A wire of length `(3)/(2)` m is cut into two parts. If the length of one of the parts of the parts is `(2)/(3)` m, then find the length of other part.

Options

A. `(5)/(6) m`
B. `(6)/(5) m`
C. `(2)/(3) m`
D. `(1)/(6) m`

Answer

To solve the problem, we need to find the length of the other part of the wire after one part has been cut. Here’s the step-by-step solution:

1. **Identify the total length of the wire**:
The total length of the wire is given as \( \frac{3}{2} \) meters.

2. **Identify the length of one part**:
One part of the wire is given as \( \frac{2}{3} \) meters.

3. **Let the length of the other part be \( x \)**:
We can denote the length of the other part as \( x \) meters.

4. **Set up the equation**:
Since the total length of the wire is the sum of the lengths of the two parts, we can write the equation:
\[ \frac{2}{3} + x = \frac{3}{2} \]

5. **Isolate \( x \)**:
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{2}{3} \) from both sides:
\[ x = \frac{3}{2} - \frac{2}{3} \]

6. **Find a common denominator**:
The denominators are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6. We will convert both fractions to have a denominator of 6:
\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]
\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

7. **Subtract the fractions**:
Now we can substitute back into our equation:
\[ x = \frac{9}{6} - \frac{4}{6} = \frac{9 - 4}{6} = \frac{5}{6} \]

8. **Conclusion**:
The length of the other part of the wire is \( \frac{5}{6} \) meters.