Division bars

Parentheses and division bars (fraction bars) are both symbols of enclosure. Whenever there are symbols of enclosure, execute any arithmetic operations inside the symbol of enclosure first. The general rule is to work from the innermost symbol of enclosure to the outermost, multiplying and dividing then adding and subtracting. Consider this example, which involves both kinds of symbols of enclosure and order of operations. 

Here we come to a very common error. Many students are tempted to divide 30 by 3 first, and then multiply by 5. But the division bar is a symbol of enclosure, so multiply 3 times 5 first and then divide 30 by 15. 

Moving a quantity across a division bar changes the sign of the exponent. This is true for numbers as well as variables or units. 

Remember to follow the rules for symbols of enclosure. The division bar is a symbol of enclosure, so do the operations in the numerator and in the denominator before performing the division. By the way, did you notice you can easily solve this problem without a calculator Try regrouping the mantissas separately from the powers of 10. 

A division bar is a symbol of enclosure do the subtraction first, keeping three decimal places ... 

If a patient receives 8.0 L of oxygen per minute, how many milliliters per second is this Notice we need to divide the units of L from the numerator and units of minutes from the denominator. You know that 60 s = 1 min and 1 mL = 1 x 10 3 L. Be careful to apply the conversion factor so that the unit we need to eliminate is on the opposite side of the division bar from the same unit in the conversion factor. Let s change minutes into seconds first, and then change liters into milliliters. Of course, you can apply the conversion factors in any order you like. 

If there is a division bar under the radical (as in tom and place each part under its own radical ... 

Between the 4° and the horizontal plane, no obstruction is allowed except for A pillars, vent window division bars, rearview mirrors and windscreen wipers (see Fig. 24). 

As an alternative, UN Regulation No. 125 includes the option, that the conical projection of all obstructions (except for A pillars, vent window division bars, rearview mirrors and windscreen wipers) between the forward 4° plane and another plane, which declines 1° on a defined area S do not exceed more than 20 % of the total area S (see Fig. 25). This option only a ddresses obstractions that fall under the forward 4° plane. It cannot be applied for obstmctions to the sides (e.g. upper edge of the doors). 

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).

Barring direct measurement of foam texture, we adopt the following reasoning. Because of the generation of foam bubbles by the snap-off and division mechanisms (4), bubble sizes are expected to be approximately that of pore bodies. Thus, the linear bubble density should scale roughly as n 6/Dwhere... 

One important distinction to note is that a fraction bar, which serves as a division symbol, is also treated as a grouping symbol. 

To perform operations with complex fractions, it is usually easiest to recall that the fraction bar means division and rewrite the complex fraction as one fraction divided by another fraction. 

The International Union of Puie and AppUed Chemistry now recommends a standard pressure of 0.1 MPa (1 bar) in place of the previously accepted standard of 101.325 kPa (1 atm). The difference in thermodynamic quantities is not significant for condensed phases, and differences in A// values are not significant even for gases, but the user of thermodynamic tables will have to note carefully the standard state chosen for any compilation of data. See Ref. 1, pp. 2—23 lUPAC Division of Physical Chemistry, Commission on Symbols, Terminology and Units, Manual of symbols and terminology for physico-chemical quantities and units, M. L. McGlashan, M. A. Paul, and D. N. Whiffen, eds., Pure andApp. Chem 51, 1 (1979), and Appendix IV, Pure and Applied Chem. 54, 1239 (1982). 

