Someone asked how to convert 2:1 sugar syrup (2 parts sugar to 1 part water) to 1:1 syrup (1 part sugar to one part water). I think the easiest way would be to weigh the syrup, divide by 3, and add that much water to the mix.
Right now, your syrup is made of three parts (2 parts sugar and 1 part water). Each of these three parts weighs roughly the same amount. So by finding how much 1/3 of the total weighs, you have estimated how much water is in the mix. By adding that much water again, you have 2/3 of the total original weight in sugar and 2/3 of the total original weight in water—or 4/3 the total original weight in a ratio of 1:1.
For example, if you have 7 pounds of 2:1 syrup, divide by 3, which equals 2.3 pounds. Now measure 2.3 pounds of water and add it to the 7 pounds of 2:1 syrup and get 9.3 pounds of 1:1 syrup—or 4/3 as much by weight as you started with (7 x 4/3 = 9.33).
Although I’ve written that you can use either weight (mass) or volume when measuring the sugar and water to make syrup, the volumes are not additive. So if you add a gallon of sugar to a gallon of water you get more than a gallon of syrup, but less than two gallons. On the other hand, if you add a pound of sugar to a pound of water you get two pounds of syrup. Therefore, you need to do all your calculations by weight.
For the reason that beekeepers assume that water and sugar can be measured by either weight or volume, click here.
By the way, I’ve been told this description is clear “if you are awake, paying attention, and adequately caffeinated.” So if you still don’t understand, you might try that.