(4) Add all the columns of units in the same way, writing down, however, the entire sum of the column which can have no number over it. 4. Add together 3 hundreds 5 tens 7 units; 4 hundreds 8 tens 9 units, and 9 hundreds 8 tens 1 unit. Ans. 1 thousand 8 hundreds 2 tens 7 units, or 1827 units. 5. Add together 4 units 5 tenths 6 hundredths; 7 units 3 tenths 2 hundredths; 9 units 4 tenths 5 hundredths. Ans. 21.33 6. Add together 5 dol. 3 dimes 1 ct. 2 m.; 4 dol. 7 dimes 6 cts. 4 m., and 7 dol. 4 m. Ans. $17.08 REMARK 2.-The object of the last three examples is to show the pupil the great advantage, so far as arithmetical calculations are concerned, that would result if the DECIMAL SYSTEM, already adopted for our MONEY, were applied to WEIGHTS and MEASURES. 7. Add together 21 £ 3 s. 7 d.; 14 £ 5 s. 3 d.; 19 £ Ans. 68 £ 5 s. 2 d. 11 s. 9 d., and 13 £ 4 s. 7 d. 8. Add together 1037 £ 712 £0 s. 31 d.; 1123 £ 19 s. 9. Add together 3248 £ 9 s. 8d.; 456 £ 5 s. 2 d., and 591 £ 17 s. 11 d. Ans. 4296 £ 12 s. 9 d. 10. Add together 10 yd. 1 ft. 9 in.; 7 yd. 2 ft. 4 in., and 18 yd. 1 ft. 5 in. Ans. 36 yd. 2 ft. 6 in. 11. Find the sum of 12 yd. 3 qr. 1 eighth; 7 yd. 2 qr. 1 eighth; 37 yd. 1 qr. 1 eighth. 12. Find the sum of 39 r.; 1165 A. 1 R. 34 r.; Ans. 57 yd. 3 qr. 1 eighth. 75 A. 2 R. 18 r.; 4823 A. 3 R. 23 A. 3 R. 19 r. Ans. 6088 A. 3 R. 30 r. 13. Add together 3 m. 6 r. 1 ft. and 7 fur. 2 yd. 5 in Ans. 3 m. 7 fur. 6 r. 2 yd. 1 ft. 5 in. SUBTRACTION OF COMPOUND NUMBERS. 86. To subtract compound numbers. EXAMPLES. 1. From 4571 £ 13 s. 2 d. take 3562 £ 19 s. 7 d. 2. From 4276 cu. yd. 16 ft. 1084 in. take 809 cu. yd. 23 ft. 1523 in. 3. From 6 bu. 3 pk. 5 qt. take 2 bu. 1 pk. 3 qt. (1) PROBLEM.-What is the difference between 4571 £ 13 s. 2 d. and 3562 £ 19 s. 7 d. (2) SUBTRACTION.-Since 7 d. can not be taken from 2 d. add 12 d. (=1 s.) to the 2 d., making 14 d. Now, 7 d. from 14 d. leave 7 d. Since the minuend has been increased by 1 shilling, the subtrahend must be increased by 1 s. (Repeat the conclusion of REMARK under ex. 41, section 32.) Since 20 s. can not be taken from 13 s. add 20 s. (=1 £) to 13 s., making 33 s. Now, 20 s. from 33 s. leave 13 s. Since the minuend has been increased by 1 £, the subtrahend must be increased by 1 £. Now, 3563 £ from 4571 £ leave 1008 £. (3) RESULT.-Hence, the difference is 1008£ 13 s. 7d. In the same way recite (2) and (3). RULE. (1.) Write the numbers as in 85. (2.) Subtract the units of the lowest value in the subtrahend from the corresponding units of the minuend, and place the difference under the column. (See (3) above.) But if the number in the subtrahend is larger than that in the minuend, add the number standing over the column to the minuend, and subtract from the sum the number in the subtrahend. (3.) If the number standing above any column has been employed in the subtraction, add 1 to the units of the next higher value in the subtrahend; after which proceed exactly as with the preceding column, and so on till all the columns have been subtracted. 