Question

dividing fractions and mixed numbers
example:
$2 \frac{2}{3} \div 1 \frac{1}{2} = \frac{8}{3} \div \frac{3}{2}$
$\frac{8}{3} \div \frac{3}{2} = \frac{8}{3} \times \frac{2}{3}$ dividing by a number is the same as multiplying by its reciprocal.
$\frac{8}{3} \times \frac{2}{3} = \frac{16}{9} = 1 \frac{7}{9}$
a. $4 \frac{1}{3} \div 1 \frac{1}{3}$
b. $5 \frac{5}{6} \div \frac{2}{3}$
c. $2 \frac{3}{4} \div \frac{1}{2}$
d. $1 \frac{6}{7} \div 2 \frac{3}{4}$
e. $8 \div \frac{3}{4}$
f. $5 \frac{4}{5} \div \frac{7}{8}$
g. $12 \div \frac{3}{8}$
h. $4 \frac{1}{2} \div 1 \frac{4}{5}$
i. $3 \frac{7}{8} \div \frac{6}{7}$

Explanation:

Part a: \( 4\frac{1}{3} \div 1\frac{1}{3} \)

Step1: Convert mixed numbers to improper fractions.

\( 4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3} \), \( 1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3} \)

Step2: Change division to multiplication by reciprocal.

\( \frac{13}{3}\div\frac{4}{3}=\frac{13}{3}\times\frac{3}{4} \)

Step3: Multiply numerators and denominators.

\( \frac{13\times3}{3\times4}=\frac{13}{4}=3\frac{1}{4} \)

Step1: Convert mixed number to improper fraction.

\( 5\frac{5}{6}=\frac{5\times6 + 5}{6}=\frac{35}{6} \)

Step2: Change division to multiplication by reciprocal.

\( \frac{35}{6}\div\frac{2}{3}=\frac{35}{6}\times\frac{3}{2} \)

Step3: Multiply and simplify.

\( \frac{35\times3}{6\times2}=\frac{105}{12}=\frac{35}{4}=8\frac{3}{4} \)

Step1: Convert mixed number to improper fraction.

\( 2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4} \)

Step2: Change division to multiplication by reciprocal.

\( \frac{11}{4}\div\frac{1}{2}=\frac{11}{4}\times2 \)

Step3: Multiply and simplify.

\( \frac{11\times2}{4}=\frac{11}{2}=5\frac{1}{2} \)

Answer:

\( 3\frac{1}{4} \)

Part b: \( 5\frac{5}{6} \div \frac{2}{3} \)