​Kathryn, a college​ student, works part time at a coffee house. She worked 2 StartFraction 7 Over 20 EndFraction
 hours on​ Monday, 4 and one half
 on​ Tuesday, 5 and three fourths
 on​ Wednesday, 6 and one fourth
 on​ Thursday, and 7 on Friday. How many hours did she work​ altogether?

To find the total number of hours Kathryn worked, we need to add all the hours she worked each day. The hours are given as mixed numbers, so we'll convert them into improper fractions first to make the addition easier.

The hours worked each day are:
- **Monday**: \( 2 \frac{7}{20} \) hours
- **Tuesday**: \( 4 \frac{1}{2} \) hours
- **Wednesday**: \( 5 \frac{3}{4} \) hours
- **Thursday**: \( 6 \frac{1}{4} \) hours
- **Friday**: \( 7 \) hours

### Step 1: Convert each mixed number into an improper fraction.

1. **Monday**: 
   \[
   2 \frac{7}{20} = \frac{2 \times 20 + 7}{20} = \frac{47}{20}
   \]

2. **Tuesday**:
   \[
   4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}
   \]
   To add this with the other fractions, we convert it to have a denominator of 20:
   \[
   \frac{9}{2} = \frac{9 \times 10}{2 \times 10} = \frac{90}{20}
   \]

3. **Wednesday**:
   \[
   5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}
   \]
   To add this with the other fractions, we convert it to have a denominator of 20:
   \[
   \frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20}
   \]

4. **Thursday**:
   \[
   6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{25}{4}
   \]
   To add this with the other fractions, we convert it to have a denominator of 20:
   \[
   \frac{25}{4} = \frac{25 \times 5}{4 \times 5} = \frac{125}{20}
   \]

5. **Friday**:
   \[
   7 = \frac{7}{1}
   \]
   To add this with the other fractions, we convert it to have a denominator of 20:
   \[
   \frac{7}{1} = \frac{7 \times 20}{1 \times 20} = \frac{140}{20}
   \]

### Step 2: Add all the fractions.

Now, we can add all the fractions:
\[
\frac{47}{20} + \frac{90}{20} + \frac{115}{20} + \frac{125}{20} + \frac{140}{20}
\]
Since all the fractions have the same denominator, we simply add the numerators:
\[
47 + 90 + 115 + 125 + 140 = 517
\]
So the total is:
\[
\frac{517}{20}
\]

### Step 3: Convert the improper fraction to a mixed number.

To convert \( \frac{517}{20} \) into a mixed number:
\[
517 \div 20 = 25 \text{ R } 17
\]
So, \( \frac{517}{20} = 25 \frac{17}{20} \).

### Final Answer:
Kathryn worked **25 hours and 17 minutes** altogether.

---

Would you like further details or any clarification on this solution?

Here are some related questions to explore:
1. How would you convert mixed numbers into improper fractions for addition?
2. What is the process to add fractions with different denominators?
3. How do you convert an improper fraction into a mixed number?
4. What are some real-life situations where you might need to add fractions like this?
5. How can you simplify a fraction after adding multiple fractions?

**Tip:** Always try to convert all fractions to have a common denominator before adding them. This simplifies the process!

Kathryn, a college student, works part time at a coffee house. She worked 2 7/20 hours on Monday, 4 and 1/2 on Tuesday, 5 and 3/4 on Wednesday, 6 and 1/4 on Thursday, and 7 on Friday. How many hours did she work altogether?

Learn how to calculate the total hours worked by Kathryn by adding mixed numbers and fractions. The solution involves converting mixed numbers to improper fractions and performing addition with a common denominator. Suitable for Grades 5-7.

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