to the 2 qr. makes 6 qr.; 3 qr. from 6 qr. leaves 3 qr., which we write. 15 cwt. from 18 cwt. leaves 3 cwt., which we write. Therefore, the difference required is 3 cwt. 3 qr. 2 lb. Instead of making the upper number, 19 cwt., less by 1, the result would have been the same, if we had increased the corresponding lower number, 15 cwt., by 1. Rule.- Write the less number under the greater, so that denominations of the same kind shall stand in the same column. Beginning at the right, subtract each denomination of the subtrahend from the corresponding denomination of the minuend. If the number of any denomination in the subtrahend is greater than that of the same denomination in the minuend, increase the upper number by as many units of that denomination as make one of the next higher, before subtracting; and consider the number of the next higher denomination of the minuend diminished by one. REVIEW. For what is Square Measure used? (91.) Solid Measure? (95.) Liquid Measure? (96.) Dry Measure? (97.) What is Time? (98.) For what is Circular Measure used? (107.) How do you subtract? How do you proceed when any number of the minuend exceeds the number of the same denomination in the subtrahend? What is the Rule? The Proof? 16. From a chest containing 30 lb. 10 oz. 11 dr. of tea, have been taken 9 lb. 15 oz. 15 dr.; what quantity remains? Ans. 20 lb. 10 oz. 12 dr. 17. From a piece of calico containing 32 yd. 2 qr. 2 na., there have been cut off for a dress 11 yd. 3 qr. 2 na. ; how much remains? Ans. 20 yd. 3 qr. 18. From a pile of wood containing 19 C. 86 cu. ft., there have been sold 13 C. 96 cu. ft.; how much remains? Ans. 5 C. 118 cu. ft. 19. A farmer raised 106 bushels of wheat, and sold 36 bu. 3 pk. 2 qt. 1 pt.; how much had he left? Ans. 69 bu. 5 qt. 1 pt. 20. If it were possible for a ship to sail around the world by a direct course, how much of its 360° of circumference would remain to be completed when 196° 55′ 42′′ had been accomplished? Ans. 163° 4' 18". 123. The rule applies to finding the difference between two dates. 21. A man was born May 16, 1819; how old was he April 9, 1865? It is quite common to count every month as containing 30 days, which, in this case, would have given the difference 1 day less, and to that extent wanting in exactness. REVIEW. — What is a number? (11.) A Simple Number? (119.) A Compound Number? (120.) Explain the method of finding the difference between two dates. 22. A note was given April 30, 1865, and paid March 17, 1866; how long did it run? 23. Required the time between the discovery of America by Columbus, Oct. 12, 1492, and the Declaration of Independence, July 4, 1776. MULTIPLICATION. 124. 1. Let it be required to find the product of 4 bu. 3 pk. 4 qt. 1 pt. multiplied by 7. 7 times 4 qt. are 28 qt. which, with the 3 qt. added, are 31 qt., or 3 pk. 7 qt.; we write the 7 qt., and reserve the 3 pk. to add to the product of the pecks. 7 times 3 pk. are 21 pk., which, with the 3 pk. added, are 24 pk., or 6 bu. 0 pk.; we write the 0 pk., and reserve the 6 bu. to add to the product of bushels. 7 times 4 bu. are 28 bu., which, with the 6 bu. added, are 34 bu., which we write. Therefore the product required is 34 bu. 0 pk. 7 qt. 1 pt. Rule. - Beginning at the right, multiply each denomination of the compound number in its order, and reduce each product to the next higher denomination; write the remainder, if any, underneath, and add the quotient to the next product. PROOF. - The same as in simple numbers. With which denomination do you begin to multiply? How do you reduce each product? Recite the Rule. 9. How many acres in an estate consisting of 5 farms, each measuring 70 A. 2 R. 14 P.? Ans. 352 A. 3 R. 30 P. 10. How much wood in 4 ranges, each containing 5 cords, 6 cord feet? 2 qt. 1 pt.? Ans. 23 C. 11. How much wine in 6 casks, each containing 49 gal. Ans. 297 gal. 3 qt. 12. How much grain in 15 barrels, each containing 3 bu. 1 pk. 4 qt.? 13. Multiply 64 wk. 17 h. 38 m. by 11. REVIEW.- How is Addition of Compound Numbers proved? Subtraction of Compound Numbers? |