Question

Two brothers want to share a large field equally.

Answer 1

Yes, the partition gives the two brothers equal shares.

Step-by-step explanation:

Step 1:

Assume the entire field has an area of B. So one brother takes $\frac{1}{12} B$, $\frac{1}{6}B$, and $\frac{1}{4} B$

So we need to calculate how much this brother takes in terms of B.

To do this we calculate how much $\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B$ is.

Step 2:

To add $\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B$,

First take the LCM of the denominators 12, 6, and 4

The LCM is 12, we multiply the denominator to get the LCM value, this same value is multiplied to the numerator too.

$\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B = \frac{1(1)}{12(1)} B + \frac{1(2)}{6(2)} B + \frac{1(3)}{4(3)} B \\\\\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B= \frac{1B +2B+3B}{12} = \frac{B}{2}$

Step 3:

One brother gets $\frac{1}{2} B$, so we need to calculate how much the other brother gets.

The other brother's share = $B - \frac{1}{2} B = \frac{1}{2}B$

So both the brothers get equal shares