https://file.aiquickdraw.com/mathbot/file/1729869652255qq91p9wz.jpg

The expression shown in the image is:

\[
2 \frac{2}{3} \times 2 \frac{2}{4} + 6 \frac{2}{3} : 4 \frac{2}{3}
\]

Let’s break this down step-by-step.

### 1. Convert mixed fractions to improper fractions:
- \( 2 \frac{2}{3} = \frac{8}{3} \)
- \( 2 \frac{2}{4} = 2 \frac{1}{2} = \frac{5}{2} \)
- \( 6 \frac{2}{3} = \frac{20}{3} \)
- \( 4 \frac{2}{3} = \frac{14}{3} \)

So, the expression becomes:

\[
\frac{8}{3} \times \frac{5}{2} + \frac{20}{3} \div \frac{14}{3}
\]

### 2. Perform the multiplication:
\[
\frac{8}{3} \times \frac{5}{2} = \frac{40}{6} = \frac{20}{3}
\]

### 3. Perform the division:
\[
\frac{20}{3} \div \frac{14}{3} = \frac{20}{3} \times \frac{3}{14} = \frac{60}{42} = \frac{10}{7}
\]

### 4. Add the two results:
\[
\frac{20}{3} + \frac{10}{7}
\]

To add these fractions, we need a common denominator. The least common denominator of 3 and 7 is 21. So:

\[
\frac{20}{3} = \frac{140}{21}, \quad \frac{10}{7} = \frac{30}{21}
\]

Now add them:

\[
\frac{140}{21} + \frac{30}{21} = \frac{170}{21}
\]

### Final answer:
\[
\frac{170}{21}
\]

Would you like further details on any part of this process or have additional questions?

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Here are some related questions:
1. How do you convert mixed numbers to improper fractions?
2. What is the process of finding a common denominator when adding fractions?
3. How do you multiply and divide fractions with different numerators and denominators?
4. Can you explain why multiplying by the reciprocal is used in division of fractions?
5. How can you simplify large fractions into mixed numbers?

**Tip:** Always simplify fractions at every step to keep calculations manageable and reduce errors!

Solve the following expression: 2 2/3 × 2 2/4 + 6 2/3 ÷ 4 2/3

Learn how to solve the expression involving mixed numbers and fractions: 2 2/3 × 2 2/4 + 6 2/3 ÷ 4 2/3. The solution covers converting mixed numbers to improper fractions, performing multiplication, division, and addition of fractions. Suitable for Grades 5-7 students.

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