Question

Add.

3/5+7/8+3/10

Enter your answer in the box as a mixed number in simplest form.

Answer 1

To add the fractions \( \frac{3}{5} + \frac{7}{8} + \frac{3}{10} \), we first need to find a common denominator.

The denominators are 5, 8, and 10. The least common multiple (LCM) of these numbers is 40.

Next, we convert each fraction to have a denominator of 40:

1. For \( \frac{3}{5} \):
\[
\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}
\]

2. For \( \frac{7}{8} \):
\[
\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}
\]

3. For \( \frac{3}{10} \):
\[
\frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40}
\]

Now, we can add the fractions:
\[
\frac{24}{40} + \frac{35}{40} + \frac{12}{40} = \frac{24 + 35 + 12}{40} = \frac{71}{40}
\]

To convert \( \frac{71}{40} \) to a mixed number, we divide 71 by 40:
- 71 divided by 40 is 1 with a remainder of 31.

Thus, we can express \( \frac{71}{40} \) as:
\[
1 \frac{31}{40}
\]

Now, the fraction \( \frac{31}{40} \) is already in simplest form since 31 is a prime number and does not have common factors with 40.

Therefore, the final answer in mixed number form is:
\[
1 \frac{31}{40}
\]