Question

1. $5\frac{1}{4} \div 8\frac{1}{2}$
2. $\frac{8}{16} \div \frac{16}{8}$
3. $4 \div 3\frac{2}{3}$
4. $\frac{2}{5} \div 5\frac{6}{9}$

Explanation:

Problem 5

Step1: Convert mixed numbers to improper fractions

$5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}$, $8\frac{1}{2}=\frac{8\times2+1}{2}=\frac{17}{2}$

Step2: Rewrite division as multiplication by reciprocal

$\frac{21}{4}\div\frac{17}{2}=\frac{21}{4}\times\frac{2}{17}$

Step3: Simplify and calculate

$\frac{21\times2}{4\times17}=\frac{21}{34}$

Problem 6

Step1: Rewrite division as multiplication by reciprocal

$\frac{8}{16}\div\frac{16}{8}=\frac{8}{16}\times\frac{8}{16}$

Step2: Simplify and calculate

$\frac{8\times8}{16\times16}=\frac{64}{256}=\frac{1}{4}$

Problem 7

Step1: Convert mixed number to improper fraction

$3\frac{2}{3}=\frac{3\times3+2}{3}=\frac{11}{3}$, write 4 as $\frac{4}{1}$

Step2: Rewrite division as multiplication by reciprocal

$\frac{4}{1}\div\frac{11}{3}=\frac{4}{1}\times\frac{3}{11}$

Step3: Calculate product

$\frac{4\times3}{1\times11}=\frac{12}{11}=1\frac{1}{11}$

Problem 8

Step1: Convert mixed number to improper fraction

$5\frac{6}{9}=\frac{5\times9+6}{9}=\frac{51}{9}=\frac{17}{3}$

Step2: Rewrite division as multiplication by reciprocal

$\frac{2}{5}\div\frac{17}{3}=\frac{2}{5}\times\frac{3}{17}$

Step3: Calculate product

$\frac{2\times3}{5\times17}=\frac{6}{85}$

Answer:

1. $\frac{21}{34}$
2. $\frac{1}{4}$
3. $\frac{12}{11}$ or $1\frac{1}{11}$
4. $\frac{6}{85}$