# MathBench>Miscellaneous

## Parts and wholes

The Recipe
• 12 oz corn-oil butter
• 10 oz eggs
• 13 oz flour
• 21 oz sugar

Earlier I said that proportions and percentages help you determine the relationship (or ratio) between the parts and the whole. I still stand by that statement, but…

It’s important to carefully define what I mean by “part” and “whole”, and this can change depending on what question I’m interested in at the moment. Ah, what fickle creatures scientists are…

So, if I ask, what percentage of the carbs come from sugar, it helps to know that flour and sugar are the only sources of carbs in the cake, and therefore what I’m looking for is a relationship between sugar (the “part”) and sugar+flour (the “whole”).

### What percentage of the carbs come from sugar?

(To make this problem interactive, turn on javascript!)

• I need a hint: Proportion: sugar / (flour + sugar)
• ... another hint ... : 21 / (21 + 13)
• ... another hint ... : 21/34 = 0.618

### Or I might want to know what percent of the recipe consists of dry ingredients

(To make this problem interactive, turn on javascript!)

• I need a hint: dry / all ingredients
• ... another hint ... : (sugar + flour) / (sugar + flour + butter + eggs)
• ... another hint ... : (21 + 13) / 56