If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:3:46

let's compare five six and five eighths let's think about what they mean five six means five out of six pieces if you have a whole let's say a whole cake and you cut it into six pieces five six is five of those six pieces five eighths again is five pieces that's something that's the same we're both talking about five pieces but this time we split our cake into eight pieces so it's five out of eight pieces we can represent that by drawing it maybe we can draw here's one whole and then another one so these are two equal holes and on one of them we can shade five six and the other five eight that way we can look and compare them so four five six if we divide this whole we were using the example of cake into six equal sized pieces not sure if those are perfect but let's say those are six equal sized pieces five six is talking about five of those pieces so one two three four five this image represents five six now four five eight let's think about it for a second well the piece is in five eighths be bigger or smaller than five six are eight bigger or smaller than six well we can draw and see if we have the same size hole which we need to have the same size hole and we draw and we split it into eight pieces this time so now we have fourths and eight these pieces these eighths one eighth is smaller than a six because this time we had to split the cake between eight people so we got smaller pieces now again we can shade five of them seems like five pieces might be equal to five pieces but we can look and see four five and now we can look and see the five six takes up more space takes up more area this is a larger amount and the reason is because each six each piece is larger so five larger pieces is more than five smaller pieces or is greater than and remember with our symbol the open side the larger side should be facing our larger number so five six is greater than five eighths here's one more but this time let's try to compare them without drawing let's just think about what these mean two fifths means two pieces out of five so one hole will split five ways and we got two of the pieces two thirds needs that same hole we'll split three ways and we got two of the pieces well which two pieces are larger the two thirds are larger because if we only have to split our pieces three ways we can have larger pieces so the two fifths are smaller these two smaller pieces are less these two smaller pieces are less than the two larger pieces and again the open end of our symbol should be facing the larger number so two fifths is less than two thirds