Division of fractions

To change an improper fraction to a mixed number, divide die denominator into the numerator. The quotient (die result of die division of diese two numbers) is die whole number. Then place die remainder over the denominator of die improper fraction. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

Figure 1. An unrooted phylogenetic tree of the myosins based on the amino acid sequence comparison of their head domains demonstrating the division of the myosin superfamily into nine classes. The lengths of the branches are proportional to the percent of amino acid sequence divergence and a calibration bar for 5% sequence divergence is shovk n. The different classes of myosins have been numbered using Roman numerals in rough order of their discovery and hypothetical models of the different myosin structures are shown. Question marks indicate either hypothetical or unknown structural features, and only a fraction of the known myosins are shown. (Taken, in modified form, from Cheney et al., 1993).

If the unit simply divides the inlet stream into two or more outlet streams, each with the same composition as the inlet stream, then the split-fraction coefficient for each component will have the same value as the fractional division of the total stream. A purge stream is an example of this simple division of a process stream into two streams the main stream and the purge. For example, for a purge rate of 10 per cent the split-fraction coefficients for the purge stream would be 0.1. 

For reactor design purposes, the distinction between a single reaction and multiple reactions is made in terms of the number of extents of reaction necessary to describe the kinetic behavior of the system, the former requiring only one reaction progress variable. Because the presence of multiple reactions makes it impossible to characterize the product distribution in terms of a unique fraction conversion, we will find it most convenient to work in terms of species concentrations. Division of one rate expression by another will permit us to eliminate the time variable, thus obtaining expressions that are convenient for examining the effect of changes in process variables on the product distribution. 

Electrofining A process for purifying petroleum fractions by extracting them with various liquid reagents and then assisting their separation by means of an electric field. Developed by the Petreco Division of Petrolite Corporation, and first operated in California in 1951. 

Mercapsol A process for removing mercaptans from petroleum fractions, using aqueous sodium or potassium hydroxide containing cresols and solubility promoters. Developed by the Pure Oil Company, a division of the Union Oil Company of California, and first operated in West Virginia in 1941. 

VPSA [Vacuum pressure swing adsorption] Also known as VSA. A version of PSA in which the adsorbed gas fraction is desorbed by reducing the pressure, rather than by displacement. Proprietary versions developed by the Linde Division of Union Carbide Corporation are known as OxyGEN and NitroGEN. Invented by L Air Liquide, France, in 1957. 

Figure 15.10. Figure 15.10(a) represents the total volume as one PFR, with reaction taking place leading to a particular fractional conversion at the outlet. Figure 15.10(b) represents the same total volume divided into three parts, not necessarily equal, in series. Since the mere division of V into three parts does not alter the operating conditions from point to point, the two configurations are equivalent, and lead to the same final conversion. That is, from equation 15.2-2,... 

The nearest approach to the desired end is attained by repeating the process of distillation. In the case of low-boiling substances it can be done in one operation with the help of so-called fractionating columns, which are devices introduced into the gaseous phase before final condensation occurs. In the several divisions of these columns, which can be constructed in various forms (Fig. 13), vapours are liquefied by air cooling, and the vapours which are formed later must pass through this liquid which lies in their path. In this way... 

Niall, H. D. Fractions 2, 1 (1969). News of Biochemical Instrumentation, Palo Alto, Calif. Spinco Division of Beckman Instruments, Inc. 

Think of the division of money as being divided into three parts — one part in the 5 percent fund and two-thirds in the 10 percent fund. Rather them use fractions, let the whole three-thirds be represented by 3x. Then let x represent the amount of money invested at 5 percent and 2x represent the amount invested at 10 percent. Write the two interest terms, add them up, and set them equal to 20,000. 

The contribution of the y-spectra to knowledge about radionuclide fractionation is limited pure and nearly pure f3 emitters (e.g., 89Sr, 90Sr, and 91Y) are not detectable by y-spectrometry only relative magnitudes of the y-emitters can be determined from the spectra. Quantitative information on the radiochemical composition was obtained by radiochemical analyses performed by Tracerlab, Division of Laboratory for Electronics, Inc., Richmond, Calif. 

Our water-column sampling techniques include in-line filtration using an all-Teflon sampling device with quartz fiber filters (0.7- xm nominal size cutoff) to differentiate between dissolved and particulate phases (21). Particulate concentrations (nanograms per gram) and subsequent calculations of partitioning between particle and aqueous phases (log KD) are based on this particle size division. This fractionation scheme precludes direct estimates of colloidal influences on Hg transport. 

Numbers may be combined using the arithmetic operations of addition ( + ), subtraction (—), multiplication (x) and division (/ or -). The type of number (integer, rational, irrational) is not necessarily maintained under combination. Thus, for example, addition of the fractions 1/4 and 3/4 yields an integer, but division of 3 by 4 (both integers) yields the rational number (fraction) 3/4. When a number (say, 8) is multiplied by a fraction (say, 3/4), we say in words that we want the number which is three quarters of 8 which, in this case, is 6. 

Two substitutions are necessary to obtain the diffusion algorithm. First, division of both members of Equation 20.3 by C, the bulk concentration, transforms all concentration to fractional values ... 

Figure 1. Separation and further division of first three fractions of the bitumen...

Separation, division of the feedstock into various streams (or fractions) depending upon the nature of the crude material. 

Belyaeva, E. Yu., Perminova, I. V., Kudryavtsev, A. V., and Novikov, A. P. (2006). Compension of non-exclusion effects during gel-permeation fractionation of humic substances. In Humic Substances—Linking Structure to Lunctions, Vol. 45-1, Frimmel F. H., and Abbt-Braun G., eds., Book Series Division of Water Chemistry, Engler-Bunte Institute, University of Karlsruhe, Karlsruhe, pp. 217-220. 

In operationally defined speciation the physical or chemical fractionation procedure applied to the sample defines the fraction isolated for measurement. For example, selective sequential extraction procedures are used to isolate metals associated with the water/acid soluble , exchangeable , reducible , oxidisable and residual fractions in a sediment. The reducible, oxidisable and residual fractions, for example, are often equated with the metals associated, bound or adsorbed in the iron/manganese oxyhydroxide, organic matter/sulfide and silicate phases, respectively. While this is often a convenient concept it must be emphasised that these associations are nominal and can be misleading. It is, therefore, sounder to regard the isolated fractions as defined by the operational procedure. Physical procedures such as the division of a solid sample into particle-size fractions or the isolation of a soil solution by filtration, centrifugation or dialysis are also examples of operational speciation. Indeed even the distinction between soluble and insoluble species in aquatic systems can be considered as operational speciation as it is based on the somewhat arbitrary definition of soluble as the ability to pass a 0.45/Am filter. 

In water studies it is standard practice to filter the sample soon after collection, usually through a 0.45p,m membrane disc (made of cellulose acetate, cellulose nitrate or polycarbonate). This process arbitrarily divides the sample components into soluble and insoluble fractions, but as shown in Table 2.3, the average size of different chemical species varies widely, and some differentiation between species can be obtained through using filter media of different pore sizes. For example, fully dissolved compounds can be separated from finer colloidal forms by using gel filtration and dialysis, and sub-division of the total content into fractions based on particle or molecular size (see Section 2.3) has been used for speciation of elements in waters. 

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