years 5. Mary is 9 years 7 months old, and Alice is 8 8 months old. What is the sum of their ages ? 6. A farmer sold two turkeys; one weighed 10 pounds 11 ounces, and the other 11 pounds 7 ounces. was the weight of both? DEFINITION. What 350. Addition of Compound Numbers is the process of uniting two or more compound numbers of the same kind to find their sum. WRITTEN EXERCISES. 351.-1. What is the sum of 15lb. 5oz. 15pwt.; 7lb. 9oz. 12pwt.; and 6oz. 4pwt.? SOLUTION.-Write the numbers so 15 lb. 5 oz. 15 pwt. that figures expressing units of the 7 9 6 12 23 lb. 9 oz. 11 pwt. same denomination shall be in the same columns. Begin with the pennyweights, and add the pennyweights, ounces and pounds separately. The sum of the pennyweights is 31 pennyweights, or 1 ounce 11 penny weights. Write the 11 pennyweights under the column of pennyweights, and reserve the 1 ounce to add with the ounces. The sum of the ounces is 21 ounces, or 1 pound 9 ounces. Write the 9 ounces under the column of ounces, and reserve the 1 pound to add with the pounds. The sum of the pounds is 23 pounds, which write under the column of pounds. The entire sum is 23 pounds 9 ounces 11 pennyweights. 2. What is the sum of 6mi. 120rd. 3yd.; 7mi. 160rd. 5уd.; and 55rd. 3yd.? 3. What is the sum of 15gal. 3qt. 1pt.; 7gal. O qt. 1pt.; and 2qt. Opt. ? 352. Rule for Addition of Compound Numbers. Write the numbers so that units of the same denomination shall stand in the same column. Begin with the lowest denomination, and add the numbers of each denomination separately. If the sum is less than one of the next higher denomination, write it as a part of the required result. If the sum is equal to or exceeds one of the next higher denomination, reduce it to that denomination, write the remainder, if any, as a part of the required result, and add the units of the higher denomination with the column of that denomination. 7. What is the sum of 2d. 7h. 6m.; 5d. 13h. 25m.; 11h. 11m.; and 7d. 15h. 55m.? 8. Add 1° 30′ 15′′ 19° 45′ 17′′; and 31° 40′ 16′′. 9. A boy gathered in one day, 1pk. 3qt. 1pt. of berries; another day, 1pk. 5qt. 1pt.; and a third day, 2pk. 2qt. 1pt. How many berries did he gather in all ? 10. In one field there are 17A. 120 sq. rd.; and in another 15A. 140 sq. rd. How much land is there in both fields? 11. In one car there are 16T. 11cwt. 75lb. of coal; in another, 15T. 19cwt. 31lb.; and in a third, 14T. 17cwt. 50lb. How much coal is there in the three cars? SECTION XXXII. SUBTRACTION OF COMPOUND NUMBERS. 354.-1. In one sack there are 2bu. 3pk. of wheat, and in another, 1bu. 2pk. How much more is there in one sack than in the other? 2. If 5ft. 10in. be cut from a line 7ft. 9in. long, how much of the line will be left? SOLUTION.--There will be left of the line the difference between 7 feet 9 inches and 5 feet 10 inches. 7 feet 9 inches less 10 inches are 6 feet 11 inches; and 6 feet 11 inches less 5 feet are 1 foot 11 inches. Hence, there will be left 1 foot 11 inches. 3. If you should have in a cask 11gal. 3qt. of molasses, and should sell 8gal. 3qt. of it, how much would there be left? 4. From 10h. 30m. subtract 8h. 40m. 5. In one firkin there are 12lb. 8oz. of butter, and in another 9lb. 12oz. How much more is there in the one than in the other? 6. In one load there are 2cd. 1 cd. ft. of wood, and in another load 1cd. 7 cd. ft. How much is required to make the smaller load equal the greater? DEFINITION. 355. Subtraction of Compound Numbers is the process of finding the difference between two compound numbers of the same kind. WRITTEN EXERCISES. 356.-1. From 17bu. 2pk. 6qt. take 8bu. 3pk. 4qt. 17 bu. 2 pk. 6 qt. 8 3 4 8 bu. 3 pk. 2 qt. SOLUTION. Write the subtrahend under the minuend, so that units of the same kind shall stand in the same columns. Begin at the right and subtract the units of each denomination of the subtrahend from those of the same denomination in the minuend. 4 quarts from 6 quarts leaves 2 quarts, which is the difference of the quarts. Since 3 pecks cannot be taken from 2 pecks, take 1 bushel from the 17 bushels, leaving 16 bushels, and add it, reduced, to the 2 pecks, thus obtaining 6 pecks; then, 3 pecks from 6 pecks leaves 3 pecks, which is the difference of the pecks. 8 bushels from 16 bushels leaves 8 bushels, which is the difference of the bushels. The entire difference is 8 bushels 3 pecks 2 quarts. 2. From 13lb. 5oz. 16pwt. subtract 9lb. 7oz. 14pwt. 3. From 6gal. 2qt. Opt. subtract 4gal. 3qt. 1pt. 4. From 22yd. 2qr. 2na. subtract 13yd. 3qr. 3na. Write 357. Rule for Subtraction of Compound Numbers. the subtrahend under the minuend, so that units of the same denomination shall be in the same column. Begin with the lowest denomination, and subtract the units of each denomination of the subtrahend from those of the same denomination in the minuend, if possible, and write the difference beneath. If the number of any denomination of the subtrahend is greater than that of the same denomination in the minuend, increase the number in the minuend, by adding to it as many units as make one of the next higher denomination, and subtract; then, regarding the numberof the next higher denomination of the minuend as one less, proceed as before. 7. A man who has started on a journey of 63mi. 160rd. has traveled 44mi. 125rd. 3yd. How much farther has he to travel to complete his journey? |