(This Table equally refers to Parts I. and II.) III. Multiplication, when the multiplier is a single figure. plier 'is a compound number. V. Multiplication, when the multiplier is 10, 100, 1000, &c. VI. Do. when the multiplier is 20, 300, &c. VII. Do. when the multiplier consists of any number of IX. Division, to find how many' times one number is contained in X. Division. Explanation of Fractions. Their Notation. What is to be done with the remainder after division. X1. Division, when the divisor is 10, 100, &c. XII. To find what part of one number another is, or to find the ratio XIII. To change an improper fraction to a whole or mixed number. -XIV. To change a whole or mixed number to an improper fraction. XV. To multiply a fraction by a whole number, by multiplying the XVI. Division, to divide a number into parts. To multiply a whole XVII. To divide a fraction by a whole number. To multiply a frac- XVIII. To multiply a fraction by dividing the denominator. Two ways to multiply, and two ways to divide, a fraction. common denominator. To reduce them to lower terms XXI. How to find the divisors of numbers. To find the greatest com- mon divisor of two or more numbers. To reduce fractions to XXII. To find the least common multiple of two or more numbers. To reduce fractions to the least common denominator. fraction, when the purpose is to find how many times the divi- and a whole number, or of two fractions. XXIV. To divide a whole number by a fraction, or a fraction by a fraction; a part of a number being given to find the whole. This is on the same principle as that of dividing a number into XXV. Decimal Fractions. Numeration and notation of them. XXVI. Addition and Subtraction of Decimals. To change a common INDEX TO PARTICULAR SUBJECTS. { Compound Multiplication Page. Example. Division Miscellaneous examples 211 1....25 28 43....50 92 65..113 104 43....74 215 58....68 78 130..142 224 110..113 36 102..106 103 33....41 214 52....57 58 158..166 220 85....86 .221 87....92 .222 103..109 .218 69....72 ..218 73....84 79 1....49 101 '13....26 .229 141..144 103 28....32 .234 . 188..198 .235 199..205 236 { ..240 Oct 18400 ARITHMETIC. PART I. ADDITION. The student may perform the following examples in his mind. 1. James has 3 cents and Charles has 5; how many have they both ? 2. Charles bouglit 3 bunns for 16 cents, a quart of cherries for 8 cents, and 2 oranges for 12 cents ; how many cents did he lay out ? 3. A man bouglit a hat for 8 dollars, a coat for 27 dollars, a pair of boots for 5 dollars, and a vest for 7 dollars; how many dollars did the whole come to ? 4. A man bought a firkin of butter for 8 dollars, a quarter of veal for 45 cents, and a barrel of cider for 3 dollars and 25 cents; how much did he give for the whole ? 5. A man sold a horse for 127 dollars, a load of hay for 15 dollars, and 3 barrels of cider for 12 dollars ; how much did he receive for the whole ? 6. A man travelled 27 miles in one day, 15 miles the next day, and 8 miles the next ; how many miles did he travel in the whole ? 7. A man received 42 dollars and 37 cents of one person, 4 dollars and 68 cents of another, and 7 dollars and 83 cents of a third; how much did he receive in the whole ? 8. I received 25 dollars and 58 cents of one man, 45 dollars and 83 cents of another, and 8-dollars and 39 cents of a third; how much did I receive in the whole ? The two last examples may be performed in the mind, they will be rather difficult. A more convenient method will soon be found. NUMERATION. 10,000 2 35 25 20,030 3 58/26 50,705 6327 67,083 5 70/23 300,050 6 84 29 476,089 7 96/30 707,720 8 100 31 1,000,370 9 103 32 5,600,073 10 11033 8,081,305 11 113 34 59,006,341 12 127 35 305,870,400 13 308 36 590,047,608 14 520 37 1,000,000,000 15 738 38 3,670,000,387 16 1,000 39 45,007,070,007 17 1,001 40 680,930,100,700 18 1,010 41 50,787,657,000,500 19 1,100 42 270,000,838,003,908 20 1,018 43 68,907,605 21 2,107 44 56,000,034,750 22 3 250 45 6,703,720,000,857 23 5,796 Write in figures the following numbers. 1. Thirty-four. 2. Fifty-seven: 3. Sixty-three. 4. Eighty 5. One hundred. 6. One hundred and one. 7. One hundred and ten. 8. Three hundred and eleven. 9. Five hundred and seventeen. 10. Eight hundred and fifty. 11. Nine hundred and eighty-six. 12. One thousand and one. 13. One thousand and ten. 14. Three thousand, one hundred and one. 15. Five thousand and sixty. |