SUBTRACTION NOTE. For definitions of terms see page 340. 1. Tell which is the minuend, which the subtrahend, and which the difference, in each of the above: 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. 2. In example b, what figures represent units of the third decimal order? Of the second integral order? Of the first decimal order? Of the first integral order? Only like numbers can be subtracted. The denomination of the difference is the same as that of the minuend and the subtrahend. There are eighty-one primary facts of subtraction - twice as many less 9, as there are primary facts of addition. See page 340. = The primary facts of subtraction should be learned while learning the forty-five primary addition facts. 8 + 5 13; 13 - 8 = 5, and 135 = 8. The eighteen subtraction facts that require special drill are suggested by the nine addition facts given on page 13. Copy the following and check. Then solve, and prove by one of the methods of proof given on page 24: a. From 35642 subtract 12456. b. From 87544 subtract 64358. c. From 90070 subtract 13256. d. From the sum of 8539, 2647, 3984, 1461, 7353, 6016, and 2364, subtract 22364. e. From the sum of 1352, 3425, 2640, 3724, 6575, 7360, and 6276, subtract 21352. f. From 8 thousand 1 hundred 64, subtract 3 thousand 2 hundred 75. g. From 6 thousand 7 hundred 25, subtract 1 thousand 8 hundred 36. h. From seven thousand four hundred sixty-five, subtract two thousand three hundred fifty-four. i. Find the sum of the eight differences, a to h.* It is sometimes convenient to find the difference of two numbers by observing how many must be added to the smaller number to give a sum equal to the larger number. Thus, to find the difference of 280 and 500, it may be observed that 20 added to 280 makes 300, and 200 added to 300 makes 500; hence the difference is 20+ 200, or 220. 1. The difference of 760 and 1000 is 2. The difference of 1290 and 1500 is 3. The difference of 430 and 710 is 4. The difference of 325 and 500 is 5. The difference of 548 and 900 is j. Find the sum of the five differences, 1 to 5. *To the Pupil. Do not allow yourself to make one error. the eight differences and their sum accurately, on first trial. Find The subtraction of decimals is in no way different from the subtraction of simple numbers; but care must be exercised in writing the numbers preparatory to subtracting them. The decimal point in the subtrahend should be directly under the decimal point in the minuend. The decimal point in the difference should be written under the other decimal points. Copy the following and check. Then subtract, and prove by one of the methods given on page 24 : a. From 124.905 subtract 15.245. d. From 693.998 subtract 72.64. e. Find the sum of the four differences, a to d. MISCELLANEOUS PROBLEMS 1. The sum of two numbers is 12; one of the numbers is 5; the other number is f. 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 numbers is 8; the less number is 11; the other number is g. The difference of two numbers is 2.3254; the less number is 7.6746. What is the other number? 3. The difference of two numbers is 7; the greater number is 19; the other number is h. The difference of two numbers is 2.3943; the greater number is 10. What is the less number? 4. The difference is 6; the subtrahend is 2; the minuend is ? 2.216 Copy the following and check. Then subtract, and prove by one of the methods given on page 24: a. From $1346.75 subtract $850.42. b. From $3407.08 subtract $506.37. c. From $8653.25 subtract $149.58. d. From $6592.92 subtract $493.63. e. From $5463.27 subtract $635.21. f. From $4536.73 subtract $364.79. g. Find the sum of the six differences, a to ƒ. In selling goods it is quite common to determine the amount of change due the customer by adding to the cost of the goods enough to make the sum equal the amount paid. Thus, if the goods cost $2.65 and the customer gives the salesman a five-dollar bill, the salesman puts down a dime and says "75"; a quarter and says"three dollars"; $2 and says "five dollars." He has given the customer 10, 25, and $2.00, $2.35, the difference of $5 and $2.65. 1. A customer bought $7.25 worth of goods. He gave the salesman a ten-dollar bill. He should receive in change h. Find the sum of the eight answers, 1 to 8. BANK ACCOUNTS a. On the morning of Jan. 5, Mr. Albert Carter had to his credit in the bank $824.70. During the day he deposited $61.40, and "checked out " as follows: $69.50, $78.25, $81.66, and $93.77. How much had Mr. Carter to his credit in the DEBIT 69 50 CREDIT 824 70 78 25 61 40 66 93 77 81 bank at the close of the day? NOTE. The pupil should copy the above lines and figures, solve the problem, and write his answer (in red ink, if convenient) as the balance in the debit column. He should then "foot" the two columns and write the sums (in black ink) in the proper places. The footings should be alike. b. Mr. Smith's account for Jan. 5 was as follows: Amount to his credit in the morning, $136.25. Deposited during the day, $94.21 and $56.45. Checked out, $11.15, $24.30, $53.25, and $15.05. Find the balance of his account at the close of the day. c. Mr. Harvey's account for Jan. 5 was as follows: Amount to his credit in the morning, $55.20. Deposited during the day, $250. Checked out, $34.65. Balance? d. Find the total amount to the credit of Carter, Smith, and Harvey on the morning of Jan. 5. e. Find the sum of the deposits of Carter, Smith, and Harvey, Jan. 5. |