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SUBTRACTION.

68. Subtraction (in arithmetic) is the process of taking one number from (out of) another.

Note 1.—The word number, as here used, stands for measured magnitude, or number of things.

69. The minuend is the number from which another

number is taken.

70. The subtrahend is the number taken from another number.

71. The difference is the number obtained by subtracting.

72. The sign —, which is read minus, indicates that the number that follows the sign is to be taken from (out of) the number that precedes it; thus, 8-3, means, that 3 is to be taken from (out of) 8.

73. Principles.

1. Only like numbers can be subtracted.

2. The denomination of the difference is the same as that of the minuend and the subtrahend.

74. Primary Facts Of Subtraction.

There are eighty-one primary facts of subtraction which should be learned while learning the facts of addition. (Note 2,

p. 443.)

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76. Observe that in written problems in subtraction the subtrahend is usually placed 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 column.

Subtraction—Simple Numbers.

79. Find the difference of 8274 and 5638.

Operation. Explanation.

8274 Eight is greater than 4. In the minuend, take one

5638 unit of the second order from the 7 units of the second

c)ooc order. 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.

2. From 87544 subtract 64358.

3. From 90070 subtract 13256.

4. From 8164 subtract 3275.

5. From the sum of 8539, 2647, 3984, 1461, 7353, 6016, and 2364, subtract 22364.

6. From the sum of 1352, 3425, 2640, 3724, 6575, 7360, and 6276, subtract 21352.

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.

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 0)

15.432 equals 10 units of the third decimal order. Two from

1 2 928 ^ leaves 8

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. One from 2 leaves 1.

The difference of 28.36 and 15.432 is 12.928.

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 numbers 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. From 10 subtract 7.6744.

(b) Find the sum of the four results.

To The Pupil Work with care. Make no errors. The sum of

the results should be correct on first trial.

84.

Subtraction—United States Money.

Find the difference of $27.25 and $14.51.

Operation.

$27.25 $14.51

$12.74

Explanation.
One cent from 5 cents = 4 cents.
Five dimes from 12 dimes = 7 dimes.
Four dollars from 6 dollars (7-1) = 2 dollars.
One ten-dollars from 2 ten-dollars = 1 ten-dollars.
The difference of $27.25 and $14.51 is $12.74.

85. ProblemsAddition And Subtraction*

Find the sum that each depositor has to his credit:
A. B.

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E. Deposit, $1000

F. Deposit, $864. (a) Find the amount of the six balances.

Deposit $824.70

Check $69.50

Check 78.25

Check 81.66

Deposit 61.40

Check 93.76

Balance

Checks, $275, $324, $400.
Checks, $375, $146, $279.

* That bank clerk who makes one error a day in carrying out his balances, which he does not himself discover and correct, will not retain his position.

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