# Math that matters (Part I–Missing Women)

If we want kids/adults to learn math, we might as well make it relevant. Here are a few relevant calculations (that employ nothing more than algebra) which I find very relevant to our future. Imagine these calculations being taught to an 8th grade algebra class! Here is the first installment:

Missing women

Most people are not aware that females were systematically removed from the population during the 20th Century and it is a practice that continues today. How do we know? Well, as Nobel Prize winning economist, Amartya Sen, noted back in the 1990s, if we look at sex ratios of nations, we find several that have ratios that are far from 1:1. Pakistan and China have ratios of 0.94:1 and India has a ratio of 0.93:1 (in 2016) (these numbers are pretty much the same as they were in 1990, though Pakistan has improved slightly from 0.91:1). Given that women live longer than men, nations should have sex ratios above 1–most European nations are above 1.03:1. Given these “small” differences among nations, one might just dismiss the low ratios as “normal” variation. Unfortunately, this would be a huge mistake. Here is the math to determine what a ratio of 0.93:1 means, in comparison to a 1.03:1.

First, let’s define the variables needed:
F = number of females in a population
M= number of males in a population
T = total population = F + M
R = sex ratio = F/M

So the above two equations have 4 variables (F, M, T, & R)…if you know two (and you do, T and R, from Internet sources), you should be able to use simple algebra to compute the other two, F and M.

Again, the equations are: (1) T = F + M and (2) R = F/M

Here is how you solve these two equations:
Solving (2) for M yields (3) M = F/R, substituting (3) into (1) yields, F + F/R = T; this can be rewritten as: F(1+(1/R)) = T
which can be rewritten as
(4) F = T/(1 + 1/R)

So, you can determine how many females are in a population using this equation. This can be considered the Actual Females (Fact).

So, with a population of 1 billion (1,000,000,000; which is smaller than both India’s and China’s current population) and a sex ratio of R=0.94, we use equation (4) to solve for Fact as such:

Fact = 1,000,000,000/(1 + 1/0.94) = 485 million
So, Mact = 1 billion – 485 million = 515 million

Now to determine the Expected Females (Fexp) in a “healthy” society, with F/M = 1.03, we use equation (4) again with this new R value.
Fexp = 1,000,000,000/(1 + 1/1.03)) = 507 million
So, Mexp = 493 million

Now you can determine the “missing females” (Fmiss) using this simple formula:
Missing Females = Fmiss = Expected Females – Actual Females = Fexp – Fact

In our example above (the hypothetical nation of 1 billion people), we find:

Fmiss = 507 million – 485 million = 22 million

Is this a large number? Well, when one considers that between 50-60 million people died in World War II, I’d say it is! Also, this is only for one country (say China or India). If you were to add up all the nations in the world with “missing women,” it comes to close to 100 million! Now that is an abominable figure, isn’t it? Yet, how many of you have heard of this figure before? If you are wondering why women are missing, do some research. It isn’t a pretty story. (I wrote about this issue over 10 years ago and got it published in a local paper’s front page. Sadly, as I recall, it hardly drew any attention.)

Just to put these numbers in perspective it is sometimes valuable to imagine what a sex ratio looks like when you bring it down to a scale that we can see. Let’s say, if you had a party of 100 people and a sex ratio of 0.94, you would have 52 men and 48 women. This would hardly be noticeable, would it? Hence, now we see why we need to do the large-scale calculations to expose something very sinister.