When a petition has been filed for the election of trustees to manage a district containing twenty thousand acres or more, the board, or, if the district extends into more than one county, the boards of the counties by joint action, shall, before the election, divide the district into three election districts for the purpose of securing a proper distribution of trustees in the district, and the division shall be so made that each election district will have substantially equal voting power and acreage, as nearly as may be. After the division is made there shall be elected one trustee for each of the election districts, but at the election all the qualified voters for the entire district shall be entitled to vote for each trustee. The division here provided for shall be for the purposes only of a proper distribution of trustees in the district and shall not otherwise affect the district or its management and control.