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 1 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 30 102..106 42 34....38 103 33...,41 214 52....57 58 158..166 85....86 87....92 2992 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 . 236 240 220 221 . 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 bought 3 bunne 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 bought a hat for 8 dollars, a coat for 27 dollars, a pair of boots for 5 do'jars, 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 hole ? The two last examples may be performed in the mind, bat they will be rather difficult. A more convenient method will soon be found. NUMERATION. 1. Write in words the following numbers. 1 27124 10,000 2 35 25 20,030 3 58/26 50,705 63 27 67,083 70/23 300,050 8429 476,089 96 30 707,720 8 100 31 1,000,370 9 10332 5,600,073 10 110133 8,081,305 11 13 34 59,006,341 12 12735 305,870,400 13 308!36 590,047,608 14 52037 1,000,000,000 16 735138 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 1,01843 68,907,605 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. I 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. 21 16. Ten thousand and five. 22. Ninety-seven millions, thirty-five thousand, eight hundred and five. 23. Fifty millions, seventy thousand, and eight. 24. Three hundred millions, and fifty-seven. 25. Two billions, fifty-three millions, three hundred and five thousand, two hundred. 26. Fifty billions, two hundred and seven millions, sixtyseven thousand, two hundred. 27. Eighty-seven millions, and sixty-three. 28. Six hundred billions, two hundred and seven thousand, and three. 29. Thirty-five trillions, nihe millions, and fifty-eight. · 30. Six hundred and fifty-seven trillions, seven billions, ninety-seven thousand, and sixty-seven. 31. Seventy millions, two hundred and fifty thousand, three hundred and sixty-seven. 32. Four hundred and seven trillions, and eighty-seven thousand. 33. Thirty-five billions, ninety-eight thousand, one hun. dred. 34. Forty millions, two hundred thousand, and seventyfour. 35. Eighty-three millions, seven hundred and sixty-three thousand, nine hundred and fifty-seven. ADDITION. II. 1.* A man bought a watch for fifty-eight dollars, a cane for five dollars, a hat for ten dollars, and a pair of boots for six dollars. What did he give for the whole ? 2. In an orchard there are six rows of trees; in the two first rows, there are fifteen trees in each row; in the third row, seventeen; in the fourth row, eleven; in the fifth row, * See First Lessons, sect. I. |