To determine how many hours Mrs. Nygaard will need to work over the weekend to finish grading, we first need to find the total hours she will work during the week and then subtract that from the total time she needs (12 hours).
Let's add up the hours she will grade for each day:
- Monday: 1 and three-fourths hours = \( 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \) hours
- Tuesday: 1 and one-half hours = \( 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \) hours
- Wednesday: 1 and one-fifth hours = \( 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \) hours
- Thursday: 2 hours = 2 hours
- Friday: 1 and one-fourth hours = \( 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \) hours
Now let's convert all of these hours to have a common denominator (the least common multiple of 4, 2, 5, 1, and 4 is 20):
- Monday: \( \frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20} \)
- Tuesday: \( \frac{3}{2} = \frac{3 \times 10}{2 \times 10} = \frac{30}{20} \)
- Wednesday: \( \frac{6}{5} = \frac{6 \times 4}{5 \times 4} = \frac{24}{20} \)
- Thursday: \( 2 = \frac{2 \times 20}{1 \times 20} = \frac{40}{20} \)
- Friday: \( \frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20} \)
Now let's add these fractions together:
\[ \frac{35}{20} + \frac{30}{20} + \frac{24}{20} + \frac{40}{20} + \frac{25}{20} = \frac{35 + 30 + 24 + 40 + 25}{20} = \frac{154}{20} \]
Calculating \( \frac{154}{20} \):
\[ \frac{154 \div 2}{20 \div 2} = \frac{77}{10} = 7.7 \text{ hours} = 7 \frac{7}{10} \text{ hours} \]
Now let's subtract this from the 12 hours for grading:
\[ 12 - 7.7 = 12 - 7.7 = 4.3 \text{ hours} = 4 \frac{3}{10} \text{ hours} \]
Thus, Mrs. Nygaard will need to work 4 and \( \frac{3}{10} \) hours over the weekend to finish grading the projects. Therefore, the answer is:
4 and StartFraction 3 over 10 EndFraction hours.
6 answers