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. $9\frac{1}{2} \div 9\frac{4}{6} = \underline{\quad\quad}$

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