Let's solve each of the problems shown in the image step-by-step:

Problem j

$4.56 \times 10^4$

To evaluate this, we multiply 4.56 by $10^4$ (or 10,000): $4.56 \times 10,000 = 45600$

So, the answer to part j is: $45600$

Problem k

$(8 + 4) \times (15 - 9)$

1. First, evaluate inside the parentheses:

   • $8 + 4 = 12$
   • $15 - 9 = 6$

2. Now, multiply the results: $12 \times 6 = 72$

So, the answer to part k is: $72$

Problem l

$2 \frac{3}{4} + 5 \frac{3}{7}$

To add these mixed numbers, we convert them to improper fractions:

1. Convert $2 \frac{3}{4}$: $2 \frac{3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

2. Convert $5 \frac{3}{7}$: $5 \frac{3}{7} = \frac{35 + 3}{7} = \frac{38}{7}$

Now we add $\frac{11}{4} + \frac{38}{7}$ by finding a common denominator:

3. The least common multiple of 4 and 7 is 28. Convert each fraction: $\frac{11}{4} = \frac{11 \times 7}{4 \times 7} = \frac{77}{28}$ $\frac{38}{7} = \frac{38 \times 4}{7 \times 4} = \frac{152}{28}$

4. Add the fractions: $\frac{77}{28} + \frac{152}{28} = \frac{229}{28}$

5. Convert $\frac{229}{28}$ back to a mixed number: $229 \div 28 = 8 \text{ R } 5, \text{ so } \frac{229}{28} = 8 \frac{5}{28}$

So, the answer to part l is: $8 \frac{5}{28}$

Would you like any further details on these solutions? Here are some related questions to explore further:

1. How would you express $4.56 \times 10^4$ in scientific notation?
2. What would happen if we used different values in part k, like $(8 + 4) \times (15 - 10)$?
3. How do you simplify the addition of mixed numbers?
4. Can you practice converting improper fractions back to mixed numbers with different examples?
5. What if we needed to solve $(8 + 5) \times (15 - 9)$?

Tip: When adding fractions, always look for the least common denominator to make calculations easier.