1. A printing apparatus that outputs an image comprising: a color image obtaining unit configured to obtain a color image having multiple colors, which includes a predetermined color portion and a black portion; a monochrome image generating unit configured to generate a monochrome image from the color image, wherein the monochrome image generating unit darkens the predetermined color portion of the color image and lightens the black portion; and a monochrome image printing unit configured to print the generated monochrome image, wherein the monochrome image generating unit is configured to generate the monochrome image by weighting gradation values of each multiple color with respective weighting coefficients, wherein the multiple colors are red, green, and blue; and the monochrome image generating unit is configured to calculate the gradation value of the monochrome image by a formula {Y=r(R)+g(G)+b(B)+α}, wherein: Y represents a gradation value of the brightness of the monochrome image, R represents a red gradation value on the color image, G represents a green gradation value on the color image, B represents a blue gradation value on the color image, and r, g, b, and α are constant values; and wherein the monochrome image generating unit is configured to execute both of: assigning Y as a new lower limit when the calculated Y is equal to or less than an old lower limit; and assigning Y as a new upper limit when the calculated Y is equal to or more than an old upper limit, wherein constant α is set to a value larger than 0 and smaller than 1 depending on an extent to which black is made into a lighter color, the total sum of the constant values r, g, b, and α equals 1, and whichever constant corresponding to the color to darken out of constants r, g, and b, is set to a negative value, when: the predetermined color is not black; each of R, G, B and Y has the lower limit of 0 and the upper limit of 1; and each of R, G, B, and Y is normalized such that R=G=B=0 or Y=0 represents black, and R=G=B=1 or Y=1 represents white.