Question

2 wholes and 1 third plus 1 whole an 2 fiths

Answer 1

To add the mixed numbers \( 2 \frac{1}{3} \) and \( 1 \frac{2}{5} \), follow these steps:

1. **Convert mixed numbers to improper fractions:**
- For \( 2 \frac{1}{3} \):
\[
2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}
\]
- For \( 1 \frac{2}{5} \):
\[
1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5}
\]

2. **Add the improper fractions:**
- To add \( \frac{7}{3} + \frac{7}{5} \), first find a common denominator. The least common multiple of \( 3 \) and \( 5 \) is \( 15 \).
- Convert both fractions:
\[
\frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15}
\]
\[
\frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15}
\]

3. **Now add them:**
\[
\frac{35}{15} + \frac{21}{15} = \frac{35 + 21}{15} = \frac{56}{15}
\]

4. **Convert back to a mixed number:**
- Perform the division \( 56 \div 15 = 3 \) with a remainder of \( 11 \).
- So, \( \frac{56}{15} = 3 \frac{11}{15} \).

Thus, \( 2 \frac{1}{3} + 1 \frac{2}{5} = 3 \frac{11}{15} \).