The greatest number of 1/3 meter long ribbons she will get is the quotient of dividing 3/4 by 1/3 while the remaining ribbon will be the remainder.
3/4 ÷ 1/3 = 3/4 x 3/1 = 9/4 = 2 1/4
Therefore, she will cut two 1/3 meter long ribbons and 1/4 meter long ribbon will remain from the original ribbon.