To find out how many miles Regina rode in total, we need to add the two distances she traveled:

1. Distance from her house to school: $3 \frac{3}{8}$ miles
2. Distance from school to her friend's house: $4 \frac{3}{5}$ miles

Step 1: Convert the mixed numbers to improper fractions

First, we convert each mixed number to an improper fraction.

• $3 \frac{3}{8}$ can be converted as follows: $3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}$

• $4 \frac{3}{5}$ can be converted as follows: $4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{20 + 3}{5} = \frac{23}{5}$

Step 2: Add the fractions

To add these fractions, they must have a common denominator. The denominators are 8 and 5, so the least common denominator (LCD) is 40.

Convert each fraction to have a denominator of 40: $\frac{27}{8} = \frac{27 \times 5}{8 \times 5} = \frac{135}{40}$ $\frac{23}{5} = \frac{23 \times 8}{5 \times 8} = \frac{184}{40}$

Now, add the fractions: $\frac{135}{40} + \frac{184}{40} = \frac{135 + 184}{40} = \frac{319}{40}$

Step 3: Simplify and convert to a mixed number

Divide the numerator by the denominator to convert back to a mixed number: $\frac{319}{40} = 7 \frac{39}{40}$

So, Regina rode a total of $7 \frac{39}{40}$ miles.

Would you like any further details on this problem?

Related Questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the process of finding a least common denominator?
3. How do you simplify an improper fraction?
4. Can you explain how to add fractions with different denominators?
5. How do you convert an improper fraction back into a mixed number?

Tip:

Always ensure that when adding fractions, you find a common denominator before performing the addition. This will make the process smoother and help you avoid mistakes.