To simplify the expression \( 2 \frac{1}{2} \times 1 \frac{4}{1} + 2 \), first convert the mixed numbers to improper fractions.
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Convert \( 2 \frac{1}{2} \): \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{(improper fraction: } \frac{5}{2}\text{)} \]
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Convert \( 1 \frac{4}{1} \): \[ 1 \frac{4}{1} = 1 \times 1 + 4 = 1 + 4 = 5 \quad \text{(improper fraction: } \frac{5}{1}\text{)} \]
So now the expression becomes: \[ \frac{5}{2} \times \frac{5}{1} + 2 \]
Next, multiply the fractions: \[ \frac{5}{2} \times \frac{5}{1} = \frac{5 \times 5}{2 \times 1} = \frac{25}{2} \]
Now, add \( 2 \) (which can be expressed as \( \frac{2}{1} \)). To add these two fractions, convert \( 2 \) to a fraction that has the same denominator:
- Convert \( 2 \) to \( \frac{4}{2} \) (since \( 2 = \frac{2 \times 2}{1 \times 2} = \frac{4}{2} \)).
Now add: \[ \frac{25}{2} + \frac{4}{2} = \frac{25 + 4}{2} = \frac{29}{2} \]
Thus, the final simplified expression is: \[ \frac{29}{2} \]
This can also be written as a mixed number: \[ 14 \frac{1}{2} \]
So, the simplified result is: \[ \frac{29}{2} \text{ or } 14 \frac{1}{2} \]
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