Question

solve the equations.

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

10.

Explanation:

Problem 1: \( 1\frac{3}{8} \div 1\frac{4}{9} \)

Step 1: Convert mixed numbers to improper fractions

\( 1\frac{3}{8} = \frac{1\times8 + 3}{8} = \frac{11}{8} \)
\( 1\frac{4}{9} = \frac{1\times9 + 4}{9} = \frac{13}{9} \)

Step 2: Divide the fractions (multiply by reciprocal)

\( \frac{11}{8} \div \frac{13}{9} = \frac{11}{8} \times \frac{9}{13} = \frac{99}{104} \)

Step 1: Convert mixed numbers to improper fractions

\( 2\frac{1}{3} = \frac{2\times3 + 1}{3} = \frac{7}{3} \)
\( 1\frac{3}{4} = \frac{1\times4 + 3}{4} = \frac{7}{4} \)

Step 2: Divide the fractions (multiply by reciprocal)

\( \frac{7}{3} \div \frac{7}{4} = \frac{7}{3} \times \frac{4}{7} = \frac{4}{3} = 1\frac{1}{3} \)

Step 1: Convert mixed numbers to improper fractions

\( 4\frac{1}{5} = \frac{4\times5 + 1}{5} = \frac{21}{5} \)
\( 3\frac{1}{2} = \frac{3\times2 + 1}{2} = \frac{7}{2} \)

Step 2: Divide the fractions (multiply by reciprocal)

\( \frac{21}{5} \div \frac{7}{2} = \frac{21}{5} \times \frac{2}{7} = \frac{6}{5} = 1\frac{1}{5} \)

Answer:

\( \frac{99}{104} \)

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