To find out how many yards Mr. Thomas shoveled in one hour, we can follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- First, convert the mixed number for the yards shoveled. [tex]\(12 \frac{1}{2}\)[/tex] yards can be converted to an improper fraction.
- [tex]\(12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{24 + 1}{2} = \frac{25}{2}\)[/tex].
- Similarly, convert the mixed number for the hours taken. [tex]\(2 \frac{1}{2}\)[/tex] hours can be converted to an improper fraction.
- [tex]\(2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{4 + 1}{2} = \frac{5}{2}\)[/tex].
2. Division of Two Fractions:
- To find the rate of shoveling per hour, divide the total yards by the total hours.
- The calculation involves dividing [tex]\(\frac{25}{2}\)[/tex] yards by [tex]\(\frac{5}{2}\)[/tex] hours.
- Recall that dividing by a fraction is the same as multiplying by its reciprocal.
3. Calculate the Reciprocal and Multiply:
- The reciprocal of [tex]\(\frac{5}{2}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex].
- Now multiply [tex]\(\frac{25}{2}\)[/tex] by [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{25}{2} \times \frac{2}{5} = \frac{25 \times 2}{2 \times 5} = \frac{50}{10} = 5
\][/tex]
Therefore, Mr. Thomas shoveled 5 yards of sand per hour.
