Penny sells shoes at the local store and recently set up a display to help sell shoes. One third of the shoes in the display are high-tops. One third of the shoes are boots, and one sixth of the shoes are flats. Eight of the shoes are sandals. How many shoes are in the display?
For this problem we need to start with the 8 sandals we know of. These represent some fraction of the total amount of shoes in the display. We need to figure out what that fraction is.
Going back to the beginning, we had 1/3 of the display taken up by high-tops, 1/3 by boots and 1/6 by flats. So far we have 2/3 and 1/6 taken up. We add these two fractions by multiplying 2/3 by 2 on top and bottom. This way we'll have common denominators.
2/3*2/2+1/6=4/6+1/6=5/6. We now know that 5/6 of the display is taken up by other shoes and that the 1/6th that's left belongs to the 8 sandals. From here, since we know that there 8 shoes in 1/6th of the display, we just need to multiply 8 shoes by 6 parts.
8*6=48 shoes total. (1/6*6=1 whole)
Hope this helped!