same point in the heavens, how far will the Moon have gained on the Sun in 24 hours ? Ans. 12° 11' 27". 37. A farmer raised 136bu. of wheat; if he sells 49bu. 2pk. 7qt. 1 pt., how much has he remaining ? Ans. 86bu. 1pk. Oqt. 1 pt. 38. If from a stick of timber containing 2T. 18ft. 1410in. there be taken 38ft. 1720in., how much will be left ? Ans. 1T. 19ft. 1418in. MULTIPLICATION OF COMPOUND NUMBERS. OPERATION. f. 8. d. 147. MULTIPLICATION of Compound Numbers is the process of taking a compound number any proposed number of times. Ex. 1. What will 6 bales of cloth cost, at 7£. 12s. 7d. per bale? Ans. 45£. 15s. 6d. Having written the multiplier under the lowest denomination of the multiMultiplicand 7 12 7 plicand, we multiply thus: 7d. X 6 Multiplier 6 42d. 3s. 60. We write the 6d. Product 45 1 5 6 under the number multiplied, and re serve the 3s. to be added to the product of the shillings. Then, 12s. X 6 = 72s., and 3s. (carried) 758. = 3£. 15s. We write the 15s. under the column of shillings, and reserve the 3£. to be added to the product of the pounds. Again, 7£. X 6 = 42£., and 3£. (carried) = 45£. This, placed under the column of pounds, gives 45£. 15s. 6d. RULE. - Multiply each denomination of the compound number as in multiplication of simple numbers, and carry as in addition of compound numbers. Proof. - Write down by themselves the several products obtained by multiplying each denomination of the multiplicand by the multiplier, and these partial products added together will equal the entire product, if the work be right. (Art. 60.) Note. — Going a second time carefully over the work is a good way of testing its accuracy. On learning Division of Compound Numbers, the pupil will find that rule a better inethod of proving multiplication of compound numbers. EXAMPLES 2. Multiply 1£. 8s. 7d. 2far. by 7. Ans. 10£. Os. 4d. 2far PROOF BY ADDITION. OPERATION. 8 93 9fd. X 8 76d. 0£. 6s. 4d. 8 8s. x 8 64s. 3£. 4s. Od. Ans. 19 10 4 2£. X8 16£. 16£. Os. Od. 2£. 8s. 9 d. X 8 19£. 10s. 4d. Note. — The answers to the following examples may be found in corre sponding numbers of examples in Division of Compound Numbers. 9. Multiply 16A. 2R. 4p. 19yd. 7ft. 79in. by 11. 10. Multiply 10yd. 3qr. 3na. by 5. 11. Multiply 17tun 2hhd. 50gal. Iqt. by 7. 12. Multiply 29hhd. 61gal. 3qt. 1 pt. 3gi. by 7. 13. Multiply 19bu. 2pk. 7qt. 1 pt. by 6. 14. What is the value of 13y. 316d. 15h. 27m. 39s. X 8? 15. Multiply 16deg. 39m. 3fur. 39rd. 5yd. 2ft. by 9. 16. If a man gives each of his 9 sons 23A. 3R. 193p., what do they all receive ? 17. If 12' men perform a piece of labor in 7h. 24m. 30s., how long would it take 1 man to perform the same task ? 18. If 1 bag contain 3bu. 2pk. 4qt., what quantity do 8 bags contain ? OPERATION, cwt. qr. T. Ib. 6 = 143. When the multiplier is a composite number, and none of its factors exceed 12. Ex. 1. What will 35 loads of coal weigh, if each load weighs 2T. lcwt. 2qr. 6lb. ? We find the num ber 35 equal to the 2 1 2 weight of 1 load. product of 7 and 5; 7 we therefore multiply 14 10 3 17 = the weight of 1 load by 7, and then that 5 product by 5; and the 7 2 14 2 10 = Hence, when the multiplier is a composite number, Multiply by its factors in succession. swer. EXAMPLES 4 2. Bought 90 hogsheads of sugar, each weighing 12cwt. 2qr. 11lb.; what was the weight of the whole ? 3. What cost 18 sheep at 5s. 9]d. apiece? 6. If 1 share in a certain stock be valued at 13£. 8s. 9fd., what is the value of 96 shares ? 7. If 1 spoon weighs 3oz. 5pwt. 15gr., what is the weight of 120 spoons ? 8. If a man travel 24m. 7fur. 4rd. in 1 day, how far will he go in 1 month ? 9. If the earth revolve 0° 15' per minute, how far does it revolve per hour ? 10. Multiply 39A. 3R. 17p. 30yd. 8ft. 100in. by 32. 