The way to read this is first look at the top column header to know what universe you're starting with. If the column is "Married couple family households", then everything in that column will only include married couple family households (eg. the row that says "Total households", for that column, is total households THAT ARE married couple family households.
Then, when looking at a row with a percentage, check what's above the indented section to see what the denominator for that percentage is. So "Households for with one or more people under 18 years" is under "Total households"... so if it's in the column for "Married couple family households", then that means, of all the households that are married couple households, what percentage have people under 18 years?
I think you might be misunderstanding with your contention that the math doesn't work. The percentages of male- and female-headed no-spouse family households with kids are independent of each other, and both are independent of the percentage of married family households with kids.
Your assumption that a+b+c+d=all works for the absolute numbers (count up the total number of households and they equal the total in the first column). It doesn't work for percentages, since they need to be weighted by the size of the population. 41.8% of married family household have kids, 55% of male-no-spouse family households have kids, 62% of female-no-spouse family households have kids. Together, that's about 79 million households. But then, there are 42 million non-family households, of which less than 1% have kids. So that brings down the total percentage for all households to 30.7%.