The American Tutor's Guide, &c. O Peria PART I. THE INTRODUCTION. NUMERATION Teacheth to read or write any number by these ten charac. ters, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, and their values differ ac. oraing to the place they stand in, as may be seen by the fol'wing TABLE. 1 Three hundred and 21 4 3 2 1 Fifty-four thousand 321 6 5 4 3 2 1 Seven million 654321 8 7.6 5 4 3 2 1 Nine hundred and 87654321 8 9 8 7 6 5 4 3 2 1 Eight thousand 987654321 7 8 9 8 7 6 5 4 3 2 1 Seventy-eight thous. 987654321 4 8 9 8 7 6 5 4 3 2 1 (Six hundred and 78087654321 42. MG *9. 4859607182 100000000000 99999999999. QUESTIONS FOR EXERCISE. at number added to 853791, will re ke the sum o co n of thousands of millions. OG Hundreds of thousands. 43. M TO WRITE NUMBERS. RULE. Write down the figures as their values are expressed and supply every deficiency in the order with ciphers. EXAMPLES. Write down in proper figures the following numbers. 1. Twenty-three. Ans. 23 3. One hundred and six. Ans. 2. Fifty-seven. 4. Seven hundred and eighty-nine. 5. Nine thousand three hundred and ten. Ans. 6. Six hundred and thirty thousand five hundred and eighty. two. Ans. 7. Three million two hundred and sixty thousand, one hundred and five. Ans. To express in words at length any number proposed in figures. RULE. To the value of each figure, write the name of its. place, beginning at the left and reading towards the right. EXAMPLES. Write in words the following numbers. 1 9 Ans. Nine. 6. 35284 Ans. 2 17 7. 471805 3 84 8. 9178436 4 103 9. 12300654 5. 4381 10. 625847931 micitin 69 SIMPLE ADDITION Teachteth to add two or more sums together, to make on whole or total sum. EXAMPLES. (1.) (2.) (3.) (4.) 6768973524 8976254307 6276942578 9757893461 310941375 235483219 4849675261 6975134208 87 idred. 53742; 6042 , 174; 55 and 3 into Ans ind Ans. QUESTIONS FOR EXERCISE. 8. A merehant is indebted to A. $1205 ; to B. $738 to C. $71; to D. $19; and to E. $3874. i demand the amount of his debts ? Ans. 9. A merchant has received the following sums, 811l. 5171. 2431. 131. 1851. and 35181. I demand the whole sum. 10. Bought 6 pipes of brandy containing as follows, viz. No. 1. 120; No. 2. 118; No. 3. 125; No. 4. 121; No. 5. 127 ; and No. 6. 119 gallons. How many gallons in the whole ? Ane. 11. The difference between two numbers is 307, the lesser is 479. What is the greater number? Ans. 12. Add together 3 times 48351; 5 times 87004; 4 times 7482 and 6 times 12345. Ans. 13. In the city of Pekin in China, is a bell weighing 120000lbs. at Nankin in the same empire, another of 50000lbs. and at Erfort in Upper Saxony, the great bell weighs 25400lbs. Quere, the weight of the three ? Ans. 14. The Roman emperor Julius Cæsar, was killed by Brutus, 44 years before Christ, and Louis the XVÍ. King of France was beheaded, Anno Domini 1793'; the distance of time between the events is required ? Ans. 15. The distance from Portland in the province of Maine sto Boston is 125 miles, from Boston to New-York 250, from New-York to Philadelphia 95, from Philadelphia to Balti. more 102, from Baltimore to Richmond in Virginia 176, from Richmond to Charleston, S. Carolina, 540, and from Charleston, to Savannah, in Georgia 119; what is the distance from Portland to Savannah ? Ans. 16. Money was first made of gold and silver at Argos 894 years before Christ. How many years has it been in use? Ans. SIMPLE SUBTRACTION Teacheth to take a less number from a greater, and shews the remainder or difference. EXAMPLES. (3.) 97531 5465768792 Tak.e 5731 46802 2312019876 - 41. -510079137486 - 374859607182. 43 100000000000 99999999999. QUESTIONS FOR EXERCISE. at number added to 855791, will roke the sum o and you S.C.I 8. What number subtracted from 2745301 will make the remainder to be 1785392 ? Ans. 9. America was discovered by Columbus in 1492, and its independence declared in 1776. How many years have elap. sed between those æres ? Ans. 10. In the city of Pekin in China, is a bell weighing, it is said, 120000lbs. and at Nankin, in the same country, is another weighing 50000lbs. the first exceeds the great bell at Erfort, in Upper Saxony, by 94600lbs. How much then is the German bell inferior in weight to the second ? Ans. 11. General George Washington was born in 1732, /and died in 1799 ; what was his age when this event took place and how many years since ? Ans. his age, and since. 12. A merchant has to receive $817, $512, $601, $21 and $1358; and has to pay rent $150, and bis note at the bank for $3352 ; whither will he have money to borrow or to spare, and how much? Ans. 13. You were born 34 years after me ; how old shall I be when you are 17 ? and how old will you be when I am 70 years of age ? Ans. I shall be years. The number to be multiplied is called the multiplicand. MULTIPLICATION TABLE, 6 7 8 2.10 11 12 4 6 10 12 14 16 18 201 22 24 6 9115 181 21 241 27 30 33 36 S 16 24 28 32 36 40 10 1 15 20 25 301 35 40 45 50 55 60 12 18 24 30 36 421 481 54 60 66| 72 14 21 28 35 42 491 561 63 701 77 84 16 24 32 40 48 56 64 72 18 27 36 54 63 72 81 90 201 31 40 50 60 70 80 90 100 22 33 55 66 77 88 99 110 12 36 48 60 721 841.961108120113 8 12 20 48 5 807 9 |