Let's break down the problem step by step.

Step 1: Calculate the product of $\frac{4}{5}$ and $\frac{12}{2}$

$\frac{4}{5} \times \frac{12}{2} = \frac{4 \times 12}{5 \times 2} = \frac{48}{10} = \frac{24}{5}$

Step 2: Calculate the quotient of $\frac{45}{5} \div \frac{4}{5}$

Dividing fractions involves multiplying by the reciprocal of the divisor: $\frac{45}{5} \div \frac{4}{5} = \frac{45}{5} \times \frac{5}{4} = \frac{45 \times 5}{5 \times 4} = \frac{225}{20} = \frac{45}{4}$

Step 3: Add the results from Step 1 and Step 2

Now, add $\frac{24}{5}$ to $\frac{45}{4}$. To add these fractions, we need a common denominator.

The least common denominator (LCD) of 5 and 4 is 20. Convert the fractions: $\frac{24}{5} = \frac{24 \times 4}{5 \times 4} = \frac{96}{20}$ $\frac{45}{4} = \frac{45 \times 5}{4 \times 5} = \frac{225}{20}$

Now add the two fractions: $\frac{96}{20} + \frac{225}{20} = \frac{96 + 225}{20} = \frac{321}{20}$

Final Answer

The result is $\frac{321}{20}$, which can also be written as $16\frac{1}{20}$ or $16.05$ in decimal form.

Would you like a more detailed explanation, or do you have any questions?

5 Related Questions:

1. How do you find the least common denominator of two fractions?
2. What is the process for multiplying and dividing fractions?
3. How can fractions be converted into decimals and vice versa?
4. What is the difference between proper and improper fractions?
5. How can mixed numbers be added or subtracted?

Tip: When adding or subtracting fractions, always ensure they have the same denominator before performing the operation.