Reducing fractions

Cobalt is strongly adsorbed by Mn oxides. There are close relationships between Co and the easily reducible fraction of Mn (Mn oxides) in soils (Jarvis, 1984) and will be in detail discussed in next chapter. Cobalt is frequently accumulated in Mn nodules in soils (Mckenzie, 1975). It was suggested that the Co2+ ion was first sorbed, then slowly oxidized to Co3+ and became incorporated into the surface layers of the crystal lattice, releasing the Mn2+ ion into the solution (Bums, 1976 Mckenzie, 1975). X-ray photoelectron spectroscopy showed that Co3+ was present on the surface of bimessite after the sorption of the Co2+ ions took place (Murray and Dillard, 1979). Traina and Donor (1985) suggested that the Mn release during Co2+ sorption resulted not only from the oxidation of Co2+ to Co3+, but also... 

Ehrlich et al. (submitted) measured Cu isotopic fractionation between aqueous Cu(II) and covellite between 2 and 40°C (Fig. 10). The temperature-dependent isotope fraction is fairly large 3%o) and hints at a redox control of Cu isotopic variability in abiotic systems. Marechal and Sheppard (2002) conducted experiments at 30 and 50°C between malachite and a chloride solution for Cu isotope fractionation and between smithsonite and a nitrate solution for Zn. They found that, in this temperature range, Cu in malachite is 0.2 to 0.4%o lighter than in the chloride solution. Replacing the chloride by nitrate ion reduces fractionation which indicates that the coordination of the Cu ion dictates isotopic fractionation. In contrast, Zn isotope fractionation between smithsonite and fluid is extremely small (<0.1%o). 

Fia. 2. Fractionation of human serum high-density lipoprotein ap>oprotein (apo HDD, scheme 2. Such a procedure takes advantage of the dimer— monomer conversion of fraction IV induced by the cleavage of the single disulfide bridge. R-IV = reduced fraction IV 8ME — 3-meroaptoethanol. Peaks — fraction HI = fraction IV fraction V. 

Proportions are created from fractions, and the traditional way of reducing fractions is to find a number that divides the numerator and denominator evenly and divide each part of the fraction by that number. Reducing fractions is sometimes referred to as cancelling. In the following proportion, the numbers in the fraction on the left are each divisible by 5. After reducing the fraction on the left, you can cross-multiply and solve the equation for x. 

TABLE 2.1 Methylation analysis of intact, desulfated, and desulfated/carboxyl-reduced fractions prepared from the sea cucumber 5. japonicas GAG... 

From the previous example, you can see that the common factors of 24 and 18 are 1,2,3, and 6. This list also shows that we can determine that the greatest common factor of 24 and 18 is 6. Determining the greatest common factor is useful for reducing fractions. 

Zinc can be found in all investigated sediments, 25% in the carbonate fraction and 40% in the easily-reducible fraction (Fig. 8-12). Solely the content of the organic and resi-... 

The purpose of the sintering operation is to convert the preform into a product with increased strength and reduced fraction of voids. Massive billets are generally sintered in an air-circulating oven heated to 365 to 380°C (689 to 716°F). Both the sintering temperature and time have a critical effect on the degree of coalescence, which in turn affects the final properties of the product. 

We ve seen how to write fractions and how to express real-life situations as fractions. We ve also learned to classify fractions as proper or improper and how to classify pairs of fractions as like or unlike. By converting unlike fractions to like fractions, we saw how to compare them. In the next chapter, well use these skills to help us add and subtract fractions. Many tests ask for answers to be put in simplest form. Now that we know how to reduce fractions, we can always write our answers in simplest form. We re ready to start REALLY working with fractions. 

If possible, reduce fractions before adding them. Be sure that after you reduce them, the fractions are still like fractions ... 

Step 1. Extraction of the acid soluble fraction (i.e., carbonates) with CH3COOH Step 2. Extraction of the reducible fraction (i.e., iron/manganese oxides) with hydroxyl amine hydrochloride... 

Metal contamination of soils is primarily due to the application of sewage sludge, manure, phosphate fertilizers, atmospheric deposition, and traffic emissions. The most common heavy metal ions found in soils are Zn, Cu, Ni, Pb, Cr, and Cd. As mentioned earlier (see Section 6.3.1.4), sequential extraction techniques can differentiate among the metal forms in a soil, typically the acid soluble fraction (e.g., carbonates), the reducible fraction (e.g., iron/manganese oxides), and the ox-idizable fraction (i.e., metals in low oxidation states). 

Reducible fraction of metals bound to iron and manganese oxides (extraction by hydroxylamine hydrochloride)... 

Figure 7.5 Separation of La-EMFs from the TCB extract by chemical reduction mass spectra of (a) TCB extract, (b) the fraction not reduced, and (c) the reduced fraction [74], (Reprinted with permission from T. Tsuchiya et aL, Reduction of endohedral metallofullerenes a convenient method for isolation, Chemistry of Materials, 16, 4343 346, 2004. 2004 American Chemical Society.)...

More recently a modified Q cycle scheme has been proposed by Crofts and colleagues [38], in which the actual existence of Q was invalidated. The apparent displacement of the midpoint potential of Q, as compared to the Q pool was interpreted as due to the large size of the pool, so that a sufficient supply of electron to the oxidoreductase could be provided by a small reduced fraction of the pool. In this scheme the RCs are proposed to function in pairs as compared to the Z>/c, complexes, so that per flash a doubly reduced quinol is available to the oxidoreductase the quinol is then oxidized at the site (now visualized as a site in rapid exchange equilibrium with the pool) in a concerted reaction on the FeS center, reducing the b cytochrome sequence and cytochrome c,. After the oxidation of two quinols two electrons are delivered to the secondary electron donors of two RCs. The other two electrons are utilized to reduce a molecule of oxidized Q in a second reducing site of the oxidoreductase, either following two turnovers of cyt. b reduction, or via the concerted action of a dimer of the b/c complex (evidence for a dimeric structure of the complex is available for N. crassa mitochondria and for... 

Renal toxicity has been attributed to sequelae from the development of the capillary leak syndrome. Vascular leak resulted in significant extravascular fluid accumulation (ascites, pleural effusions, peripheral edema) and weight gains of as much as 17 kg in 3 weeks [11]. As in sepsis syndrome, hypotension, oliguria and reduced fractional excretion of sodium accompanied the capillary leak. 

El-LE fraction "Oxidizable organic fraction Acid reducible fraction Residual fraction ... 

We have advanced (he idea (10] that during n-butane oxidation, a dynamic deactivation by intermediates/products occurs due to their high degree of interaction with active sites. The continuous production of these species during reaction as well as their consumption due to selective (anhydride fonnation) or unselcciive (CO formation) pathways leads to a pseudo steady- state situation, in which, however, a reduced fraction of the potential sites are available for the catalytic reaction. TTte real surface is thus deactivated with respect to the clean surface. The use of olefins in the hydrocarbon feedstock enhances this phenomenon, making the effects more evident and dramatic. 

Reduce Fractions To reduce a fraction, you must find the largest factor that is common to both the numerator and the denominator, the greatest common factor (GCF). Divide both numbers by the GCF. The fraction has then been reduced, or it is in its simplest form. 

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