Question

1. \\(\frac{5}{6} \div \frac{6}{5} =\\)\
2. \\(\frac{100}{200} \div \frac{10}{20} =\\)\
3. \\(6\frac{2}{3} \div 5\frac{1}{3} =\\)\
4. \\(\frac{1}{12} \div \frac{1}{4} =\\)\
5. \\(4\frac{3}{4} \div 6\frac{1}{3} =\\)\
6. \\(\frac{7}{12} \div \frac{2}{3} =\\)

Explanation:

Step1: Reciprocal divisor, multiply

$\frac{5}{6} \div \frac{6}{5} = \frac{5}{6} \times \frac{5}{6} = \frac{25}{36}$

Step2: Convert to improper fractions

$6\frac{2}{3} = \frac{20}{3}$, $5\frac{1}{3} = \frac{16}{3}$

Step3: Reciprocal divisor, multiply

$\frac{20}{3} \div \frac{16}{3} = \frac{20}{3} \times \frac{3}{16} = \frac{20}{16} = \frac{5}{4}$

Step4: Convert to improper fractions

$4\frac{3}{4} = \frac{19}{4}$, $6\frac{1}{3} = \frac{19}{3}$

Step5: Reciprocal divisor, multiply

$\frac{19}{4} \div \frac{19}{3} = \frac{19}{4} \times \frac{3}{19} = \frac{3}{4}$

Step6: Simplify fractions first

$\frac{100}{200} = \frac{1}{2}$, $\frac{10}{20} = \frac{1}{2}$

Step7: Reciprocal divisor, multiply

$\frac{1}{2} \div \frac{1}{2} = \frac{1}{2} \times \frac{2}{1} = 1$

Step8: Reciprocal divisor, multiply

$\frac{1}{12} \div \frac{1}{4} = \frac{1}{12} \times \frac{4}{1} = \frac{4}{12} = \frac{1}{3}$

Step9: Reciprocal divisor, multiply

$\frac{7}{12} \div \frac{2}{3} = \frac{7}{12} \times \frac{3}{2} = \frac{21}{24} = \frac{7}{8}$

Answer:

1. $\frac{25}{36}$
2. $\frac{5}{4}$
3. $\frac{3}{4}$
4. $1$
5. $\frac{1}{3}$
6. $\frac{7}{8}$