Why are you asked to gram stain a mixture of gram positive and gram negative bacteria on the same slide?

The accuracy of the Gram stain is dependent on the integrity of the bacterial cell wall. Variety of things can influence the cell wall integrity. Suppose the cells have been roughly handled , gram positive cells will come out as gram-negative. If you de-colorize them for too long, Gram-positive cells will look like Gram-negative cells or if you do not decolorize enough, Gram-negatives will look like Gram-positives. Under these circumstances Gram-positive and a known Gram-negative on the same slide so that the results are reliable.

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