A film show lasted for `3 2/3` hours. Out of this time `1 1/2 ` hours was spent on advertisements. 3 2 What was the actual duration of the film?

Answer

To find the actual duration of the film, we need to subtract the time spent on advertisements from the total time of the film show. Let's break it down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
The total duration of the film show is given as \(3 \frac{2}{3}\) hours. We need to convert this mixed number into an improper fraction.

1. **Convert \(3 \frac{2}{3}\)**:
\[ 3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \]

2. **Convert \(1 \frac{1}{2}\)**:
\[ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]

### Step 2: Subtract the Time Spent on Advertisements from Total Time
Now, we need to subtract the time spent on advertisements from the total time of the film show.

\[ \text{Actual Duration of Film} = \text{Total Duration} - \text{Advertisement Time} \]
\[ \text{Actual Duration of Film} = \frac{11}{3} - \frac{3}{2} \]

### Step 3: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 2 is 6.

1. **Convert \(\frac{11}{3}\) to have a denominator of 6**:
\[ \frac{11}{3} = \frac{11 \times 2}{3 \times 2} = \frac{22}{6} \]

2. **Convert \(\frac{3}{2}\) to have a denominator of 6**:
\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]

### Step 4: Perform the Subtraction
Now we can subtract the two fractions:
\[ \text{Actual Duration of Film} = \frac{22}{6} - \frac{9}{6} = \frac{22 - 9}{6} = \frac{13}{6} \]

### Step 5: Convert Back to Mixed Number
Finally, we can convert the improper fraction \(\frac{13}{6}\) back to a mixed number:
\[ \frac{13}{6} = 2 \frac{1}{6} \]

### Final Answer
The actual duration of the film is \(2 \frac{1}{6}\) hours.

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