To solve the given expression:

$0.24 \cdot \frac{5}{6} + 4 \frac{7}{9}$

we'll break it into two parts: the multiplication and the addition.

Step 1: Calculate $0.24 \cdot \frac{5}{6}$

Convert $0.24$ to a fraction:

$0.24 = \frac{24}{100} = \frac{6}{25}$

Now, multiply this fraction by $\frac{5}{6}$:

$\frac{6}{25} \cdot \frac{5}{6} = \frac{6 \cdot 5}{25 \cdot 6} = \frac{30}{150} = \frac{1}{5} = 0.2$

Step 2: Convert $4 \frac{7}{9}$ to an improper fraction

Convert the mixed number to an improper fraction:

$4 \frac{7}{9} = \frac{4 \cdot 9 + 7}{9} = \frac{36 + 7}{9} = \frac{43}{9}$

Step 3: Add the results

Now we add $0.2$ and $\frac{43}{9}$:

Convert $0.2$ to a fraction with a common denominator of 9:

$0.2 = \frac{1}{5} = \frac{9}{45} = \frac{2}{10}$

So the expression becomes:

$\frac{2}{10} + \frac{43}{9}$

To add these fractions, find a common denominator (which is 90 in this case):

$\frac{2}{10} = \frac{18}{90}$

Now, add:

$\frac{18}{90} + \frac{43 \cdot 10}{9 \cdot 10} = \frac{18}{90} + \frac{430}{90} = \frac{448}{90}$

Simplify the fraction:

$\frac{448}{90} = \frac{224}{45} \approx 4.98$

So, the final answer is approximately $4.98$.

Would you like a more detailed explanation or have any questions about this problem?

Related Questions

1. How do you convert a decimal to a fraction?
2. How do you multiply fractions?
3. How do you convert a mixed number to an improper fraction?
4. What are common denominators, and how do you find them?
5. How do you add fractions with different denominators?
6. How do you simplify fractions?
7. Can you explain why we use the least common multiple in fraction addition?
8. What is the importance of fraction simplification in real-world problems?

Tip

Always double-check your work by converting fractions back to decimals and re-evaluating the original problem. This helps to ensure accuracy.