Multiplication Table. 11 31 41 51 6 7 8 9 10 11 12 21 41 6 8 10 12 14 16 18 20 22 24 31 6 9 12 151 18 211 24 27| 30 331 36 H1 8 12 16 20 24 28 32 36| 40| 441 48 51. 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42| 481 541 60 66 72 71 14 21 28 35| 42| 491 561 63 70 771 84 8 16 24 32 40 48 56 64 721 80 88 96 9 18 27 36 45 54 63 72 81| 90 99108 10 20 30 40 50 60 70 80 90 100|110|120 11 22 33 44 55 66 77 88.99/110 121|132 121 241 361 481 601 721 841 961108112011321144 To find the product of any two figures, by the Multi plication Table Find the multiplicand at the top, and the multiplier at the left hand column of the table; then, in the common angle of meeting of the two lines, you will find the product required : Thus, the product of 8 and 7 is 56, &c. NOTE.-This table must be learnt perfectly by heart, before the learner begins Multiplication. CASE 1. When the multiplier does not exceed 12, place the greater number uppermost, which is called the multiplicand, and the multiplier underneath, setting units under units, tens under tens, &c. then beginning at the place of units, multiply each figure in the multiplicand by the multiplier, observing to carry one, for every ten, to the next place, as in simple addition. PROOF. Before the learner is acquainted with division, he may make use of the following method of proof :-Add all the figures in the multiplicand together, cast out all the nines contained in it, and set the overplus at the right hand of a cross, as you see in the examples ; do the same with the multiplier, and set the excess at the left hand of the cross; then multiply the figures at the right and left of the cross together, cast the nines out of the product, and set the remainder 'a-top; then cast the nines out of the product, and set the remainder at the bottom, which, if the work be right, will be like the top figure. NOTE.--This short and easy method of proof is subject to this inconvenience, that a wrong operation may sometimes appear to be right; for, if you change the places of the figures in the product, ar set a' o instead of a 9, the proof will still be the same : but if the work be right, it will always appear so by this method of proof. EXAMPLES. 94708 6 Product 222072 662956 7 In the second example, beginning at the place of units, I say, 7 times 8 are 56; set down 6, and carry 5 for the five tens, saying, 7 times 0 are 0, but 5 F B carry I set down; then, 7 times 7 are 49, I set down 9, and carry 4, saying, 7 times 4 are 28, and 4 I carry are 32.; 2 being set down, I proceed, saying, 7 times 9 are 63, and 3 I carry are 66, which being the last place, I set down the whole CASE 2. When the multiplier has more figures that one, multiply each figure of the multiplicand by each figure of the multiplier, respectively, and set the first figure of each product directly under that by which you are multiplying; then add the several products together in the same order in which they stand, and the sum will be the product required. CASE 3. When there are cyphers at the right hand of the multiplicand, or multiplier, or both, place the first significant figure of the multiplier under the first significant figure of the multiplicand; then multiply as before, and to the right hand of the product annex as many cyphers as are at the right hand of the multiplicand and multiplier both. Also, when the multiplier is 10, 100, 1000, &c. place the cyphers in the multiplier at the right hand of the multiplicand, and you will have the product. EXAMPLES 3. 76231 1000 76231000 7452 26082 246 984 26827200 1008600000 CASE 4. When there are cyphers between the significant figures of the multiplier, omit multiplying by them, and place the first figure of each product of the significant figures directly under that figure you multiply by ; then add the products together, and the sum will be the total producto EXAMPLES, 2. PRACTICAL QUESTIONS. 1. If the income of a farm be 274 dollars a year, what will it amount to in 17 years? Answer, $.4658 45 men owned a prize, which amounted to . 109 per share , what was the whole ? Answer, $.4905. 3. If 1 bundie of rye produce 11 quarts, what will 859 bundles produce? Answer, 9449 quarts. 4. If 14 yards of cloth will clothe 1 man, how many yards will 473 men require ? Answer, 6622 yards. 5. Multiply 6700103 by 1043. Product, 6988207429. DIVISION. Division teaches to find how often one number is contained in another, or to separate any number into any number of equal parts. 1. Simple Division. Simple Division teaches to divide one number by another, each of which has but one denomination. Division consists of four parts : : The Dividend, or number to be divided. 2. The Divisor, or number to divide by. 3. The Quotient, or answer to the question, which shows how often the divisor is contained in the divi. dend. The Remainder, which is always less than the divisor, and sometimes nothing. |