Answer:
[tex]\frac{24}{7}[/tex] or [tex]3\frac{3}{7}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5}\div \frac{7}{30}[/tex]
Step 1: Apply the fraction rule: [tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{4}{5}\times \frac{30}{7}[/tex]
Step 2: Cross-cancel common factor: 5
[tex]=\frac{4}{1}\times \frac{6}{7}[/tex]
Step 3: Multiply fractions: [tex]\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{4\times \:6}{1\times \:7}[/tex]
Step 4: Multiply the numbers: [tex]4\times \:6=24[/tex]
[tex]=\frac{24}{1\times \:7}[/tex]
Step 5: Multiply the numbers: [tex]1\times \:7=7[/tex]
[tex]=\frac{24}{7}[/tex]
Therefore, the answer is [tex]\frac{24}{7}[/tex] or in the simplified form; [tex]3\frac{3}{7}[/tex]