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Let's solve the problems one by one:

### 35. \( 3 \frac{1}{7} + 5 \frac{2}{3} \)
Convert the mixed numbers into improper fractions:
- \( 3 \frac{1}{7} = \frac{22}{7} \)
- \( 5 \frac{2}{3} = \frac{17}{3} \)

Now, find the common denominator (LCM of 7 and 3 is 21):
\[
\frac{22}{7} = \frac{66}{21}, \quad \frac{17}{3} = \frac{119}{21}
\]
Now add the fractions:
\[
\frac{66}{21} + \frac{119}{21} = \frac{185}{21}
\]
This simplifies to \( 8 \frac{17}{21} \).

### 36. \( 19 - 8 \frac{5}{8} \)
Convert the mixed number into an improper fraction:
- \( 8 \frac{5}{8} = \frac{69}{8} \)

Convert 19 into an improper fraction with denominator 8:
\[
19 = \frac{152}{8}
\]

Now subtract the fractions:
\[
\frac{152}{8} - \frac{69}{8} = \frac{83}{8}
\]
This simplifies to \( 10 \frac{3}{8} \).

### 37. \( \frac{2}{7} \) of 154
This is a multiplication problem:
\[
\frac{2}{7} \times 154 = \frac{2 \times 154}{7} = \frac{308}{7} = 44
\]

### 38. \( 9 \frac{1}{4} \times 16 \)
Convert the mixed number into an improper fraction:
- \( 9 \frac{1}{4} = \frac{37}{4} \)

Now multiply by 16:
\[
\frac{37}{4} \times 16 = \frac{37 \times 16}{4} = \frac{592}{4} = 148
\]

Would you like more details on any specific step? Here are 5 related questions you could explore:

1. How do you find the least common denominator for adding fractions?
2. What is the process for converting mixed numbers into improper fractions?
3. How do you simplify fractions after performing operations like addition and subtraction?
4. How can you calculate fractions of whole numbers in real-world scenarios?
5. How does multiplication of a fraction and a whole number work mathematically?

Tip: Always simplify mixed numbers to improper fractions before performing operations like addition or multiplication.

Solve the following problems:
1. 3 1/7 + 5 2/3
2. 19 - 8 5/8
3. 2/7 of 154
4. 9 1/4 * 16

Solve problems involving mixed number addition, subtraction, and multiplication of fractions. Learn how to add 3 1/7 + 5 2/3, subtract 19 - 8 5/8, find 2/7 of 154, and multiply 9 1/4 by 16.

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