Simplify the following expressions :
`9/5 " of " 37/8 xx 36/74`

Answer

To simplify the expression \( \frac{9}{5} \text{ of } \frac{37}{8} \times \frac{36}{74} \), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the expression:
\[ \frac{9}{5} \times \frac{37}{8} \times \frac{36}{74} \]

### Step 2: Simplify the fractions
Next, we can simplify the fractions where possible. Notice that \( \frac{36}{74} \) can be simplified:
\[ \frac{36}{74} = \frac{18}{37} \quad \text{(dividing both numerator and denominator by 2)} \]

### Step 3: Substitute the simplified fraction
Now, we substitute this back into our expression:
\[ \frac{9}{5} \times \frac{37}{8} \times \frac{18}{37} \]

### Step 4: Cancel common factors
Now, we can cancel the common factor \( 37 \) in the numerator and denominator:
\[ \frac{9}{5} \times \frac{1}{8} \times 18 \]

### Step 5: Simplify further
Now, we can multiply:
\[ \frac{9 \times 18}{5 \times 8} \]

Calculating the multiplication:
\[ 9 \times 18 = 162 \quad \text{and} \quad 5 \times 8 = 40 \]
So we have:
\[ \frac{162}{40} \]

### Step 6: Simplify the fraction
Now, we simplify \( \frac{162}{40} \):
Both numbers can be divided by 2:
\[ \frac{162 \div 2}{40 \div 2} = \frac{81}{20} \]

### Step 7: Convert to mixed number
To convert \( \frac{81}{20} \) to a mixed number:
\[ 81 \div 20 = 4 \quad \text{(whole number)} \quad \text{with a remainder of } 1 \]
So, we can write:
\[ \frac{81}{20} = 4 \frac{1}{20} \]

### Final Answer:
Thus, the simplified expression is:
\[ 4 \frac{1}{20} \]

---