The unit of Surface is the are, which is a square decametre, or a square whose side is 10 metres. The hectare is the unit of measure for land. The unit of capacity is the Litre, which is equivalent to a cube whose edge is no of a metre, and is a little more than a quart liquid measure. MEASURES OF CAPACITY. = 10 mil'lilitres = 1 cen'tilitre. 1 Litre. 1 dec'alitre. 10 decalitres 1 hectolitre. 10 hectolitres 1 kil'olitre. The unit of Liquid Measure is the Litre, and the hectolitre of Dry Measure. In the measurement of wood, the kilolitre or cubic metre is the unit, and is called the Stere; it equals .2759 of a cord, and 10 steres = 1 dec'astere = 2.759 cords. WEIGHTS. = = = = = 10 muigrams 1 centigram. 1 Gram = nearly 151 gr. 10 Grams 1 decagram. 1 tonneau. The kilogram is the unit in general dealings, but in very large quantities the tonneau is used. We numerate the several denominations as we do abstract numbers, regarding but the one name, as Metre, Are, Litre, and Gram, or by the unit applied to the particular case, and all computations are the same as abstract numbers or U. S. money. TEST EXAMPLES 1. The sum of two numbers is 504, and one of the numbers is 253 ; what is the other number? Ans. 251. 3. The sum of two numbers is 753, and the one is 51 more than the other; what are the numbers ? Ans. 351 and 402. 3. The product of two numbers is 255, and one of the numbers is 17; what is the other number ? Ans. 15. 4. The product of three factors is 3276; two of the factors are 12 and 21 ; what is the other factor ? Ans. 13. by 12 ? 5. The divisor is 14, the quotient 35, and the remainder 5; what is the dividend ? Ans. 495. 6. What is the quotient of 65 bu. 1 pk. 3 qt. divided Ans. 5 bu. 1 pk. 64 qt. %. In 7960 farthings, how many pounds ? Ans. £8.7. 8. In £9 10s. 8d. 3 far., how many farthings? Ans. 9155 far. - 9. Multiply 3 years 7 months and 20 days by 5. Ans. 18 y. 2 m. 10 d. 10. To what term in division does' the numerator of a fraction correspond ? the denominater ? the fraction itself? 11. In the multiplication of decimals, how does the number of decimals in the product compare with that of the factors ? 12. What is the quotient of divided by 3 ? Ans. 13. What is the product of a fraction multiplied by its denominator? Give an example. 14. In the division of decimals, how does the number of decimals in the dividend compare to that of the divisor and quotient ? 15. What do you do when the divisor has more decimals than the dividend ? 16. When there is a remainder in the division of decimals, can you form a common fraction with it and the divisor, as in the division of integers ? 17. When the dividend and divisor have the same number of decimals, how may they be regarded ? 18. How do you reduce an integral number to a fraction of any given denominator ? 19. How do you reduce a fraction to its lowest terms ? 20. How do you reduce fractions to the least common denominator ? 21. Reduce 1, $, , and to the least common denominator, and then find their sum. Ans. Com. Den., 60; sum, 341. 22. What is the difference between and } ? Ans. e 23. Multiply by and explain the process. Ans. j. 24. Divide the same and explain the process. Ans. 8. 25. Is it necessary that fractions have a common denominator in order to add or subtract them? Is it necessary in order to multiply them? To divide them ? 26. How many seconds in a year of 365 days ? Ans. 31536000 sec. 27. How many seconds in the circumference of a circle ? Ans. 1296000". 28. Is there any difference in the number of seconds in a large or a small circle ? 29. The length of the front building of a house is 54 feet and the width 36 ft., the length of the wing is 48 ft. and the width 18 ft.; what is the greatest leugth of boards with which to weatherboard it without cutting any of them? Ans. 6 feet. 31. Put .375 in the form of a common fraction, and reduce it to its lowest terms. 31. Is any even number a prime number? 32. What is the shortest method of dividing by a fraction ? 33. What is the shortest method of multiplying a number of fractions ? a Ans. å 34. How does the product of any number of proper fractions compare with any one of its factors ? How of improper fractions ? 33. How does the quotient compare with the dividend, when the divisor is a proper fraction ? How when the divisor is an improper fraction ? 36. If of a yard of cloth cost 63 cents, what will a yard cost ? Ans. 12 cts. 37. If f of an acre of land cost $75, what will an acre cost ? Ans. $120. 38. If of a farm is worth $4200, what is worth? Ans. $4000. 39. If f of an acre is worth $40, what is worth? Ans. $35. 40. If f of a yard cost $31, what will f of a yard cost ? Ans. $45. 41. If P& of a farm cost $8769, what will of it cost? Ans. $29230. 42. What is the rate per hour of a boat that goes 312 miles in 331 hours ? Ans. 9.4 miles. 43. In a garrison 480 men have provisions for 9 months; how many men must leave at the end of six months that the remaining provisions may last six months longer ? Ans. 240 men. 44. Divide 369 into three parts that shall be to each other as 2, 3, and 4. Ans. 82, 123 and 164. 45. Divide 1728 into four parts in the ratio of 2, 3, 4, and 9. Ans. 192, 288, 384, 864. 46. One-third is what per cent ? --47. One-ninth is what per cent ? - 48. Two-ninths is what per cent ? 49. Forty is how many per cent of 200 ? a a |