18. Divide 10368 by 27; by 36. 19. Divide 10368 by 54; by 18. 20. Divide 2688 by 112; by 224. 21. Divide 101442075 by 4025.. WHEN THE D A. 672. A. 25203. ¶ XVIII. WHEN THE DIVISOR IS A COMPOSITE NUMBER. Q. 1. Bought 20 yards of cloth for 80 dollars; how much was that a yard? Now, as 2 times 10 are 20 (a composite number), it is plain that, if there had been but 10 yards, the cost of 1 yard would be 8 dollars, for 10 in 80, 8 times; but as there are 2 times 10 yards, it is evident that the cost of 1 yard will be but one half () as much: how much, then, will it be? RULE. Q. What, then, appears to be the rule for dividing by a composite number? A. Divide by one of its component parts first, and this quotient by the other. &c. ¶ XIX. TO DIVIDE BY 10, 100, 1000, Q. In T XII. it was observed, that annexing 1 cipher to any num ber multiplied it by 10, 2 ciphers by 100, &c. Now, Division being the reverse of Multiplication, what will be the effect, if we cut off a cipher at the right of any number? A. It must decrease or divide it by 10. Q. What will be the effect, if we cut off two ciphers? Q. Why does it have this effect? A. By cutting off cne cipher or figure at the right, the tens take the units' place, and hundreds the tens' place, and so on. RULE. Q. What, then, is the rule for dividing by 10, 100, &c.? A. Cut off as many places or figures at the right nand of the dividend, as there are ciphers in the divisor. Q. What are the figures cut off? Q. What are the other figures ? A. The quotient. Exercises for the Slate. 1. A prize, valued at 25526 dollars, is to be equally divided among 100 men; what will be each man's part? OPERATION. 255 26 255 dollars. 28, 428, 3428, 2. Divide 1786582 by 10000. A. 178,6582. 3. Divide 87653428 by 10; by 100; by 1000; by 10000; by 100000; by 1000000. A. Remainder to each, fo, 53428, 65348. Quotients, total, 100000 1000000 T XX. WHEN THERE ARE CIPHERS AT THE RIGHT HAND OF THE DIVISOR. 1. Divide 4960 OPERATION. dollars among 808 times 10 are 8|0) 496|0 nen. 62 dollars. Q. In this example, we have a divisor, 80, which is a com Dosite number; (thus, 8 times 10 are 80;) how, then, may we proceed to divide by 10, one of the component parts? A. By cutting off one place at the right hand of the dividend, as in ¶ XIX. Q. How do you obtain the 62? A. By dividing the 496 by 8, as usual. RULE. Q. As any number, which has a cipher or ciphers at the right, can be produced by two other numbers, one of which may be either 10, 100, 1000, &c., how, then, would you proceed to divide when there are ciphers at the right of the divisor? A. Cut them off, and the same number of figures from the right of the dividend. Q. How do you divide the remaining figures of the dividend? Q. What is to be done with the figures of the dividend which are cut off? A. Bring them down to the right hand of the remainder. Exercises for the Slate. 2. How many oxen, at 30 dollars a head, may be bought for 38040 dollars? A. 1268. Miscellaneous Questions on the foregoing. Q. What is the subject which you have now been attending to called? A. Arithmetic. Q. From what you have seen of it, how would you define it? A. It teaches the various methods of computing by numbers. Q. What rules have you now been through? A. Notation or Numeration, Addition, Subtraction, Multiplication, and Division. Q. How many rules do these make? Q. What are these rules sometimes called? A. The fundamental rules of arithmetic. A. Because they are the foundation of all the other rules. Q. To denote the operation of these different rules, we have certain characters; what is the name of these characters ? A. Signs. Q. What do two horizontal straight lines signify; thus, 100 cents= 1 dollar? A. Equal to; as, 100 cents 1 dollar, read, 100 cents are equal to 1 dollar. Q. What does a horizontal line crossing a perpendicular tell you to do; thus, 6+10=16? A. To add; thus, 6+10=16, read, 6 and 10 are 16. Q. What else does this sign denote ? A. A remainder after dividing. Q. What does one horizontal straight line tell you to do; thus 8-6=2? A. To subtract; thus, 8-6-2, read, 6 from 8 leaves 2. Q. What do two lines, crossing each other in the form of the Roman letter X, tell you to do; thus, 6 x 848? A. To multiply; thus, 6x8=48, read, 6 times 8 are 48. Q. What does a horizontal line, with a dot above and below it, tell you to do; thus, 8-2=4? A. To divide; thus, 824, read, 2 in 8, 4 times. Q. By consulting ¶XVII. you will perceive that Division may be represented in a different manner; how is this done? A. By writing the divisor under the dividend, with a line between them; thus, =2, read, 4 in 8, 2 times. Q. What does signify, then? 20-signify? 36? 42? 108, 144? 35? Let me see you write down on the slate the signs of Addition, Sub traction, Multiplication, and Division. Perform the following examples on the slate, as the signs indicate. 1. 87834+284 +65 +32 +100=88315, Ans. 2. 876345723-267001345—609344378, Ans. 3. 692784578 × 27839421 19286721529249338, Ans. 4. 202884150402550406, Ans. 5. 2600-600-2000+1828=3828, Ans. 6. 3600-4003200 × 4=12800, Ans. 7. 260880000 20000, Ans. 8. 18836-18, Ans. 9. 10936+1+2+2028, Ans. = 10. What is the whole number of inhabitants in the world, there being, according to Hassel, in each grand division as fol lows;-in Europe, one hundred and eighty millions; America, twenty-one millions; Australasia, &c. two millions? A. 632000000 11. What was the number of inhabitants in the following New England towns, in 1820, there being in Portland, Portsmouth, Salem, 8,581; 12,731; Boston, 43,298; 11,767; 8,327? 12. What was the number of inhabitants in the following towns, there being in New York, 123,706; Philadelphia, 108,116; Baltimore, 62,738; 1 Washington, 13,247; Albany, 12,630; 13. How many more inhabitants were there in New York than Philadelphia? Philadelphia than Baltimore? Baltimore than Boston? Boston than New Orleans? New Orleans than Charleston? Charleston than Albany? Albany than Provi dence? Providence than New Haven? A. Total, 115,379. 14. At 73 cents a bushel, what will 42 bushels of salt cost? What will 800 bushels? A. 61466 cents. 15. What will 2970 Dushels? What 8900 bushels? A. 866310 cents. 16. James had 37 cents, William 10 times as many as James, Rufus 15 times as many as William, Thomas 26 times as many as Rufus, Harry 45 times as many as Thomas, and Stephen 24 times as many as Harry; how many did they all have? A. 162487757. 17. There are 60 minutes in one hour; how many hours are there in 120 minutes? In 4800 minutes? A. 82 hours. 18. In 172800 minutes? In 1036800 minutes? A. 20160 hours. 1. At 10 mills a yard, how many cents will 4 yards of cloth cost? Will 6 yards? Will 8? |