Simplify the following expressions :
`36 div 4 " of " 1/2 + 3/4 xx 3/2`.

Answer

To simplify the expression \( 36 \div 4 \text{ of } \frac{1}{2} + \frac{3}{4} \times \frac{3}{2} \), we can follow these steps:

### Step 1: Understand the expression
The expression consists of two parts: \( 36 \div 4 \text{ of } \frac{1}{2} \) and \( \frac{3}{4} \times \frac{3}{2} \).

### Step 2: Simplify \( 36 \div 4 \text{ of } \frac{1}{2} \)
The term "of" in this context means multiplication. Therefore, we can rewrite the expression as:
\[ 36 \div (4 \times \frac{1}{2}) \]
Calculating \( 4 \times \frac{1}{2} \):
\[ 4 \times \frac{1}{2} = \frac{4}{2} = 2 \]
Now, we can substitute back into the expression:
\[ 36 \div 2 \]

### Step 3: Perform the division
Now, we divide:
\[ 36 \div 2 = 18 \]

### Step 4: Simplify \( \frac{3}{4} \times \frac{3}{2} \)
Next, we simplify the second part:
\[ \frac{3}{4} \times \frac{3}{2} \]
Multiplying the fractions:
\[ \frac{3 \times 3}{4 \times 2} = \frac{9}{8} \]

### Step 5: Combine the results
Now we combine the results from Step 3 and Step 4:
\[ 18 + \frac{9}{8} \]

### Step 6: Convert 18 to a fraction
To add these two numbers, we convert 18 into a fraction with a denominator of 8:
\[ 18 = \frac{18 \times 8}{8} = \frac{144}{8} \]

### Step 7: Add the fractions
Now we can add:
\[ \frac{144}{8} + \frac{9}{8} = \frac{144 + 9}{8} = \frac{153}{8} \]

### Step 8: Convert to a mixed number
Finally, we can convert \( \frac{153}{8} \) into a mixed number:
\[ 153 \div 8 = 19 \quad \text{(with a remainder of 1)} \]
So, \( \frac{153}{8} = 19 \frac{1}{8} \).

### Final Answer:
The simplified expression is:
\[ 19 \frac{1}{8} \]

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