A wire of length `(3)/(2)m` is cut into two parts. If the length of one 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 step by step, we can follow these instructions:

### Step 1: Understand the problem
We have a wire of total length \( \frac{3}{2} \) meters, which is cut into two parts. One part has a length of \( \frac{2}{3} \) meters. We need to find the length of the other part.

### Step 2: Set up the equation
Let the length of the other part be \( x \). According to the problem, the sum of the lengths of both parts must equal the total length of the wire. Therefore, we can write the equation:

\[ x + \frac{2}{3} = \frac{3}{2} \]

### Step 3: 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:

\[ x = \frac{3}{2} - \frac{2}{3} \]

### Step 4: Find a common denominator
To perform the subtraction, we need a common denominator. The denominators here are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6. We will convert both fractions to have this common denominator:

\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]
\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

### Step 5: Perform the subtraction
Now we can substitute these values back into the equation:

\[ x = \frac{9}{6} - \frac{4}{6} \]

Now, subtract the numerators:

\[ x = \frac{9 - 4}{6} = \frac{5}{6} \]

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

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