To add $5 \frac{2}{3} + 4 \frac{7}{10}$, follow these steps:

Step 1: Convert mixed numbers to improper fractions

$5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}$ $4 \frac{7}{10} = \frac{4 \times 10 + 7}{10} = \frac{40 + 7}{10} = \frac{47}{10}$

Step 2: Find a common denominator

The least common denominator (LCD) between 3 and 10 is 30.

Convert both fractions to have a denominator of 30: $\frac{17}{3} = \frac{17 \times 10}{3 \times 10} = \frac{170}{30}$ $\frac{47}{10} = \frac{47 \times 3}{10 \times 3} = \frac{141}{30}$

Step 3: Add the fractions

$\frac{170}{30} + \frac{141}{30} = \frac{170 + 141}{30} = \frac{311}{30}$

Step 4: Convert improper fraction to mixed number

$\frac{311}{30} = 10 \frac{11}{30}$

So, $5 \frac{2}{3} + 4 \frac{7}{10} = 10 \frac{11}{30}$.

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How do you subtract mixed numbers?
2. Can you convert a decimal into a mixed number?
3. What are the steps for multiplying two mixed numbers?
4. How do you simplify fractions after addition?
5. How do you find the least common denominator for three fractions?

Tip: When adding mixed numbers, it's often easier to convert them to improper fractions first, as it simplifies the calculation.