Calculate the value of `4/(2 1/3) + 3/(1 3/4) - 5/(3 1/2)`.

Answer

To calculate the value of \( \frac{4}{2 \frac{1}{3}} + \frac{3}{1 \frac{3}{4}} - \frac{5}{3 \frac{1}{2}} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 2 \frac{1}{3} \) to an improper fraction:
\[ 2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = \frac{7}{3} \]

2. Convert \( 1 \frac{3}{4} \) to an improper fraction:
\[ 1 \frac{3}{4} = 1 \times 4 + 3 = 4 + 3 = \frac{7}{4} \]

3. Convert \( 3 \frac{1}{2} \) to an improper fraction:
\[ 3 \frac{1}{2} = 3 \times 2 + 1 = 6 + 1 = \frac{7}{2} \]

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{4}{\frac{7}{3}} + \frac{3}{\frac{7}{4}} - \frac{5}{\frac{7}{2}} \]

### Step 3: Simplify Each Fraction
To simplify each term, we multiply by the reciprocal:
1. For \( \frac{4}{\frac{7}{3}} \):
\[ \frac{4}{\frac{7}{3}} = 4 \times \frac{3}{7} = \frac{12}{7} \]

2. For \( \frac{3}{\frac{7}{4}} \):
\[ \frac{3}{\frac{7}{4}} = 3 \times \frac{4}{7} = \frac{12}{7} \]

3. For \( \frac{5}{\frac{7}{2}} \):
\[ \frac{5}{\frac{7}{2}} = 5 \times \frac{2}{7} = \frac{10}{7} \]

### Step 4: Combine the Terms
Now we combine the simplified fractions:
\[ \frac{12}{7} + \frac{12}{7} - \frac{10}{7} \]

### Step 5: Perform Addition and Subtraction
Combine the numerators over the common denominator:
\[ \frac{12 + 12 - 10}{7} = \frac{14}{7} \]

### Step 6: Simplify the Result
Now simplify \( \frac{14}{7} \):
\[ \frac{14}{7} = 2 \]

### Final Answer
The value of the expression \( \frac{4}{2 \frac{1}{3}} + \frac{3}{1 \frac{3}{4}} - \frac{5}{3 \frac{1}{2}} \) is \( 2 \).

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