Ans. 24891017. Ans. 40795847 251 18344 (8.) Divide 1642807347 by 6600, or 1100.6. (9.) Divide 5482961147 by 1344, or 8.8.7.3. (10.) Divide 764206043241 by 2744, or 8.7.7.7. Ans. 2785007441705. (11.) Divide 72146950640 by 96000, or 12000.8. (12.) Divide 3332168411071 by 28224000, or 12000.8.7.7.6. Ans. 75153070649 96000 Ans. 11806114747071 28224000 CASE IV. To perform division more concisely than by the rule generally used. RULE. Multiply the divisor by the quotient figures as before, and subtract each figure of the product from the dividend, as you produce it; always remembering to carry as many units to the next figure as were borrowed before. EXAMPLES. (1.) Divide 3104675846 by 833. 833)3104675846(3727101733 the quotient. Exercising the preceding Cases. (1.) Divide 719051047192776115211 by 12. Ans. 599209205993980096001. (2.) Divide 8890896691492249389482962974987 by 987. Ans. 9008000700600050040003002001. (3.) Divide 42797882534025500424 by 425. Ans. 100700900080060000423. (4.) Divide 4500092301078221090166 by 11.11.12. Ans. 30992371219546977207282. (5.) Divide 656458931996524171800 by 700489070. Ans. 937143718740. (6.) The remainder of a division sum is 76, the dividend 5130652, and the quotient 38868; what is the divisor? (See Note 3. page 20.) Ans. 132. (7.) The following certain quantities of a division sum being given, viz. the dividend 7014596, remainder 68, and divisor 72; required the quotient? (See Note 3. page 20.) Ans. 97424. (8.) What number multiplied by 79 will give the same product as 158 by 87 ? Ans. 174. (9.) The divisor, quotient, and remainder of a division sum are 240, 345902, and 92; required the dividend? (See Note 3. page 20.) Ans. 83016572. (10.) Required the remainder of a division sum whose dividend, quotient, and divisor, are 47296478, 569837, and 83? (See Note 3. page 20.) Ans. 7. Note 17. To divide a whole number by a whole number with a fraction joined to it. Multiply the integral part of the divisor by the denominator of the fraction, add in the numerator, and note the sum; then multiply the dividend by the denominator of the fraction, and divide the product by the sum noted, and we shall have the true quotient. If the dividend contain a fraction, and not the divisor, then multiply both the whole numbers by the denominator of the fraction, taking care to add in the numerator of the fraction in the dividend. Note 18. To divide one number by another when both contain fractions -Multiply the integral part of each by the denominator of its fraction, and add in the numerator; of these two sums, multiply that belonging to the dividend by the denominator in the divisor, and divide the product by the product of the other sum and denominator in the dividend. 3848)55464437(1441331=Ans. 602) 7995364(13281181 = Ans. 68 689 9904363 7 8 481 7923491 8 7 Note 19. All the variations that can take place in dividing a fraction by a whole number, are exhibited in the following example. (17.) 3)468248 4)1560823 2)390203 5)19510 6)3902 65031=Ans. First. The first divisor gives 2 over, therefore merely put down the 2 as the numerator, and the divisor for the denominator, thus, 3. Secondly. The second divisor gives 2 over, therefore multiply the denominator of the fraction by what is over (viz. 2), and add in the numerator; now, if you can divide this sum by the divisor, put the quotient for a new numerator, under which write the denominator for the true fraction. Thirdly. The third divisor gives nothing over, in this case the numerator of the fraction can be divided by the divisor, and the quotient will be the new numerator, under which place the denominator for the true fraction. Fourthly, The fourth divisor gives nothing over, therefore multiply the divisor by the denominator of the fraction for a new denominator, over which place the numerator for the true fraction. Fifthly, The fifth divisor gives 2 over, therefore multiply the denominator of the fraction by what is over (viz. 2), and add in the numerator for a new numerator, then multiply the divisor by the denominator of the fraction for a new denominator; this will be the true fraction. *It should be remembered that the remainder is always of the same denomination as the dividend. EXAMPLES FOR PRACTICE. (1.) Divide 58764791 by 7. 5. 3. 4. & 6. Compound Addition. COMPOUND ADDITION is the method of collecting several numbers of different denominations into one sum. RULE.* 1. Place the numbers so that those of the same denomination may stand directly under each other, and draw a line below them. 2. Add up the figures in the lowest denomination, and find how many units, or ones, of the next higher denomination are contained in their sum. 3. Set down the remainder, and carry the rest to the next denomination, which add up as before, and so on through all the denominations to the highest; then this sum, together with the several parts before found, will be the answer required. The method of proof is the same as in Simple Addition. *This rule is also evident from what has been said in Simple Adaition; for, in the adding of money, as 1 in the pence is equal to 4 in the farthings, 1 in the shillings to 12 in the pence, and 1 in the pounds to 20 in the shillings, it is plain that carrying as directed is nothing more than providing a method of placing the money arising from each column properly in the scale of denominations; and this reasoning will hold good in the addition of compound numbers of any denomination whatever. N.B.-The present gold coins in circulation in England, are the Sovereign, valued at 20s., and the Half-Sovereign 10s. The silver coins are the Crown, or 5s. piece; the Half-Crown 2s. 6d.; the Shilling 12d.; the Sixpenny piece 6d. ; the Fourpenny piece 4d., and the Threepenny piece 3d. The copper coins are the Penny, equal 4 farthings; the Half-Penny, 2 farthings; the Farthing piece, 4 of which make a Penny; and the Half-Farthing, 8 of which make a Penny. The following statement is the full weight of gold and silver coins Half-sovereign 5. 31 342 Double-sovereign......... 10. 633 Sixpence.............. Five-sovereign piece..... 25. 162 Fourpence 232 Threepence...... 1.5 21 The relative proportion between gold and silver in the English coins, according to the mint regulations, both of the old and new coinage. The old coinage is as any weight of gold is to an equal weight of silver as 15-2376 to 1. The new coinage is as 14:3124 to 1. Note.-Gold coins are allowed by law to pass under the above full weight. Thus the guinea, weighing 5 dwt. 8 gr. ; the sovereign, 5 dwt, 2 gr.; and their divisions, in proportion, are a legal tender. |