Free birth control led to greatly lower rates of abortions and births to teenagers, a large study concludes, offering strong evidence for how a bitterly contested Obama administration policy could benefit women’s health. The two-year project tracked more than 9,000 women in St. Louis, many of them poor or uninsured, who were given their choice of a range of free contraceptives. These women experienced far fewer unintended pregnancies as a result, reported Dr. Jeffrey Peipert of Washington University in St. Louis in a study published Thursday. There were 6.3 births per 1,000 teenagers in the study, compared with a national rate of 34 births per 1,000 teens in 2010. There also were substantially lower rates of abortion, when compared with women in the metro area and nationally: 4.4 to 7.5 abortions per 1,000 women in the study, compared with 13.4 to 17 abortions per 1,000 women in the St. Louis region, Dr. Peipert calculated. The national rate is almost 20 abortions per 1,000 women. Women’s health specialists said the study foreshadows the potential impact of the new health care law, in which millions of women are beginning to get contraceptives without a co-payment.