To add \(1 \frac{1}{4}\) and \(1 \frac{1}{3}\), we first convert the mixed numbers to improper fractions.
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Convert \(1 \frac{1}{4}\) to an improper fraction: \[ 1 \frac{1}{4} = 1 \times 4 + 1 = 4 + 1 = 5 \quad \text{So, } 1 \frac{1}{4} = \frac{5}{4} \]
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Convert \(1 \frac{1}{3}\) to an improper fraction: \[ 1 \frac{1}{3} = 1 \times 3 + 1 = 3 + 1 = 4 \quad \text{So, } 1 \frac{1}{3} = \frac{4}{3} \]
Now, we need to add \(\frac{5}{4}\) and \(\frac{4}{3}\). To do this, we need a common denominator.
The least common multiple of 4 and 3 is 12. We convert both fractions to have a denominator of 12:
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Convert \(\frac{5}{4}\): \[ \frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12} \]
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Convert \(\frac{4}{3}\): \[ \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \]
Now we add the two fractions: \[ \frac{15}{12} + \frac{16}{12} = \frac{15 + 16}{12} = \frac{31}{12} \]
Next, we convert \(\frac{31}{12}\) back into a mixed number:
- Divide 31 by 12. The quotient is 2 and the remainder is 7.
- Thus, we have \(2\) as the whole number and \(\frac{7}{12}\) as the fractional part.
So, \(1 \frac{1}{4} + 1 \frac{1}{3} = 2 \frac{7}{12}\).
We write the final answer as follows:
- Whole number: 2
- Fraction: 7/12. Thus, the answer is:
2, 7/12
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