To calculate how much land each child received, we need to determine how much land Molly originally had, how much he donated, and what was left over for the children.
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Total Land:
Molly had \(6 \frac{2}{3}\) hectares of land. To convert this mixed number into an improper fraction: \[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3} \text{ hectares} \] -
Donations:
- Donation to the school: \( \frac{7}{8} \) hectares.
- Donation to the children's home: \( \frac{11}{2} \) hectares.
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Convert donations to a common denominator:
To find the total donations, we need to have a common denominator. The least common multiple of 8 and 2 is 8.- Convert \( \frac{11}{2} \) to eighths: \[ \frac{11}{2} = \frac{11 \times 4}{2 \times 4} = \frac{44}{8} \]
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Total Donations:
Now combine the two donations: \[ \text{Total Donations} = \frac{7}{8} + \frac{44}{8} = \frac{7 + 44}{8} = \frac{51}{8} \text{ hectares} \] -
Remaining Land:
Now subtract the total donations from the original land to find the remaining land: \[ \text{Original Land} = \frac{20}{3} \text{ hectares} \] To subtract, we need a common denominator. The least common multiple of 3 and 8 is 24.-
Convert \( \frac{20}{3} \) to twenty-fourths: \[ \frac{20}{3} = \frac{20 \times 8}{3 \times 8} = \frac{160}{24} \]
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Convert \( \frac{51}{8} \) to twenty-fourths: \[ \frac{51}{8} = \frac{51 \times 3}{8 \times 3} = \frac{153}{24} \]
Now we can find the remaining land: \[ \text{Remaining Land} = \frac{160}{24} - \frac{153}{24} = \frac{7}{24} \text{ hectares} \]
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Distribution to the Children:
The remaining land is shared between his son and daughter, which means we divide \( \frac{7}{24} \) by 2: \[ \text{Land Each Child Gets} = \frac{7}{24} \div 2 = \frac{7}{24} \times \frac{1}{2} = \frac{7}{48} \text{ hectares} \]
Thus, each child received \( \frac{7}{48} \) hectares of land.
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