Fig. 1. (opposite page) Distribution of FITC-conjugated BSA in various fibroblast cell lines under different fixation/permeabilization regimes. (A-D) Protein distribution in living cells (A) PtKj, (B) CHO, (C) 3T3, and (D) HeLa cells. The protein is excluded from the nuclei of all cells. (E-H) Protein distribution in cells extracted for 10 min with 0.1% Triton X-100 before fixation for 30 min with 3.7% formaldehyde (E) PtKi, (F) CHO, (G) 3T3, and (H) HeLa cells. Nuclear fluorescence is seen in (E) PtKj and (G) 3T3 cells. (I-L) Protein distribution in cells extracted for 10 min with 1% Triton X-100 before fixation for 30 min with 3.7% formaldehyde (I) PtKj, (J) CHO, (K) 3T3, and (L) HeLa cells. No fluorescence is detected in the cells with the exception of some nuclear fluorescence seen in (L) HeLa cells. (M-P) Protein distribution in cells fixed for 30 min with 3.7% paraformaldehyde before permeabilization for 10 min with 0.1% Triton X-100. Fluorescence is seen primarily in the cytoplasm with the exception that nuclear fluorescence is seen in (M) PtKi and (N) CHO cells. (Q-T) Protein distributions in cells fixed for 5 min with 90% methanol, 50 vaM EGTA at -20°C (Q) PtKj, (R) CHO, (S) 3T3, and (T) HeLa cells. All cells show an overall low fluorescence, fibrous-textured cytoplasmic fluorescence, and bright staining at the periphery of the nucleus. 10 mm per scale division (black bar). (Reproduced with permission from ref. 6.)... 

The reactor, manufactured by the Hanovia Division of Engelhard Industries, consists of a water-jacketed Pyrex well through which a stream of water is continuously passed. The well is placed in an appropriately shaped flask containing the solution to be irradiated.2 The essentially cylindrical flask is equipped with a side arm near the top which is connected to a water-cooled condenser. There should be sufficient clearance between the bottom of the well and the flask to allow a magnetic stirring bar. The flask is so designed that the liquid level is above the top of the lamp. 

This histogram has 10 bars (17 divisions = 10). If you would like a histogram with more bars, select TOOlS and then Options from the Probe menu ... 

The number of bars in the histogram is set to 10. We would like to see more divisions, so set the Number of Histogram... 

Contours of peak temperature (K) in asteroids as functions of size (diameter) and heliocentric distance. Accretion times corresponding to various solar distances are given at the top of the figure. Shaded vertical bars mark major divisions in the asteroid belt based on spectral interpretations of asteroid thermal histories. Modified from Grimm and McSween (1993). 

Fig. 4 Thin sections of the fungal hydrogenosome (H) from Neocallimastix frontalis. In a there is one hydrogenosome in the process of division and the inner hydrogenosomal membrane is in process of septum formation. Note that there is another hydrogenosome with a double membrane, which is not in process of division. In b all the hydrogenosomes are dividing, presenting internal septa. Bars = 100 nm. (From Benchimol et al. 1997)...

Fig. 16 General aspect of T. foetus in interphase (a) and under division (b-d). Notice that in interphase the hydrogenosomes are aligned on the costa and axostyle (a), whereas during the division they are close to the nucleus (b-d). Bars = 300 nm. (Fig. 16a from Benchimol, unpublished Fig. 16b,c from Benchimol and Engelke 2003 Fig. 16d from...

Pre-purified grade of nitrogen, argon (minimum purity 99.998% oxygen content 3 ppm) and ammonia gases obtained from Linde Division of Union Carbide were employed. The nitrogen gas pressures used in this study were between 3 and 100 bar. 

The experiments were carried out in a small flow type fixed bed reactor which has been described in a recent publication (9) along with the methods of analysis by capillary gas-liquid chromatography. Results are reported that were gained with all pure n-alkanes ranging from n-hexane to n-dodecane. Feed hydrocarbons were delivered from Fluka, Buchs, Switzerland (purum). Purity exceeded 99. 5 wt. -% in any case. The Pt/Ca-Y-zeolite catalyst (0. 5 wt. -% Pt, SK 200, Union Carbide, Linde Division volume of catalyst bed 2 cm3 particle size 0. 2 - 0. 3 mm) was calcined in a dried stream of Ng and activated in a dried stream of at atmospheric pressure prior to use. The mass of dry catalyst was 1.0 g. The total pressure and molar ratio hydrogen n-alkane were kept constant at 39 bar and 17 1, respectively, whereas the reaction temperatures and space velocities were varied. 

Figure 15.10 Biocompatible microfabrication allows trapping of a single bacterium. (A, B) SEM images of a bovine serum albumin microcontainer. (C) SEM of a container after the entrance was plugged with a bacterium inside. (D) Sequence showing the container before (1) and immediately after (2) fabrication of a plug to trap the bacterium (arrow scale bar, 10 pirn.). Cell division eventually fills the trap with no loss of bacteria (3-6) (reprinted with permission from [17] 2007 American Chemical Society).

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