It is required to multiply £7. 13. 6¼ by 13. The first quantity is made up of 7 pounds, 13 shillings, 6 pence, and 1 farthing. And 1 farth. × 13 is 13 farth. or £0 . 0 . 3¼ (219) 6 pence × 13 is 78 pence, or 0 . 6 . 6 13 shill. × 13 is 169 shill. or 8 . 9 . 0 7 pounds × 13 is 91 pounds, or 91 . 0 . 0 -------------- The sum of all these is £99 . 15 . 9¼ which is therefore £7. 13. 6¼ × 13. This process is usually written as follows: £7 . 13 . 6¼ 13 ------------- £99 . 15 . 9¼ 228. DIVISION is performed upon the same principle as in (74), viz. that if a quantity be divided into any number of parts, and each part be divided by any number, the different quotients added together will make up the quotient of the whole quantity divided by that number. Suppose it required to divide £99. 15. 9¼ by 13. Since 99 divided by 13 gives the quotient 7, and the remainder 8, the quantity is made up of £13 × 7, or £91, and £8. 15. 9¼. The quotient of the first, 13 being the divisor, is £7: it remains to find that of the second. Since £8 is 160_s._, £8. 15. 9¼ is 175_s._ 9¼_d._, and 175 divided by 13 gives the quotient 13, and the remainder 6; that is, 175_s._ 9¼_d._ is made up of 169_s._ and 6_s._ 9¼_d._, the quotient of the first of which is 13_s._, and it remains to find that of the second. Since 6_s._ is 72_d._, 6_s._ 9¼_d._ is 81¼_d._, and 81 divided by 13 gives the quotient 6 and remainder 3; that is, 81¼_d._ is 78_d._ and 3¼_d._, of the first of which the quotient is 6_d._ Again, since 3_d._ is ¹²/₄, or 12 farthings, 3¼_d._ is 13 farthings, the quotient of which is 1 farthing, or ¼, without remainder. We have then divided £99. 15. 9¼ into four parts, each of which is divisible by 13, viz. £91, 169_s._, 78_d._, and 13 farthings; so that the thirteenth part of this quantity is £7. 13. 6¼. The whole process may be written down as follows; and the same sort of process may be applied to the exercises which follow: £ _s._ _d._ £ _s._ _d._ 13)99 15 9¼( 7 13 6¼ 91 -- 8 20 --- 160 + 15 = 175 13 --- 45 39 -- 6 12 -- 72 + 9 = 81 78 -- 3 4 -- 12 + 1 = 13 13 -- 0 Here, each of the numbers 99, 175, 81, and 13, is divided by 13 in the usual way, though the divisor is only written before the first of them. EXERCISES.