times 4} = \frac{2}{20} = \frac{1}{10}[/tex][tex]\frac{5}{6} \div 7[/tex]
Write 7 as a fraction: [tex]\frac{7}{1}[/tex]. The reciprocal is [tex]\frac{1}{7}[/tex]. Multiply:
[tex]\frac{5}{6} \times \frac{1}{7} = \frac{5 \times 1}{6 \times 7} = \frac{5}{42}[/tex][tex]\frac{6}{8} \div 6[/tex]
Write 6 as a fraction: [tex]\frac{6}{1}[/tex]. The reciprocal is [tex]\frac{1}{6}[/tex]. Multiply:
[tex]\frac{6}{8} \times \frac{1}{6} = \frac{6 \times 1}{8 \times 6} = \frac{6}{48} = \frac{1}{8}[/tex] (after simplifying)[tex]\frac{12}{15} \div 5[/tex]
Write 5 as a fraction: [tex]\frac{5}{1}[/tex]. The reciprocal is [tex]\frac{1}{5}[/tex]. Multiply:
[tex]\frac{12}{15} \times \frac{1}{5} = \frac{12 \times 1}{15 \times 5} = \frac{12}{75} = \frac{4}{25}[/tex] (after simplifying)[tex]\frac{8}{10} \div 11[/tex]
Write 11 as a fraction: [tex]\frac{11}{1}[/tex]. The reciprocal is [tex]\frac{1}{11}[/tex]. Multiply:
[tex]\frac{8}{10} \times \frac{1}{11} = \frac{8 \times 1}{10 \times 11} = \frac{8}{110} = \frac{4}{55}[/tex] (after simplifying)[tex]\frac{20}{50} \div 8[/tex]
Write 8 as a fraction: [tex]\frac{8}{1}[/tex]. The reciprocal is [tex]\frac{1}{8}[/tex]. Multiply:
[tex]\frac{20}{50} \times \frac{1}{8} = \frac{20 \times 1}{50 \times 8} = \frac{20}{400} = \frac{1}{20}[/tex][tex]\frac{21}{30} \div 6[/tex]
Write 6 as a fraction: [tex]\frac{6}{1}[/tex]. The reciprocal is [tex]\frac{1}{6}[/tex]. Multiply:
[tex]\frac{21}{30} \times \frac{1}{6} = \frac{21 \times 1}{30 \times 6} = \frac{21}{180} = \frac{7}{60}[/tex] (after simplifying)[tex]\frac{5}{10} \div 20[/tex]
Write 20 as a fraction: [tex]\frac{20}{1}[/tex]. The reciprocal is [tex]\frac{1}{20}[/tex]. Multiply:
[tex]\frac{5}{10} \times \frac{1}{20} = \frac{5 \times 1}{10 \times 20} = \frac{5}{200} = \frac{1}{40}[/tex][tex]\frac{8}{20} \div 40[/tex]
Write 40 as a fraction: [tex]\frac{40}{1}[/tex]. The reciprocal is [tex]\frac{1}{40}[/tex]. Multiply:
[tex]\frac{8}{20} \times \frac{1}{40} = \frac{8 \times 1}{20 \times 40} = \frac{8}{800} = \frac{1}{100}[/tex]
Each step involves writing the whole number as a fraction and multiplying by its reciprocal. After multiplying, it's important to simplify the fraction to its lowest terms.
