Question

dividing with mixed numbers #1
divide.

1. $3\frac{1}{2} \div \frac{1}{2} =$
2. $\frac{3}{4} \div 1\frac{2}{6} =$
3. $\frac{7}{8} \div 6\frac{1}{4} =$
4. $8\frac{1}{3} \div \frac{1}{9} =$
5. $2\frac{4}{10} \div 3\frac{8}{10} =$
6. $5\frac{1}{7} \div 4\frac{2}{7} =$
7. $\frac{5}{6} \div 4\frac{1}{4} =$
8. $7\frac{2}{5} \div \frac{9}{10} =$
9. $2\frac{2}{5} \div 4\frac{3}{5} =$
10. $5\frac{2}{3} \div \frac{4}{5} =$

Explanation:

Problem 1: \( 3\frac{1}{2} \div \frac{1}{2} \)

Step 1: Convert mixed number to improper fraction

\( 3\frac{1}{2} = \frac{3\times2 + 1}{2} = \frac{7}{2} \)

Step 2: Divide by multiplying by reciprocal

\( \frac{7}{2} \div \frac{1}{2} = \frac{7}{2} \times \frac{2}{1} = 7 \)

Step 1: Simplify and convert mixed number

\( 1\frac{2}{6} = 1\frac{1}{3} = \frac{1\times3 + 1}{3} = \frac{4}{3} \)

Step 2: Divide by multiplying by reciprocal

\( \frac{3}{4} \div \frac{4}{3} = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \)

Step 1: Convert mixed number to improper fraction

\( 6\frac{1}{4} = \frac{6\times4 + 1}{4} = \frac{25}{4} \)

Step 2: Divide by multiplying by reciprocal

\( \frac{7}{8} \div \frac{25}{4} = \frac{7}{8} \times \frac{4}{25} = \frac{7}{50} \)

Answer:

\( 7 \)

Problem 2: \( \frac{3}{4} \div 1\frac{2}{6} \)