Question

c. $4 \div \frac{2}{3}$
f. $\frac{1}{4} \div 2\frac{2}{5}$
i. $\frac{3}{4} \div 3\frac{2}{5}$

Explanation:

Part c: \( 4 \div \frac{2}{3} \)

Step1: Recall division of fractions rule

To divide by a fraction, multiply by its reciprocal. So \( 4 \div \frac{2}{3}=4\times\frac{3}{2} \)

Step2: Simplify the multiplication

\( 4\times\frac{3}{2}=\frac{4\times3}{2}=\frac{12}{2} = 6 \)

Step1: Convert mixed number to improper fraction

\( 2\frac{2}{5}=\frac{2\times5 + 2}{5}=\frac{12}{5} \)

Step2: Apply division of fractions rule

\( \frac{1}{4}\div\frac{12}{5}=\frac{1}{4}\times\frac{5}{12} \)

Step3: Multiply the fractions

\( \frac{1\times5}{4\times12}=\frac{5}{48} \)

Step1: Convert mixed number to improper fraction

\( 3\frac{2}{5}=\frac{3\times5+2}{5}=\frac{17}{5} \)

Step2: Apply division of fractions rule

\( \frac{3}{4}\div\frac{17}{5}=\frac{3}{4}\times\frac{5}{17} \)

Step3: Multiply the fractions

\( \frac{3\times5}{4\times17}=\frac{15}{68} \)

Answer:

\( 6 \)

Part f: \( \frac{1}{4} \div 2\frac{2}{5} \)