Question

An electrician has 10 1/2 in. of wire. He cut 2 9/16 in. for his first job of the day and 4 3/8 in. for his second job. How much wire does the electrician have left? Express your answer in simplest form.

Answer 1

To determine how much wire the electrician has left, we need to follow these steps:

1. First, convert all mixed numbers and fractions to improper fractions.
2. Subtract the lengths of wire used from the total length.

**Step 1: Convert to improper fractions**

The total amount of wire:
\[
10 \frac{1}{2} = \frac{21}{2}
\]

The length of wire cut for the first job:
\[
2 \frac{9}{16} = \frac{2 \times 16 + 9}{16} = \frac{32 + 9}{16} = \frac{41}{16}
\]

The length of wire cut for the second job:
\[
4 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}
\]

**Step 2: Convert all fractions to a common denominator**

The denominators of the fractions are 2, 16, and 8. The least common multiple of these denominators is 16.

Now we convert each fraction to have a denominator of 16:
- The total wire:
\[
\frac{21}{2} = \frac{21 \times 8}{2 \times 8} = \frac{168}{16}
\]
- The first job:
\[
\frac{41}{16} \quad \text{(no change needed)}
\]
- The second job:
\[
\frac{35}{8} = \frac{35 \times 2}{8 \times 2} = \frac{70}{16}
\]

**Step 3: Calculate the total length of wire used**

Now we add the lengths used for both jobs:
\[
\frac{41}{16} + \frac{70}{16} = \frac{41 + 70}{16} = \frac{111}{16}
\]

**Step 4: Subtract from the total length of wire**

Now we subtract the total amount of wire used from the initial total:
\[
\frac{168}{16} - \frac{111}{16} = \frac{168 - 111}{16} = \frac{57}{16}
\]

**Step 5: Convert back to a mixed number (if necessary)**

Now, we convert \(\frac{57}{16}\) back to a mixed number:
\[
57 \div 16 = 3 \quad \text{(remainder 9)}
\]
Thus,
\[
\frac{57}{16} = 3 \frac{9}{16}
\]

**Final Answer:**
The electrician has \(\boxed{3 \frac{9}{16}}\) inches of wire left.