Question

The table shows the number of hours that Catherine worked last week what is the total number of hours that Catherine worked on these three days

monday 5 1/2
wednesday 6 3/4
friday 4 2/3

Answer 1

To find the total number of hours Catherine worked on those three days, we need to first convert the mixed numbers into improper fractions, and then add them together.

1. Convert the mixed numbers to improper fractions:
- **Monday**: 5 1/2 = \( \frac{11}{2} \)
(5 * 2 + 1 = 11)
- **Wednesday**: 6 3/4 = \( \frac{27}{4} \)
(6 * 4 + 3 = 27)
- **Friday**: 4 2/3 = \( \frac{14}{3} \)
(4 * 3 + 2 = 14)

2. Find a common denominator to add the fractions. The least common multiple of 2, 4, and 3 is 12.

Now we convert each fraction:
- For Monday: \( \frac{11}{2} = \frac{11 \times 6}{2 \times 6} = \frac{66}{12} \)
- For Wednesday: \( \frac{27}{4} = \frac{27 \times 3}{4 \times 3} = \frac{81}{12} \)
- For Friday: \( \frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12} \)

3. Now, add the fractions:
\[
\frac{66}{12} + \frac{81}{12} + \frac{56}{12} = \frac{66 + 81 + 56}{12} = \frac{203}{12}
\]

4. Convert the improper fraction back to a mixed number:
203 divided by 12 is 16 with a remainder of 11. So:
\[
\frac{203}{12} = 16 \frac{11}{12}
\]

Therefore, the total number of hours that Catherine worked on these three days is **16 11/12 hours**.