The reciprocal of 2/3 is 3/2, so multiply both sides by 3/2: r=10*3/2=15; or if the original equation was 2/(3r)=10, then the reciprocal is 3r/2. Multiply by 3r/2: 1=30r/2=15r. So we have 15r=1. The reciprocal of 15 is 1/15 and, multiplying by this we get r=1/15.