SIMPLE ADDITION. DEFINITION.-Simlpe Addition teaches to add togeth. er several sums of the same denomination. Rule.-Set down units under units, tens under tens, and hundreds under hundreds, &c. Begin to add in the place of units, add all in that column, carry one for eveten that is in the sum of units, to the place of tens, and set' down all that is over ten, or tens; add up the col. umn of tens, carry one for every ten to the next column, and set down all that is over; thus proceed through all the columns to the last ; observe to set down the whole sum in the last column. PROOF.-Begin at the top add downwards, carry as be: fore, and if the work is right, the sum will be the same as it was when added upwards. 1. Add together 345674, 98736, 456752 and 7654. Ans. 908816. 2. Add 94321, 675431, 1234 and 76432 together, Ans. 847418. 3. Add 642 1, 94742, 6752 and 875432 together. Ans. 983347, 4.. Add 67432, 9889.1, 65641 and 77421 together. Ans. 309385. 50 Add 9944, 2343, 78764 and 94929 together. Ans. 185980 6. I lent a friend 942 dollars, at one time, at another 741, at another 91; what is the whole sum lent? Ans. 1774 dolls. 7. A man killed 4 hogs, weighing as follows ; one 396, one 472, one 510 and one 371; what did they all weigh? Ans. 1749. 8. I killed an ox, his quarters weighed 642, his hide 105, his tallow 92 ; what did they all weigh? Ans. 839. 9. A man gave to three sons as follows, to one 3427 dolls. to another 3025 dolls. to another 2947 dolls. ; what did he give to all of them? Ans. 9399. 10. A man's taxes were as follows for 3 years ; the first 142 dolls. second 165, the third 210 dolls. ; what did he pay in three years. Ans. 517. SIMPLE SUBTRACTION. Definition.-Simple Subtraction teaches to take a less number from a greater, that is of the same denomination, and thereby find the difference, or remainder. Rule.Write the largest number down first; and the smallest underneath, units under units, &c. begin to subtract in the place of units; and take the under from the upper figure; set down the remainder : If at any time any particular figure in the lower line is larger than the one immediately over it, subtract the under figure from ten ; to the remainder add the upper figure and set ir down; and carry one to the next figure in the lower line; thus proceed through the whole. Proof. Add the remainder and the lower line together, and if the work is right the sum will be like the upper line. Practical Questions in Subtraction. 1. What is the difference between 24567 and 7456? Ans. 17111. 2. I lent a friend 2456 dolls. and received in part 1342 dollars“; what remains due? Ans. 1114 dolls, 3. A merchant owes 34323 dolls, his effects are worth but 22749 dollars ; how much will he fall in debt? Ans. 11574 dolls. 4. A merchant has an estate in his hands valued at 52394 dolls. he owes 31399 dolls. ; what is he worth after paying his debts ? Ans. 20995. dolls. 5. A merchant sent a ship and cargo to sea, valued at 11497 dolls, and on her return, she and her valued at 16579 dolls. ; what was his gain? Ans. 5082 dolls. 6. A ship builder built a ship, which cost him 6241 dolls. and he sold her for 5927 dolls, , what did he lose? Ans. 314 dolls. 7. A. borrowed of B. 9427 dolls, and he paid him at one time 4249 dollars, at another time 1427 dollars, and at another time 947 dollars; what remains due ? Ans. 2804. cargo was SIMPLE MULTIPLICATION. DEFINITION.- Simple Multiplication is a compendious way of adding; as 9 multiplied by 6 is equal to 54, and is the same as if 9 were set down 6 times and added up: The number to be multiplied is called the multiplicad, The number given to multiply by, is called the multiplier. * The number arising from the operation is called the product. The following table must be committed to memory before any progress can be made in Multiplication. *The multiplicand and multiplier are in general terms called Factors, 11 21 31 41 51 61 78.7 9 10 11 12 24 6 / 8 / 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 3 | 6 | 9 | 12 | 15 | 18 21 | 24 | 27 | 30 | 33 | 36 4 1 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 5 10 15 20 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66. 72 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 84 8| 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 96 9 | 18 | 27 | 36 | 45 | 54 | 63 72 81 90 99 | 108 10 1 20 30 40 50 60 | 70 | 80 90 | 100 110 120 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 1121 | 132 12 | 24 | 36 | 48 60 | 72 | 84 96 108 / 120 132 / 144 CASE I. When the multiplier is a single figure. RULE.—Under the multiplicand write down the multiplier, in the place of units; draw a line underneath, and multiply every figure of the multiplicand, by the multiplier; observing to carry one for every ten to the next product. The whole product of the last figure multiplied, must be set down, P2001.Cast the nines from the multiplicand; and all that is over put at the right of a cross, (which is made thus X); then cast the nine from the multiplier, and all that is over, put at the left of the cross; then cast the nines from the product, and put all that is over at the top of the cross. Then multiply the figure on the left of the cross with the one on the right; cast the 9's from the product, and what is over, put at the bottom of the cross; and if the top and bottom figures are alike, the work is right. Note. The preceding method of proof is liable to one error, viz. if any of the figures in the product should happen to be transposed, as if 468 in the product should happen to be written 648, the work would prove, and an error would still exist. Second method of Proof:-Divide the product by the multiplier, and if the work is right the quotient will be like the'multiplicand. This method can be used only by those who have attained to a knowledge of division. CASE II. When the multiplier consists of several figures. RULE.--Set down the multiplier under the multiplicand, units under units, &c. multiply each figure in the multiplier into every figure in the multiplicand, singly, as in case first, observing to set down the first figure of the product exactly under the figure by which you are multiplying; then add the several products together, their sum will be the product required. Questions. No. Multiplicands: Multipliers. Products. 1. 24567 X by 123 3021741 2. 12434 by 432 5371488 3. 12345 x by 246 3036870 4. 45678 by 15210774 5. 23243 by 46532486 6. 24567 hy 4001 138302567 23456 Х by 1003 23526368 8. 90042 Х by 9009 811188378 9. 701231 Х by '1231 863215361 |