Molly had a 6/2/3ha Of land he donated 7 over 8 to a school and 11 over 2 hectare.To children's home, the rest of the land was shared among his son and daughter find the size of the land that each child got

Answer 1

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.

1. Total Land:
   Molly had $6\frac{2}{3}$ hectares of land. To convert this mixed number into an improper fraction: $$6\frac{2}{3}=6+\frac{2}{3}=\frac{18}{3}+\frac{2}{3}=\frac{20}{3}\text{ hectares}$$

2. Donations:

   • Donation to the school: $\frac{7}{8}$ hectares.
   • Donation to the children's home: $\frac{11}{2}$ hectares.

3. 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: $$\frac{11}{2}=\frac{11\times 4}{2\times 4}=\frac{44}{8}$$

4. Total Donations:
   Now combine the two donations: $$\text{Total Donations}=\frac{7}{8}+\frac{44}{8}=\frac{7+44}{8}=\frac{51}{8}\text{ hectares}$$

5. 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: $$\frac{20}{3}=\frac{20\times 8}{3\times 8}=\frac{160}{24}$$

   • 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: $$\text{Remaining Land}=\frac{160}{24}-\frac{153}{24}=\frac{7}{24}\text{ hectares}$$

6. Distribution to the Children:
   The remaining land is shared between his son and daughter, which means we divide $\frac{7}{24}$ by 2: $$\text{Land Each Child Gets}=\frac{7}{24}÷2=\frac{7}{24}\times \frac{1}{2}=\frac{7}{48}\text{ hectares}$$

Thus, each child received $\frac{7}{48}$ hectares of land.