TE SIMPLE SUBTRACTION EACHETH to take a less number, called the subtrahend, from a greater of the same denomination, termed the minuend, and thereby to shew the difference. RULE. Put the less number under the greater, with units under units, tens under tens, &c. then begin at the right hand, and take the lower figure from that above it; but if it be greater than that above, take it from 10, and add the upper figure to the remainder, set down the result, and carry 1 to the next place; and so proceed. PROOF. Add the remainder to the less number, and the sum, if right, will be equal to the greater. Application. 1 Borrowed 1090l. and paid 909l. how much remains? answer 92 answer 1811 2 A man was born in the year 1728, what is his age in. the year 1820? 3 A boy who had one thousand nuts sold 286, gave away 60 and lost 437; how many had he left? answer 217 4 There were 4 bags, containing 1st. 34dels. 2d. 5odols. 3d. 1oodols. 4th. 150dols. but one of them being lost, only 234 dols. remained; which bag was lost? answer 100d. bag. 5 Having a piece of ground 172 feet long, and rented to A at one end 57 feet, and to B 42 feet at the other end; how much was left between them? A 2 answer 73 feet. 6 Bought 6 Bought of A two barrels of flour, each weighing 175. tare per barrel 15 b.-of B 3 ditto, each 183/b. tare per ditto 2016.....of C 4 ditto, each 196/b. tare per ditto 17. how many lbs. of flour neat? answer 1525lbs. 7 Suppose A had owing to him on bond 4781. and interest due thereon 987. and received at two payments each 1991. how much is unpaid? answer 1781. 8 A vintner bought 20 pipes of brandy, containing 2459 gallons, and sold 14 pipes, containing 1682 gallons? how many pipes and gallons were left? answer 6 pipes, 777 gallons. 9 If the amount of a bond be 4700 and payments be made of 14787. 13191. 8261. and 6281. how much remains unpaid? answer 4491 SIMPLE MULTIPLICATION IS a concise way of adding numbers of the same name. The number arising from the operation is called the product. Note. The multiplier and multiplicand are alfo called factors, and the product is fometimes termed, fact, or rectangle. TABLE. 1 2 3 4 5 6| 7| 8| 9| 10| 11| 12 3 691215|18|21|24 27 30 33 36 48|12|16|20|24|28|32||36| 40|44| 48 10|15|20|25|30|35|40| 45 50 55 60 6|12|18|24|30|36|42|48| 54|60| 661 72 7|14|21|28|35|42|49|56| 63| 70| 77 84. S|16|24|32|40|48|56|64 72 80 88 96 Դ |18|27|36|45|54|63|72|81| 90 | 99|108 10|20|30|40|50|60|70 80 90 100 110 120 11|22|33|44|55|66|77|88 99|110|121|132 12|24|36|48|60|72|84|96| 108 | 120 | 132 | 144 CASE CASE 1. When the mutiplier does not exceed 12? RULE. Place the multiplier under the multiplicand; multiply the several figures successively from right to left, carry the tens.and set down the overplus as in addition. PROOF. Repeat the operation with the factors changed; or multiply the double of one factor by half the other. When the multiplier is the exact product of two factors in the multiplication table; RULE. Multiply by one of said factors, and the product of that by the other; the last product will be that required. EXAMPLES. 1 Multiply 5740632 by 32 facit 183700224 2 3 4 3740016 by 56. 7063115 by 96 7034652 by 144 209440896 678059040 1012989888 Note. When the multiplier exceeds 12 and is less than 20, multiply by the units figure, and add to the product of each figure that which is next on the right hand. EXAMPLES. Make as many products as there are figures in the multiplier, omitting ciphers, and place the first figure of each product exactly under its multiplier; add the products together, and their sum will be the number sought. Note. If ciphers be in one or both factors at the right hand, annex them to the product. EXAMPLES. 1 Suppose 40 men were concerned in the payment of a debt, and each man paid 2564d. how much was the debt? answer 102560d. and 2 How many square feet are in a floor 46 feet in length 35 in breadth? answer 1610 3 If 9876 be multiplied by six thousand, seven hundred and eighty-nine, what is the product? answer 67048164 4 Bought 342 bales of linen, in each bale 56 pieces, and in each piece 25 yards; how many pieces and yards were therein ? answer 19152 pieces, 478800 yards. 5 A merchant bought 7 bales of cloth, in each bale 11 pieces, and in each piece 29 yards; how many pieces and yards were there? answer 77 pieces, 2233 yards. 6 Sold 8 bales of linen, in 4 of which were 9 pieces each, and in each piece 27 yards, in the other 4 were 12 pieces each, and in each piece 31 yards; how many pieces and yards were there? answer 84 pieces, and 2460 yards... 7 A linen draper bought 10 bales of cloth, viz. No. 2, each 367 yards; No. 3, 4, 5, each 407 yards; No. 6, 7, 8, each 228 yards; No. 9, 10, each 300 yards; how many yards in all? answer 3239 8 What is the product of 13578 multiplied by 4938? answer 67048164 9 Admit an orchard consisting of 126 trees one way, 109 the other, and 1007 apples on each tree; how many trees and apples are in said orchard? answer 13734 trees, 13830138 apples. 10 A certain island contains 52 counties, each county 42 parishes, each parish 246 houses, and each house 10 persons; how many parishes, houses and persons, are in the island? answer 2184 parishes, 537264 houses, 5372640 persons. SIMPLE DIVISION. IVISION of integers is the reverse of multiplication, DIVI and shews how often one number is contained in another. It consists of four parts, viz. First. The dividend, or number to be divided. Fourth, The remainder (if any) which must be less than the devisor, and of the same name with the dividend. Simple division is of two kinds, viz. short and long. SHORT. |
