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. XXIII. To divide a whole number by a fraction, or a fraction by a sor is contained in the dividend. To find the ratio of a fraction 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 Measure of circles, parallelograms, triangles, &c.. Geographical and Astronomical questions ..233 181..187 .234 188..198 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 bunns for 16 cents, a quart of cherries for Scents, 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 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 vcal 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, but they will be rather difficult. A more convenient method will soon be found. 16. Ten thousand and five. 17. Thirty thousand, five hundred, and four. 18. Sixty-seven thousand, and forty. 19. Five hundred thousand, and seventy-one. 20. Two hundred and seven thousand, six hundred. 21. Four millions, sixty thousand, and eighty-four. 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, t:vo hundred. 27. Eighty-seven millions, and sixty-three. 28. Six hundred billions, two hundred and seven thousand, and three. 29. Thirty-five trillions, nine 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 hundred. 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. |