11. If a man be 2d. 5h. 17m. 19 sec. in walking 1 degree, how long would it take him to walk round the earth, allowing 365 days to a year? 149. When the multiplier is not a composite number, and exceeds 12; or when a composite number one of whose factors exceeds 12. Ex. 1. What is the value of 453 tons of iron at 18£. 17s. 11d. a ton ? 10 tons = 188 19 2,15 = 944 15 10 - Value of 50 tons 10 100 tons = 1889 11 8,X4=7558 6 8 = Value of 400 tons Ans. 8 5 5 9 16 3 = Value of 453 tons. Since 453 is not a composite number, we cannot resolve it into factors; but we may separate it into parts, and find the value of each part separately: Thus, 453 400 + 50 + 3. In the operation, we first multiply by 10, and obtain the value of 10 tons, and this product we multiply by 10, and obtain the value of 100 tons. Then, to find the value of 400 tons, we multiply the last product by 4; and to find the value of 50 tons, we multiply the value of 10 tons by 5; and to find the value of 3 tons, we multiply the value of 1 ton by 3. Adding the several products, we obtain 8559£. 16s. 3d. for the answer. Hence, Having resolved the multiplier into any convenient parts, as of units, tens, &c., multiply by these several parts, and add together the products thus obtained for the required result. EXAMPLES. 2. Multiply 2hhd. 19gal. Oqt. 1 pt. by 39. 3. Multiply 3bu. 1pk. 4qt. lpt. Igi. by 53. 4. Multiply 16ch. 7bu. 2pk. Oqt. Opt. by 17. 5. What will 57 gallons of wine cost at 8s. 31d. per gallon ? 6. Bought 29 lots of wild land, each containing 117 A. 3R. 27p. ; what were the contents of the whole ? 7. Bought 89 pieces of cloth, each containing 37yd. 3qr. 2na. 2in.; what was the whole quantity ? 8. Bought 59 casks of wine, each containing 47gal. 3qt. 1pt.; what was the whole quantity ? 9. If a man travel 17m. 3fur. 13rd. 14ft. in one day, how far will he travel in a year? 10. If a man drink 3gal. 1qt. 1pt. of beer in a week, how much will he drink in 52 weeks ? 11. There are 17 sticks of timber, each containing 37ft. 978in. ; what is the whole quantity ? 12. There are 17 piles of wood, each containing 7 cords 98 cubic feet; what is the whole quantity ? DIVISION OF COMPOUND NUMBERS. sons. OPERATION. f. 8. d. far. 93s.; = 47d.; 150. Division of Compound Numbers is the process of dividing compound numbers into any proposed number of equal parts. Ex. 1. Divide 139£. 13s. 11d. 2far. equally between 5 per Ans. 27£. 18s. 9d. 2far. Having divided 139£. by 5, we find the quotient to be 27£., and 4£. re5) 139 13 11 2 maining; We place the quotient 27£. under the 139£., and the remainder 27 18 9 2 4£. reduced to shillings = 80s.; 80s. + the 13s. in the dividend 93s. 5 18s. and a remainder of 3s. We write the quotient 18s. under the shillings in the dividend ; and the remainder 3s. reduced to pence 36d. ; 36d. + 11d. in the dividend 47d. 5 9d. and a remainder of 2d. We write the quotient 9d. under the pence in the dividend; and the remainder 2d. reduced to farthings =8far., + the 2far. in the dividend 10far.; 10far. · 5 2far. The quotient 2far. we write under the farthings in the dividend; and thus find the answer to be 27£. 188. 9d. 2far. RULE. — Divide as in division of simple numbers, each denomination in its order, beginning with the highest. If there be a remainder, reduce it to the next lower denomination, adăing in the number already contained in the dividend of this denomination, if any, and divide as before. PROOF.. - The same as in simple numbers. NOTE. — When the divisor and dividend are both compound numbers, they must be reduced to the same denomination, and the division then is that of simple numbers. EXAMPLES. NotB. — The answers to the following examples are found in the corresponding numbers of examples in Multiplication of Compound Numbers. |