**Core Concept:** Infant mortality rate (IMR) is a measure of child health in a population. It is defined as the number of deaths per 1,000 live births. The denominator in calculating IMR is the total number of live births in a given population.

**Why the Correct Answer is Right:**
The denominator of infant mortality rate is the total number of live births. In this case, the correct answer is "total number of live births" because the denominator represents the base from which we calculate the infant mortality rate. IMR is a ratio statistic, and the denominator ensures that the rate is not affected by differences in population size.

**Why Each Wrong Option is Incorrect:**
A. **Option A:** Total number of births (live + stillbirths) - This is incorrect because stillbirths are also included in the numerator of IMR calculation, while the denominator should only include live births.
B. Total number of births (live + stillbirths) / 2 - This is incorrect because the denominator should only include live births, not the total number of births.
C. Total number of births (live + stillbirths) / 2 + 1 - This is incorrect because it adds an extra term (1) to the denominator, making the calculation incorrect.
D. Total number of births (live + stillbirths) - This is incorrect because stillbirths are included in the denominator, but should be subtracted to avoid double counting.

**Clinical Pearl / High-Yield Fact:**
Calculating infant mortality rate (IMR) accurately requires a clear understanding of the relationship between numerator, denominator, and interpretation of the result. This helps in assessing the health status of a population and comparing the health status between different regions or time periods.