Simple operation of 31:1 * 3:1 + 41:1 * 4:1 + 51:1 * 5:1
=(30+1 1/2)*1/3+(40+1 1/3)*1/4+(40+1 1/4)*1/5
=10+(3/2)*(1/3)+10*(4/3)(1/4)+10+(5/4)(1/4)
=30+1/2+1/3+1/4
=30+13/12
=31 1/12
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