(4/6) / (7/13) = 2/3 * (13/7) = 26/21 or 15/21
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13/8 ÷ 3/4 = 11/6 or 15/6
0.6667
1/4 divided by 6 = 1/4 multiplied by 1/6 = 1/24
6/13 divided by 6/12 = 6/13 * 12/6 = 72/78 (reducible to 12/13) This is immediately confirmed because dividing by 6/12 or 1/2 is effectively multiplication by 2.
78 divided by 6 equals 13.