INTRODUCTION TO ARITHMETIC. PART VI. CONTAINING COMPOUND DIVISION, ARITHMETICAL CHARACTERS, AND DECIMALS, COMPOUND DIVISION. KEY TO CARD No. 25. LESSON 1. Divide £784 16s. 4d. between four men. £. S. d. 4)784 16 4 Pounds. Four in 7-1 and 3 over-4 in 196 4 1 38-9 and 2 over-4 in 24-6 times. Four in 4-1. Quotient in words, One hundred and ninety-six pounds four shillings and one penny. This is each man's part. KEY TO CARD No. 25. LESSON 2. Divide £1454 19s. between 8 men. d. q. £. S. 8)1454 19 0 0 Pounds. How many times 8 in? 1 181 17 4 2 and 6 over-How many times S in 65? 8 and 1 over-How many times 8 in 14? 1 and 6 over to carry to the shillings. Shillings. Six pounds over make 120s. and 19 make 139How many times 8 in 139? 17 and 3 over I carry to the pence.* Pence. Three shillings over I carried make 36 penceHow many times 8 in 36? 4 times and 4 over I carry to the farthings. Farthings. Four pence over I carried make 16 farthings-How many times 8 in 16? 2. Answer, £181 17 4 2. KEY TO CARD No. 25. LESSON 3. Divide £1173 12s. 9d. by 12. £. S. d. q.ll 12)1173 12 9 % How many times 12 in 117? Pounds. 이 97 16 0 39 and 9 over-How many times 12 in 93 7 and 9 over I carry to the shillings. Shillings. Nine pounds over I carried make 180s. and 12 make 192. How many times 12 in 192? 16. Pence. Twelve in 9-0-carry 9 to the farthings. Farthings. Nine pence I carried make 36 farthings-How many times 12 in 36? 3. Answer, £97 16 0 3. KEY TO CARD No. 25. LESSON 4. If 19 yards of broadcloth cost £35 12 6, what is that a yard? * Set 139 shillings on some part of your slate for a memorandum and divide by 8, as in Short Division. Set the quotient 17 in the place of shillings, and carry the 3 over to the pence. N £. S. d. 19)35 12 6(1£ 19. 16 20€ 19)332(17s. 19 142 133 .9 12 19)114(6d. 114 Ans. £1 17 6 Directions for the calculation of lesson 4. Place the £35 12s. 6d, on your slates as you see it on the Card, with 19 before it for a divisorThen seek how many times 19 in 35say 1; set 1 off at the right hand for a quotient; this is 1 pound, because you can have once 19. in 35, Now multiply 19 the divisor, by 1 and place the product under 35 -subtract-the remainder is 16This is 16 pounds to be multiplied by 20 to bring it into shillings, and the 12s. must be added in the product, which will make 332s. Thus, 0 times 6 is 0, but 2 in the 12s. makes 2; set 2 in the place of units. Then, twice 6 are 12, and 1 in the 12s. above makes 13; set 3 in the place of tens-carry 1. Then, twice 1 makes 2 and 1 I carried makes 3; set another 3 in the place of hundreds. Thus you have for a product, 332s., or in this case a dividend. How many times 19 in 332? First seek how many times 19 in 33? say 1-place 1 off at the right for a quotient-multiply 19 by 1-place the product under 33-subtract—the remainder is 14. Bring down the 2 to the right side of 14, makes 142-seek how many times 19 in 142-7 times— place 7 on the right of 1 in the quotient. makes 17s. This Now multiply 19 by 7-place the product under 142-subtract-the remainder is 9s. to be reduced to pence Multiply 9 by 12, the number of pence in a shil fing, and bring in the 6d. of the given sum above, makes 114 pence. Again; how many times 19 in 114? 6 times— place 6 off at the right for a quotient-this is 6 pence Multiply 19 by 6-place the product under 114subtract, and nothing remains. Recapitulation.. In the first quotient you had 1 pound; in the second 17 shillings, and in the third 6 pence. These make for an answer, £1 17 6. KEY TO CARD No. 25. LESSON 5. If 23 barrels of pork cost £179 17 7, what iş that a barrel? Pounds. How many times 23 in 179? times-place 7 in the quotient for pounds. Multiply 23 by 7-place the product under 179-subtractthe remainder is 18 pounds to be reduced to shillings, to which add the 17s. in the given sum, as in lesson 4. This reduction will make 377s. How many times 23 in 377? seek first how many times 23 in 37-1; set 1 in the quotient. Multiply 23 by 1-place the product under 37-subtract-the remainder is 14-bring down the 7 makes 147. How many times 23 in 147? 6 times-place 6 in the quotientthis makes 16s. Multiply 23 by 6-place the quotient under 147-i subtract the remainder is 9s. to be reduced to pence; multiply 9 by 12, the number of pence in a shilling, and add to the product the 7 pence in the given sum above; this operation makes 115 pence. Now, how many times 23 in 115? 5 times-place 5 in the quotient; this makes 5 pence. Multiply 23 by 5-place the product under 115-subtract-the remainder is 0. Recapitulation. Your first quotient was £7; the second 16s. and the third 5d.-making in the whole, for an answer, £7 16 5. KEY TO CARD No. 25. LESSON 6. Bought 26 watches for £239 4 0, what did each one cost? 26 f. S. d. 6)239 4 4 0(9£ 234 ..5 20 26)104(4s. 104 Pounds. How many times 26 in 239 ? 9 times-set 9 in the quotient for pounds; multiply 26 by 9-place the product under 239-subtract -the remainder is £5 to be multiplied by 20 to reduce it into shillings, and at the same time add in the 4 shillings in the given sum, which makes 104s. Shillings. How many times 26 in 104?-4 times-place 4 in the quotient for shillings and multiply 26 by 4place the product under 104-subtract-nothing re mains. Thus you have in the first quotient £9, and in the second 4s.; making for an answer £9 4s. the price of each watch. |