ber as many cyphers as belong to the multiplier, and the thing is done. To multiply by any number of 9s at once, place to the right of the multiplicand as many cyphers, or dots, as there are 9s in the multiplier; subtract the given multiplicand from this new one, and the thing is done. * Any sum multiplied by 9, will produce nine-tenths of the same sum multipled by 10; therefore, if a cypher be annexed to the multiplicand, it increases it ten fold; if multiplied by 9, it increases it nine fold; the difference of these products is evidently equal to once the given multiplicand; whence the reason for subtracting it as above. CASE 8. When the multiplier is any number between 12 and 20, as 13, 14, &c. the operation can be performed at once, thus: Multiply by the right hand figure of the multiplier only, taking care to add to each product, that figure of the multiplicand which stands to the right of the one multiplied; carrying for every In example 1. Say 3 times 3 are 9, which put down; again, say 3 times 6 are 18, and 3, its right hand figure, make 21, set down 1, and carry 2; next, say 3 times 4 are 12 and 2 make 14 and 6, 20, 0 and carry 2. So proceed to the last; what you carry then, add to the last figure, and the thing is done. I would here observe, that there are rules for multiplying by any number of figures in one line; but when the multipliers consist of such numbers as the following, viz. 23, 41, 111, 119, 108, 3749, the operations become too inconvenient for practice; I therefore omit them. * 3467463x13=45077019. = 3×3+6×3+3+4×3 +2+6+7×3+2+4+6×3+2+7+4×3+2+6+3×3 +2+4+1+3=45077019. SIMPLE DIVISION. 1. Simple Division is the method of measuring one pure number by another, or a concise way of performing extensive subtractions. 4'. 2. Division consists of four parts: 1. The dividend, or number to be divided. 2. The divisor, or number to divide by. 3. The quotient, or answer. The remainder, which is either O, or some number less than the divisor. RULE. 1. When the divisor is any number under 12, try how often it is contained in one, two, or three of the first, or left-hand figures of the dividend; draw a line and place the quotient figure below. 2. If one, two, &c. remain after division, it is ten, or tens, to be added to the next figure of the dividend. Try the divisor into this sum as before; place the second quotient figure to the right of the first, and so proceed to the last, and the thing is done. 3. Division is proved by multiplying the quotient by the divisor, and adding to the product the remainder (if any thing): this being always equal to the dividend, if the quotient be right. 5)647434 6)9253675 7)8595278 8)763595 9)793675 10)853136 11)795683 12)8653758 CASE 2. 1. When the divisor exceeds 12, as 23, 29, &c. try how often such divisor will go into the first two, three, &c. figures of the dividend, as in case first. 2. Place the quotient figure to the right of the dividend, multiply the divisor by it, place the product under that part of the dividend which you measured, and subtract. 3. To the remainder, bring down that figure of the dividend which stands next on the right; try the divisor into this, place the result in the quotient, multiply and subtract as before, until all the figures of the dividend are brought down and measured, and the thing is done, Operation. The divisor, 23, goes twice into the two first figures of the dividend; I then place 2 in the quotient. Next, I multiply the divisor, 23, by 2, which I place below 47, (the two first figures of the dividend,) I now subtract, and to the difference, 14, I bring down 4, the next right hand figure of the dividend; so I proceed to the last, and find that 23 is contained in 47464674, 2063681 times, and 11 |