Take 1/12 as the unit fraction. Let's look at multiples of a twelfth.
2/12=1/6 because 2 divides into 12 6 times.
3/12=1/4
4/12=1/3
5/12 doesn't simplify
6/12=1/2
7/12 doesn't simplify
8/12=2/3 common factor 4
9/12=3/4 common factor 3
10/12=5/6 common factor 2
11/12 doesn't simplify.
1/60 is another interesting unit fraction:
2/60=1/30; 3/60=1/20; 4/60=1/15; 5/60=1/12; 6/60=1/10; 8/60=2/15; 9/60=3/20; 10/60=1/6;
12/60=1/5; 14/60=7/30; 15/60=1/4; 16/60=4/15; 18/60=3/10; 20/60=1/3; 21/60=7/20;
22/60=11/30; 24/60=2/5; 25/60=5/12; 26/60=13/30; 27/60=9/20; 28/60=7/15; 30/60=1/2;
32/60=8/15; 33/60=11/20; 34/60=17/30; 35/60=7/12; 36/60=3/5; 38/60=19/30; 39/60=13/20;
40/60=2/3; 42/60=7/10; 44/60=11/15; 45/60=3/4; 46/60=23/30; 48/60=4/5; 50/60=5/6;
51/60=17/20; 52/60=13/15; 54/60=9/10; 55/60=11/12; 56/60=14/15; 57/60=19/20; 58/60=29/30.
All the rest don't simplify. The sixtieth group contains all the fractions you saw in the twelfth group. See if you can spot them: e.g., 5/12=25/60; 7/12=35/60; 11/12=55/60. Also, the sixtieth group shows all the fractions in order from least to greatest. For example, you can see that 11/12 is bigger than 13/15.
