Question

dividing with mixed numbers #2
divide.

1. \\(\frac{1}{8} \div 2\frac{1}{2} = \frac{2}{40}\\)
2. \\(4\frac{1}{3} \div \frac{1}{3} = \\)
3. \\(6\frac{1}{4} \div \frac{1}{8} = \\)
4. \\(\frac{9}{10} \div 5\frac{1}{5} = \\)
5. \\(6\frac{8}{9} \div 1\frac{1}{3} = \\)
6. \\(8\frac{2}{5} \div \frac{7}{10} = \\)
7. \\(3\frac{3}{4} \div 2\frac{2}{3} = \\)
8. \\(\frac{4}{9} \div 2\frac{5}{6} = \\)
9. \\(7\frac{7}{8} \div \frac{1}{4} = \\)
10. \\(5\frac{3}{12} \div 2\frac{1}{6} = \\)

Explanation:

Step1: Convert mixed numbers to improper fractions (for problems with mixed numbers)

For example, in problem 1: \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\)

Step2: Use the rule for dividing fractions: \(a\div b=a\times\frac{1}{b}\) (where \(b

eq0\))
Problem 1: \(\frac{1}{8}\div\frac{5}{2}=\frac{1}{8}\times\frac{2}{5}=\frac{1\times2}{8\times5}=\frac{2}{40}=\frac{1}{20}\) (Wait, the original handwritten answer was \(\frac{2}{40}\) which simplifies to \(\frac{1}{20}\), maybe a simplification step was missed)
Problem 2: \(4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3}\), so \(\frac{13}{3}\div\frac{1}{3}=\frac{13}{3}\times3 = 13\)
Problem 3: \(6\frac{1}{4}=\frac{6\times4+1}{4}=\frac{25}{4}\), \(\frac{25}{4}\div\frac{1}{8}=\frac{25}{4}\times8=\frac{25\times8}{4}=25\times2 = 50\)
Problem 4: \(5\frac{1}{5}=\frac{5\times5 + 1}{5}=\frac{26}{5}\), \(\frac{9}{10}\div\frac{26}{5}=\frac{9}{10}\times\frac{5}{26}=\frac{9\times5}{10\times26}=\frac{9}{2\times26}=\frac{9}{52}\)
Problem 5: \(6\frac{8}{9}=\frac{6\times9 + 8}{9}=\frac{62}{9}\), \(1\frac{1}{3}=\frac{4}{3}\), so \(\frac{62}{9}\div\frac{4}{3}=\frac{62}{9}\times\frac{3}{4}=\frac{62\times3}{9\times4}=\frac{62}{12}=\frac{31}{6}=5\frac{1}{6}\)
Problem 6: \(8\frac{2}{5}=\frac{8\times5+2}{5}=\frac{42}{5}\), \(\frac{42}{5}\div\frac{7}{10}=\frac{42}{5}\times\frac{10}{7}=\frac{42\times10}{5\times7}=12\)
Problem 7: \(3\frac{3}{4}=\frac{15}{4}\), \(2\frac{2}{3}=\frac{8}{3}\), \(\frac{15}{4}\div\frac{8}{3}=\frac{15}{4}\times\frac{3}{8}=\frac{45}{32}=1\frac{13}{32}\)
Problem 8: \(2\frac{5}{6}=\frac{2\times6 + 5}{6}=\frac{17}{6}\), \(\frac{4}{9}\div\frac{17}{6}=\frac{4}{9}\times\frac{6}{17}=\frac{24}{153}=\frac{8}{51}\)
Problem 9: \(7\frac{7}{8}=\frac{7\times8+7}{8}=\frac{63}{8}\), \(\frac{63}{8}\div\frac{1}{4}=\frac{63}{8}\times4=\frac{63}{2}=31\frac{1}{2}\)
Problem 10: \(5\frac{3}{12}=\frac{5\times12 + 3}{12}=\frac{63}{12}=\frac{21}{4}\), \(2\frac{1}{6}=\frac{13}{6}\), \(\frac{21}{4}\div\frac{13}{6}=\frac{21}{4}\times\frac{6}{13}=\frac{126}{52}=\frac{63}{26}=2\frac{11}{26}\)

Answer:

1. \(\frac{1}{20}\) (or \(\frac{2}{40}\) if not simplified)
2. \(13\)
3. \(50\)
4. \(\frac{9}{52}\)
5. \(5\frac{1}{6}\) (or \(\frac{31}{6}\))
6. \(12\)
7. \(1\frac{13}{32}\) (or \(\frac{45}{32}\))
8. \(\frac{8}{51}\)
9. \(31\frac{1}{2}\) (or \(\frac{63}{2}\))
10. \(2\frac{11}{26}\) (or \(\frac{63}{26}\))