Reduce the first and second quantities, if necessary, to quantities of the same denomination. Thus, in the second question, £20 15_s._ must be reduced to shillings (219). The third quantity may also be reduced to any other denomination, if convenient; or the first and third may be multiplied by any quantity we please, as was done in the second question; and, on looking at the answer in (238), and at (108), it will be seen that no change is made by that multiplication. Multiply the second and third quantities together, and divide by the first. The result is a quantity of the same sort as the third in the line, and is the answer required. Thus, to the first question the answer is (238) 208 × 156 17_s._ 4_d_. × 156 ----------pence, or, which is the same thing, -------------------. 22 22 240. The whole process in the first question is as follows:[50] yds. yds. _s._ _d._ 22 : 156 ∷ 17 . 4 12 --- 208 pence. 156 ---- 1248 1040 208 ----- 22)32448(1474¾_d._ and ¹⁴/₂₂, or ⁷/₁₁ of a farthing, 22 or (219) £6 . 2 . 10¾-⁷/₁₁. --- 104 88 ---- 164 154 ---- 108 88 -- 20 (228) 4 -- 80 66 -- 14 [50] It is usual to place points, in the manner here shewn, between the quantities. Those who have read Section VIII. will see that the Rule of Three is no more than the process for finding the fourth term of a proportion from the other three. The question might have been solved without reducing 17_s._ 4_d._ to pence, thus: yds. yds. _s._ _d._ 22 : 156 ∷ 17 . 4 156 (227) ---------- 22)£135 . 4 . 0(£6 . 2 . 10¾-⁷/₁₁ (228) 132 --- 3 × 20 + 4 = 64 44 -- 20 × 12 = 240 220 --- 20 × 4 = 80 66 -- 14 The student must learn by practice which is the most convenient method for any particular case, as no rule can be given.