Kaya ran `1 2/5` miles on Monday and `2 1/3` miles on Tuesday. What was the total distance, in miles, Kaya ran during those 2 days?

Options

A. `3 11/15`
B. `3 3/8`
C. `3 2/5`
D. `3 7/15`

Answer

To find the total distance Kaya ran over two days, we need to add the distances she ran on Monday and Tuesday. Let's break down the solution step by step.

### Step 1: Convert the mixed numbers to improper fractions
Kaya ran `1 2/5` miles on Monday and `2 1/3` miles on Tuesday. We need to convert these mixed numbers into improper fractions.

**For Monday:**
1. The mixed number is `1 2/5`.
2. To convert it, we multiply the whole number (1) by the denominator (5) and add the numerator (2):
\[ 1 \times 5 + 2 = 5 + 2 = 7 \]
3. So, `1 2/5` can be written as:
\[ \frac{7}{5} \]

**For Tuesday:**
1. The mixed number is `2 1/3`.
2. We do the same conversion:
\[ 2 \times 3 + 1 = 6 + 1 = 7 \]
3. So, `2 1/3` can be written as:
\[ \frac{7}{3} \]

### Step 2: Find a common denominator
To add the two fractions, we need a common denominator. The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.

### Step 3: Convert fractions to have the common denominator
Now we convert both fractions to have the denominator of 15.

**For Monday's distance:**
\[ \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \]

**For Tuesday's distance:**
\[ \frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \]

### Step 4: Add the two fractions
Now we can add the two fractions:
\[ \frac{21}{15} + \frac{35}{15} = \frac{21 + 35}{15} = \frac{56}{15} \]

### Step 5: Convert the improper fraction to a mixed number
To convert \(\frac{56}{15}\) into a mixed number:
1. Divide 56 by 15:
- 15 goes into 56 three times (since \(15 \times 3 = 45\)).
- The remainder is \(56 - 45 = 11\).
2. Thus, we can express \(\frac{56}{15}\) as:
\[ 3 \frac{11}{15} \]

### Final Answer
Kaya ran a total distance of \(3 \frac{11}{15}\) miles over the two days.

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