Apples and Oranges

One of the nicest things about proportions is that they can be used to solve problems involving items that don t seem to have anything in common except for their ratios to one another. For instance, if you re told that three apples can be traded for four oranges, then you can figure out how many apples you can get for 28 oranges by using a proportion. 

The Problem How many apples can you trade for your 28 oranges if the current trading rate is that three apples are worth four oranges  

Write the apples over the oranges in one fraction, and then put the 28 oranges on the bottom of the other fraction — opposite the oranges in the first fraction. Let the unknown number of apples be represented byx 

This proportion is solved by reducing across the bottom and cross-multiplying. 

It takes 21 apples to get 28 oranges. As long as you have apples across from apples and oranges across from oranges, the proportion will work. Another format for this is to have apples over apples and oranges over oranges, with the equivalence of 3 and 4 across from one another. (Refer to Working with the Math of Proportions, earlier in this chapter, if you need help with the manipulations of proportions.) 

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CUCI2 on phenyl magnesium halides also provide reasonable quantities of diphenyl. Uses include its action as a fungistat during shipment of apples and oranges, and as a heat transfer agent (dowtherms) mixed with diphenyl ether and terphenyls. 

Never compare apples and oranges if the distinction is evident or plausible. 

Pyrimidifen residues in fruits such as apple and orange are stable (>90%) after frozen storage for 2 months. 

Comparisons between observed data and model predictions must be made on a consistent basis, i.e., apples with apples and oranges with oranges. Since models provide a continuous timeseries, any type of statistic can be produced such as daily maximums, minimums, averages, medians, etc. However, observed data are usually collected on infrequent intervals so only certain statistics can be reliably estimated. Validation of aquatic chemical fate and transport models is often performed by comparing both simulated and observed concentration values and total chemical loadings obtained from multiplying the flow and the concentration values. Whereas the model supplies flow and concentration values in each time step, the calculated observed loads are usually based on values interpolated between actual flow and sample measurements. The frequency of sample collection will affect the validity of the resulting calculated load. Thus, the model user needs to be aware of how observed chemical loads are calculated in order to assess the veracity of the values. 

For any equation to be valid, every term in the equation must have the same physical character, i.e., the same net dimensifons (and consequently the same units in any consistent system of units). This is known as the law of conservation of dimensions (otherwise known as the fruit salad law — you can t add apples and oranges, unless you are making fruit salad ). Let us look further at Eq. (2-6). Since both z and x have dimensifons of length, e.g., [x] = L, [z] = L, it follows from the fruit salad law that the dimensions of a and b must be... 

Essentially what we are trying to do in this attempt at prioritization is to combine apples and oranges to make a tasty fruit salad If the recipe called for equal proportions of apples, grapes, and watermelon one would NOT use 5 apples, 5 grapes, and 5 watermelons Obviously such a fruit salad would be dominated by the watermelon since it is so much bigger. Thus, one needs to make sure that the scale of each of the components is adjusted so that one can... 

Andon, M. B., Peacock, M., Kanerva, R. L., and DeCastro, J. A. S. (1996b). Calcium absorption from apple and orange juice fortified with calcium citrate malate (CCM). /. Am. Coll. Nutr. 

Certain dimensional questions may be raised by vector equations such as (11.68), which seem to mix apples and oranges. Each vector R,) carries physical units, because its length as... 

If a store sells apples and oranges at a ratio of 2 5, it means that for every two apples the store sells, it sells 5 oranges. 

The third advantage, according to Ayres, is the possibility to accomplish year-to-year environmental auditing for large firms, industries, or even nations. The current approach is highly unsatisfactory, with a built-in incompetence to compare flows of different nature "apples" and "oranges." Exergy takes away this important imperfection. 

The same types and numbers of bioassays must always be applied to the same series of effluents discharging to a common aquatic environment. Failure to do so invalidates appraising the relative toxicity contribution of each wastewater in relation to others, as one would clearly be comparing apples and oranges in such an event. It is also important to employ bioassays (within a designated battery) that are not redundant in the toxicity information they yield (e.g., two bioassays significantly correlated to one another in terms of their effluent measurement... 

In order for chemists to use balanced equations, they need a way to count molecules and atoms. As you can imagine, molecules and atoms are so tiny that it is impossible to count them out as you would apples and oranges. 

All comparisons of the elemental composition of soil humates with aquatic humates must be viewed with caution. In recent years, the extraction methodology has changed rapidly. A soil sample extracted with base in the classical manner may have up to 20% carbohydrate and up to 10% ash, while a sample extracted with XAD resins may have less than 2% carbohydrate and 2% ash. To compare two samples extracted by two different methods would be akin to comparing apples and oranges. Fortunately, a body of literature is accumulating which reports the properties of humates extracted by a single, well-defined method. 

Dietrich, D. R. (1997). Doubting nongenotoxic mechanisms of renal cancer comparing apples and oranges in the alpha2u-globulin hypothesis. Environ Health Perspect 105, 898-902. 

Another "apples and oranges" comparison can arise when risk assessments have been performed on two or more putative alternatives, for example construction and operation of "conventional" versus "renewable energy" electric power plants. Even If the same risk measure Is used In each case, little Is gained In their comparison If the alternatives are not equivalent (or different) In some well-defined way. Changing the definition of equivalence may alter any conclusions to be drawn from a risk assessment. 

Common to these examples is that each object (geographical sites, waste disposal sites, databanks, chemicals, managing options) is characterized by more than one quantity. Objects that are characterized by several quantities (we call them attributes44 -see later for details-) often cannot be ordered, because there are conflicts between their attributes. Metaphorically we are talking of comparing apples and oranges. 

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