Fewer women are married when they give birth to their first child, although a growing number are living with the baby’s father without being wed, according to a report on women’s fertility released Tuesday.

The study on long-term trends in childbearing shows a “rise in cohabitation as a family form,” said the report written by two demographers in the Census Bureau’s fertility and family statistics branch. Roughly 6 in 10 of all women between ages 15 and 50 are mothers.

Overall, there has been a steady decline in the percentage of women who are married when they have their first child, from 70 percent in the early 1990s to just 55 percent since 2005, the report said.

The slide is even steeper among young mothers, those under the age of 23 at first childbirth: Since 2005, married mothers accounted for just 1 in 4 births among women in that age bracket.

But that doesn’t mean those who were unwed were necessarily single mothers, raising their newborn in a home in which the father was absent. About 25 percent of all first-time mothers are living with their partners, up from 14 percent two decades ago.

“The growth in cohabitation as a context for first birth has roughly paralleled the decline in marriage,” the report concluded, noting that among young mothers more babies are being born to men who are living with their partners than married to them.

The trend is partly due to long-running changes in childbearing, particularly among women who go to college. More women are delaying childbirth until they complete their education, and their birth rates spike when they are in their early 30s. In contrast, birthrates for women who never finished high school peak in their early 20s.

The census report also noted striking differences by race.

In 2012, the year the study analyzed, the lowest fertility rate was among non-Hispanic white women, with 49 births for every 1,000 women. Black and Asian women had a birth rate of 57 per 1,000 women.

Hispanics, one of the fastest-growing groups in the country, had 66 births among every 1,000 women. More than half, 52 percent, were to women who were born in the United States.

Asian women had the highest rates of childlessness, and Hispanics had the lowest.