To add the mixed numbers \(2 \frac{1}{2}\) and \(1 \frac{1}{7}\), we first convert them into improper fractions:
-
Convert \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{(improper fraction: } \frac{5}{2} \text{)} \]
-
Convert \(1 \frac{1}{7}\): \[ 1 \frac{1}{7} = 1 \times 7 + 1 = 7 + 1 = 8 \quad \text{(improper fraction: } \frac{8}{7} \text{)} \]
Next, we add the improper fractions \(\frac{5}{2}\) and \(\frac{8}{7}\). To do this, we need a common denominator.
The least common multiple of the denominators \(2\) and \(7\) is \(14\).
Now, we convert both fractions:
-
Convert \(\frac{5}{2}\) to a denominator of \(14\): \[ \frac{5}{2} = \frac{5 \times 7}{2 \times 7} = \frac{35}{14} \]
-
Convert \(\frac{8}{7}\) to a denominator of \(14\): \[ \frac{8}{7} = \frac{8 \times 2}{7 \times 2} = \frac{16}{14} \]
Now, add the two fractions: \[ \frac{35}{14} + \frac{16}{14} = \frac{35 + 16}{14} = \frac{51}{14} \]
Next, convert this improper fraction back into a mixed number. Divide \(51\) by \(14\): \[ 51 \div 14 = 3 \quad \text{(whole number part)} \] The remainder is: \[ 51 - (14 \times 3) = 51 - 42 = 9 \]
Thus, we can express \(\frac{51}{14}\) as the mixed number: \[ 3 \frac{9}{14} \]
The answer in mixed number form is \(3 \frac{9}{14}\).
In the requested format [whole number, numerator/denominator]:
- Whole number: \(3\)
- Numerator: \(9\)
- Denominator: \(14\)
So the final answer is:
3, 9/14