What is the greatest whole number that is less than (5/2) ^3 divided by (3/4) ^2

First work out (5/2) ³ by cubing both the numerator and denominator to give: 125/8

then work out (3/4) ² by squaring both the numerator and denominator to give: 9/16

then divide 125/8 by 9/16

using the stay-change-flip method of division:

the first term stays the same, the divide becomes multiply and the second fraction is flipped upside down.

so:

125/8 x 16/9 = 2000/72

then just divide 2000 by 72 to give: 27.78 to 2 d. p

therefore the greatest whole number than 27.78 is 27.