Answer :
Let’s solve each problem step-by-step:
1. Quotient of [tex]\(\frac{5}{6} \div \frac{1}{2}\)[/tex]:
[tex]\[ \frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1} = \frac{5 \times 2}{6 \times 1} = \frac{10}{6} = \frac{5}{3} \approx 1.6667 \][/tex]
The simplified answer is [tex]\(\frac{5}{3}\)[/tex] or approximately 1.6667.
2. Sum of [tex]\(\frac{8}{9} + \frac{2}{3}\)[/tex]:
[tex]\[ \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \][/tex]
[tex]\[ \frac{8}{9} + \frac{6}{9} = \frac{8 + 6}{9} = \frac{14}{9} \approx 1.5556 \][/tex]
The simplified answer is [tex]\(\frac{14}{9}\)[/tex] or approximately 1.5556.
3. Quotient of [tex]\(\frac{7}{8} \div \frac{1}{4}\)[/tex]:
[tex]\[ \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1} = \frac{7 \times 4}{8 \times 1} = \frac{28}{8} = \frac{7}{2} = 3.5 \][/tex]
The simplified answer is [tex]\(\frac{7}{2}\)[/tex] or 3.5.
4. Quotient of [tex]\(\frac{3}{4} \div \frac{1}{6}\)[/tex]:
[tex]\[ \frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times \frac{6}{1} = \frac{3 \times 6}{4 \times 1} = \frac{18}{4} = \frac{9}{2} = 4.5 \][/tex]
The simplified answer is [tex]\(\frac{9}{2}\)[/tex] or 4.5.
5. Quotient of [tex]\(\frac{15}{16} \div \frac{3}{4}\)[/tex]:
[tex]\[ \frac{15}{16} \div \frac{3}{4} = \frac{15}{16} \times \frac{4}{3} = \frac{15 \times 4}{16 \times 3} = \frac{60}{48} = \frac{5}{4} = 1.25 \][/tex]
The simplified answer is [tex]\(\frac{5}{4}\)[/tex] or 1.25.
6. Sum of [tex]\(\frac{7}{12} + \frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \][/tex]
[tex]\[ \frac{7}{12} + \frac{4}{12} = \frac{7 + 4}{12} = \frac{11}{12} \approx 0.9167 \][/tex]
The simplified answer is [tex]\(\frac{11}{12}\)[/tex] or approximately 0.9167.
7. Quotient of [tex]\(9 \frac{1}{3} \div 2 \frac{1}{3}\)[/tex]:
[tex]\[ 9 \frac{1}{3} = 9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \][/tex]
[tex]\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \][/tex]
[tex]\[ \frac{28}{3} \div \frac{7}{3} = \frac{28}{3} \times \frac{3}{7} = \frac{28 \times 3}{3 \times 7} = \frac{84}{21} = 4 \][/tex]
The simplified answer is 4.
8. Quotient of [tex]\(10 \frac{1}{5} \div 3 \frac{2}{5}\)[/tex]:
[tex]\[ 10 \frac{1}{5} = 10 + \frac{1}{5} = \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \][/tex]
[tex]\[ 3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \][/tex]
[tex]\[ \frac{51}{5} \div \frac{17}{5} = \frac{51}{5} \times \frac{5}{17} = \frac{51 \times 5}{5 \times 17} = \frac{51}{17} = 3 \][/tex]
The simplified answer is 3.
9. Quotient of [tex]\(19 \div 6 \frac{1}{4}\)[/tex]:
[tex]\[ 6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4} \][/tex]
[tex]\[ 19 \div \frac{25}{4} = 19 \times \frac{4}{25} = \frac{19 \times 4}{25} = \frac{76}{25} \approx 3.04 \][/tex]
The simplified answer is [tex]\(\frac{76}{25}\)[/tex] or approximately 3.04.
10. Quotient of [tex]\(12 \frac{1}{2} \div 2 \frac{1}{3}\)[/tex]:
[tex]\[ 12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2} \][/tex]
[tex]\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \][/tex]
[tex]\[ \frac{25}{2} \div \frac{7}{3} = \frac{25}{2} \times \frac{3}{7} = \frac{25 \times 3}{2 \times 7} = \frac{75}{14} \approx 5.3571 \][/tex]
The simplified answer is [tex]\(\frac{75}{14}\)[/tex] or approximately 5.3571.
