Question

Karen had a spool of wire 15 7/8 yards long. Karen used 3 yards of wire from the spool. How many yards of wire were left on the spool? Convert your answer to a fully simplified mixed number for full credit

Answer 1

To find out how many yards of wire were left on the spool after Karen used 3 yards, we need to subtract the amount of wire used from the total length of the spool.

1. Convert the total length of the spool from a mixed number to an improper fraction:

\[
15 \frac{7}{8} = 15 + \frac{7}{8} = \frac{15 \times 8}{8} + \frac{7}{8} = \frac{120}{8} + \frac{7}{8} = \frac{127}{8}
\]

2. Convert 3 yards to a fraction with a denominator of 8:

\[
3 = \frac{3 \times 8}{8} = \frac{24}{8}
\]

3. Now, subtract the amount used from the total length:

\[
\frac{127}{8} - \frac{24}{8} = \frac{127 - 24}{8} = \frac{103}{8}
\]

4. Convert \(\frac{103}{8}\) back to a mixed number:

\(\frac{103}{8}\) can be converted by dividing 103 by 8:

\[
103 \div 8 = 12 \quad \text{(whole number)}
\]
The remainder is:

\[
103 - (12 \times 8) = 103 - 96 = 7
\]

So,

\[
\frac{103}{8} = 12 \frac{7}{8}
\]

5. Thus, the amount of wire left on the spool is:

\[
\boxed{12 \frac{7}{8}}
\] yards.