4. From 3 thousands 4 hundreds 5 units take 5 hundreds 6 tens. Ans. 2 thou. 8 hund. 4 tens 5 units, or 2845. 5. From 7 tens 3 units 5 tenths take 4 tens 8 tenths. Ans. 3 tens 2 units 7 tenths, or 32.7 6. From 23 dol. 6 cts. 2 m. take 19 dol. 1 dime. Ans. $3.962 7. From 7 bu. 2 pk. 5 qt. take 3 bu. 3 pk. 7 qt. Ans. 3 bu. 2 pk. 6 qt. 8. From 56 bu. take 21 bu. 3 pk. 5 qt. 1 pt. Ans. 34 bu. 2 qt. 1 pt. 9. From 500 bu. take 246 bu. 3 pk. 10. From 7 yd. 2 ft. 8 in. take 4 yd. 1 ft. 9 in. Ans. 3 yd. 11 in. 11. From 19 gal. 3 qt. 1 pt. of wine take 8 gal. 2 qt. 1 pt. 12. From 20 £ take 3 s. 6 d. 13. From 4 gal. take 1 pt. 14. From 1 ton take 1 dr. Ans. 11 gal. 1 qt. Ans. 19 £ 16 s. 6 d. Ans. 3 gal. 3 qt. 1 pt. Ans. 19 cwt. 3 qr. 24 lb. 15 oz. 15 dr. 87. To find the time between two dates. RULE. Write the year, the order of the month, and the day of the month of each date, respectively, under each other. Then proceed as in 86. REMARK 1.—In finding the difference between two dates it is common to reckon 30 days to the month. EXAMPLES. 1. Find the time from Dec. 8, 1823, to Aug. 7, 1867. y. m. d. (1.) August is the 8th month and December the 12th month. (3.) September is the 9th month and July the 7th month. 4. Find the time from August 12, 1863, to July 4, 1867. Ans. 3 y. 10 m. 22 d. 5. Find the time from January 7, 1867, to February 4, 1868. Ans. 1 y 27 d. 6. Find the time from March 5, 1867, to April 3, 1870. Ans. 3 y. 28 d. 7. Find the time from May 23, 1867, to November 15, 1890. 8. Find the time from June 15, 1868, to September 10, 1874. Ans. 23 y. 5 m. 22 d. Ans. 6 y. 2 m. 25 d. 9. Find the time from October 10, 1869, to December 21, 1872. Ans. 3 y. 2 m. 11 d. REMARK 2.-The Civil Day begins at midnight. The letters P. M. are the initials of post meridiem, which mean after noon. The letters A. M. are the initials of ante meridiem, which mean before noon. 10. When it is 25 m. past 3 o'clock, A. M., December 20, how many days, hours, and minutes of that month yet remain? Ans. 11 d. 20 h. 35 m. 11. When it is 10 m. 30 sec. past 5 o'clock, P. M., February 19, 1868, how much of the month yet re mains? Ans. 10 d. 6 h. 49 m. 30 sec. 12. If I know that 5 h. 20 m. 45 sec. of to-day are yet to pass, what time is it? Ans. 39 m. 15 sec. past 6 o'clock, P. M. 13. At 10 m. 15 sec. past 3 o'clock, P. M., November 10, 1870, how many days, hours, minutes, and seconds of that year remain? Ans. 51 d. 8 h. 49 m. 45 sec. MULTIPLICATION OF COMPOUND NUMBERS. 88. To multiply a compound number. EXAMPLES. 1. Multiply 5 bu. 3 pk. 2 qt. by 5; 7 £ 3 s. 6 d. by 7; 7 hundreds 3 tens 5 units by 9. |