1. Quotient of [tex]\(\frac{5}{6} \div \frac{1}{2}\)[/tex]:
[tex]\[ \frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1} = \frac{5 \times 2}{6 \times 1} = \frac{10}{6} = \frac{5}{3} \approx 1.6667 \][/tex]
The simplified answer is [tex]\(\frac{5}{3}\)[/tex] or approximately 1.6667.
2. Sum of [tex]\(\frac{8}{9} + \frac{2}{3}\)[/tex]:
[tex]\[ \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \][/tex]
[tex]\[ \frac{8}{9} + \frac{6}{9} = \frac{8 + 6}{9} = \frac{14}{9} \approx 1.5556 \][/tex]
The simplified answer is [tex]\(\frac{14}{9}\)[/tex] or approximately 1.5556.
3. Quotient of [tex]\(\frac{7}{8} \div \frac{1}{4}\)[/tex]:
[tex]\[ \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1} = \frac{7 \times 4}{8 \times 1} = \frac{28}{8} = \frac{7}{2} = 3.5 \][/tex]
The simplified answer is [tex]\(\frac{7}{2}\)[/tex] or 3.5.
4. Quotient of [tex]\(\frac{3}{4} \div \frac{1}{6}\)[/tex]:
[tex]\[ \frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times \frac{6}{1} = \frac{3 \times 6}{4 \times 1} = \frac{18}{4} = \frac{9}{2} = 4.5 \][/tex]
The simplified answer is [tex]\(\frac{9}{2}\)[/tex] or 4.5.
5. Quotient of [tex]\(\frac{15}{16} \div \frac{3}{4}\)[/tex]:
[tex]\[ \frac{15}{16} \div \frac{3}{4} = \frac{15}{16} \times \frac{4}{3} = \frac{15 \times 4}{16 \times 3} = \frac{60}{48} = \frac{5}{4} = 1.25 \][/tex]
The simplified answer is [tex]\(\frac{5}{4}\)[/tex] or 1.25.
6. Sum of [tex]\(\frac{7}{12} + \frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \][/tex]
[tex]\[ \frac{7}{12} + \frac{4}{12} = \frac{7 + 4}{12} = \frac{11}{12} \approx 0.9167 \][/tex]
The simplified answer is [tex]\(\frac{11}{12}\)[/tex] or approximately 0.9167.
7. Quotient of [tex]\(9 \frac{1}{3} \div 2 \frac{1}{3}\)[/tex]:
[tex]\[ 9 \frac{1}{3} = 9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \][/tex]
[tex]\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \][/tex]
[tex]\[ \frac{28}{3} \div \frac{7}{3} = \frac{28}{3} \times \frac{3}{7} = \frac{28 \times 3}{3 \times 7} = \frac{84}{21} = 4 \][/tex]
The simplified answer is 4.
8. Quotient of [tex]\(10 \frac{1}{5} \div 3 \frac{2}{5}\)[/tex]:
[tex]\[ 10 \frac{1}{5} = 10 + \frac{1}{5} = \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \][/tex]
[tex]\[ 3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \][/tex]
[tex]\[ \frac{51}{5} \div \frac{17}{5} = \frac{51}{5} \times \frac{5}{17} = \frac{51 \times 5}{5 \times 17} = \frac{51}{17} = 3 \][/tex]
The simplified answer is 3.
9. Quotient of [tex]\(19 \div 6 \frac{1}{4}\)[/tex]:
[tex]\[ 6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4} \][/tex]
[tex]\[ 19 \div \frac{25}{4} = 19 \times \frac{4}{25} = \frac{19 \times 4}{25} = \frac{76}{25} \approx 3.04 \][/tex]
The simplified answer is [tex]\(\frac{76}{25}\)[/tex] or approximately 3.04.
10. Quotient of [tex]\(12 \frac{1}{2} \div 2 \frac{1}{3}\)[/tex]:
[tex]\[ 12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2} \][/tex]
[tex]\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \][/tex]
[tex]\[ \frac{25}{2} \div \frac{7}{3} = \frac{25}{2} \times \frac{3}{7} = \frac{25 \times 3}{2 \times 7} = \frac{75}{14} \approx 5.3571 \][/tex]
The simplified answer is [tex]\(\frac{75}{14}\)[/tex] or approximately 5.3571.
