Answer/ Step-by-step explanation:
To determine which division would be easier without resorting to long division calculations, the farmer can use the concept of divisibility rules.
For the 9-camp division:
The number 9 is divisible by 3, as the sum of its digits (9) is also divisible by 3.
If a number is divisible by 3, then any multiple of that number is also divisible by 3.
Since 9 is not only divisible by 3 but also a multiple of 3, dividing a total area of 8085 ha into 9 equal camps would require finding a number that is both divisible by 3 and approximately equal to 8085/9 = 898.33 ha per camp.
For the 15-camp division:
The number 15 is divisible by both 3 and 5.
The sum of its digits (1 + 5 = 6) is also divisible by 3.
Divisibility by 5 means the number must end in either 0 or 5.
Since 15 is divisible by 3 and 5, dividing a total area of 8085 ha into 15 equal camps would require finding a number that is both divisible by 3, ends in 0 or 5, and is approximately equal to 8085/15 = 539 ha per camp.
Comparing the two divisions:
Dividing by 15 allows for a greater number of factors (3 and 5) to be utilized, making it potentially easier to find an integer solution without long division calculations.
Additionally, the smaller size per camp (539 ha compared to 898.33 ha) might be more manageable for the farmer in terms of logistics and maintenance.
Thus, without performing long division calculations, the farmer could reasonably deduce that dividing the grazing land into 15 camps of equal size might be a more practical solution than dividing it into 9 camps.
