A piece of wire `3 3/4` m long broke into two pieces. One piece is `1 1/2` m long. How long is the 4 2 other piece?

Answer

To solve the problem, we need to find the length of the second piece of wire after one piece has broken off. Here’s a step-by-step solution:

### Step 1: Convert the mixed numbers to improper fractions
The total length of the wire is given as \(3 \frac{3}{4}\) m. We can convert this mixed number into an improper fraction.

\[ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \text{ m} \]

The length of the first piece is given as \(1 \frac{1}{2}\) m. We can also convert this into an improper fraction.

\[ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \text{ m} \]

### Step 2: Find the length of the second piece
To find the length of the second piece, we subtract the length of the first piece from the total length of the wire.

\[ \text{Length of the second piece} = \text{Total length} - \text{Length of the first piece} \]

Substituting the values we calculated:

\[ \text{Length of the second piece} = \frac{15}{4} - \frac{3}{2} \]

### Step 3: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple of 4 and 2 is 4. We can convert \(\frac{3}{2}\) to a fraction with a denominator of 4:

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

### Step 4: Perform the subtraction
Now we can subtract the two fractions:

\[ \text{Length of the second piece} = \frac{15}{4} - \frac{6}{4} = \frac{15 - 6}{4} = \frac{9}{4} \text{ m} \]

### Step 5: Convert the improper fraction back to a mixed number
To express \(\frac{9}{4}\) as a mixed number:

\[ \frac{9}{4} = 2 \frac{1}{4} \text{ m} \]

### Final Answer
The length of the second piece of wire is \(2 \frac{1}{4}\) m.

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