7. Tell which is the minuend, which the subtrahend, and which the difference, in each of the above examples. 76. Observe that in written problems in subtraction the subtrahend is usually written under the minuend and the difference under the subtrahend; and that, as in addition, the units of the same order are written in the same column. 1. In example 2, what figures represent units of the third decimal order? of the second integral order ? of the first decimal order? of the first integral order? 2. In example 5, what figures represent units of the first integral order? of the second integral order? 77. Observe that in subtraction of denominate numbers the figures that stand for units of the same denomination and order are usually written in the same column. 1. In example 4, what figures represent tens of pounds ? hundreds of pounds ? 2. In example 5, what figures represent bushels and units of the first order ? 78. Observe that in both addition and subtraction the decimal points, if there are any, usually appear in a column. 8274 Subtraction-Simple Numbers. 79. Find the difference of 8274 and 5638. Operation. Explanation. Eight is greater than 4. In the minuend, take one unit 5638 of the second order from the 7 units of the second order. 2636 This unit of the second order, combined with the 4 units of the first, makes 14 units of the first order. Eight units of the first order from 14 units of the first order leave 6 units of the first order. Three units of the second order from 6 (7— 1) units of the second order leave 3 units of the second order. Six is greater than 2. In the minuend take one unit of the fourth order from the 8 units of the fourth order. This unit of the fourth order, combined with the 2 units of the third order, makes 12 units of the third order. Six units of the third order from 12 units of the third order leave 6 units of the third order. Five units of the fourth order from 7 (8 — 1) units of the fourth order leave 2 units of the fourth order. The difference of 8274 and 5638 is 2636. 80. PROBLEMS. 1. From 35642 subtract 12456. 4. From the sum of 8539, 2647, 3984, 1461, 7353, 6016, and 2364, subtract 22364. 5. From the sum of 1352, 3425, 2640, 3724, 6575, 7360, and 6276, subtract 21352. 6. From 8 thousand 1 hundred 64, subtract 3 thousand 2 hundred 75. 7. From 6 thousand 7 hundred 25, subtract 1 thousand 8 hundred 36. 8. From seven thousand four hundred sixty-five, subtract two thousand three hundred fifty-four. (a) Find the sum of the eight differences. TO THE PUPIL-Do not allow yourself to make one error. the eight differences and their sum, accurately, on first trial. Find Subtraction-Decimals. 81. Find the difference of 28.36 and 15.432. Operation, Explanation. 28.36 One unit of the second decimal order (1 from 6) equals 15.432 10 units of the third decimal order. Two from 10 leaves 8. 12.928 Three from 5 (6 — 1) leaves 2. Four is greater than 3. One unit of the first integral order (1 from 8) equals 10 units of the first decimal order. 10 + 3 = 13. Four from 13 leaves 9. Five from 7 (8 — 1) leaves 2. 82. PROBLEMS. 1. From 100 take .3456 6. 100 – 44.764 2. From 100 take 5.246 7. 250 159.63 3. From 100 take 44.236 8. 250 – 36.75 4. From 100 take .6544 9. 250 – 140.37 5. From 100 take 4.754 10. 250 – 163.25 (a) Find the sum of the ten differences. 83. MISCELLANEOUS. 1. The sum of two numbers is 3.7464; one of the numbers is 1.3521. What is the other number? 2. The difference of two nužnbers is 2.3254; the less number is 7.6746. What is the greater number? 3. The difference of two numbers is 2.3943; the greater number is 10. What is the less number? 4. The difference is 3.2678; the subtrahend is 2.1356. What is the minueud ? 5. From 10 subtract 7.6744. (b) Find the sum of the five results. The sum of TO THE PUPIL.–Work with care. Make no errors. the results should be correct on first trial. Subtraction-United States Money. 84. Find the difference of $27.25 and $14.51. Operation. Explanation. Four dollars from 6 dollars (7-1)= 2 dollars. 85. PROBLEMS— ADDITION AND SUBTRACTION. * NOTE.-The following represent bank accounts of six depositors for one day. Find the sum that each depositor has to his credit at the close of the day. A. $175.30 Deposit 38.60 Check $30.50 Check $12.50 Check 21.75 Check 10.80 Deposit 54.20 Check 3.60 Check 18.34 Check 5.40 Check 6.24 Balance Balance C. D. $824.70 Check $87.50 Check $69.50 Check 89.20 Check 78.25 Check 96.40 Check 81.66 Check 94.60 Deposit 61.40 Deposit 45.80 Check 93.76 Balance (a) Find the amount of the six balances. * That bank clerk who makes one error a day in carrying out his balances, which he does not himself discover and correct, would not retain his position. Subtraction - Denominate Numbers. 86. Find the difference of 15 yd. 2 ft. 4 in. and 8 yd. 1 ft. 10 in. Operation. Explanation. 15 yd. 2 ft. 4 in. Ten inches are more than 4 in.; 1 ft. (from 8 yd. 1 ft. 10 in. the 2 ft.) equals 12 in.; 12 in. and 4 in. are 10 in. from 16 in. leave 6 in. 7 yd. O ft. 6 in. One ft. from 1 ft. (2 — 1) leaves 0 ft. Eight yd. from 15 yd. leave 7 yd. The difference of 15 yd. 2 ft. 4 in. and 8 yd. 1 ft. 10 in. is 7 yd. 6 in. 16 in.; 87. PROBLEMS. 1. From 12 yd. 1 ft. 8 in. subtract 5 yd. 2 ft. 3 in. 2. From 6 yd. 2 ft. 6 in. subtract 5 yd. 1 ft. 10 in. 3. From 9 yd. 1 ft. subtract 2 yd. 2 ft. 7 in. 4. From 6 yd. 2 ft. 5 in. subtract 4 yd. 8 in. 5. From 7 yd. subtract 5 yd. 1 ft. 1 in. 6. From 7 yd. 1 ft. 4 in. subtract 4 yd. 9 in. 7. From 11 yd. 6 in. subtract 4 yd. 1 ft. 2 in. 8. From 10 yd. 2 ft. subtract 7 yd. 5 in. 9. From 13 yd. 7 in. subtract 5 yd. 2 st. 4 in. 10. From 13 yd. subtract 4 yd. 1 ft. 11 in. (a) Find the sum of the ten differences. 88. PROBLEMS. (b) Find the sum of the eight answers. |