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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.

8 yd. 1 ft. 10 in. (from the 2 ft.) equals 12 in.; 12 in. and n J o jf 6 • 4 in. are 16 in.; 10 in. from 16 in. leave G

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.

87. Problems.

1. From 12 yd. 1 ft. 8 in. subtract 5 yd. 2 ft. 3 in.

2. From 8 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.

(a) Find the sum of the eight differences.

88. Problems.

1. How many days from April 25 to May 1?

2. How many days from April 25 to May 10?

3. How many days from April 25 to May 20?

4. How many days from April 25 to June 1?

5. How many days from April 25 to June 10?

6. How many days from April 25 to June 30?

7. How many days from April 25 to July 5?

(b) Find the sum of the seven answers.

Algebraic Subtraction.

89. Kegarding the following minuends as representing A's gain (or loss), and the subtrahends as representing B's gain (or loss), subtract B's from A's.*

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Note.—The positive differences for Monday, Tuesday, Thursday, and Friday indicate that A's gain was greater (or his loss less) than B's. The negative differences for Wednesday and Saturday indicate that A's gain was less (or his loss greater) than B's.

90. Regard the following minuends as representing distances one boat sails from a given point, and the subtrahends as representing distances another boat sails from the same point. Distances sailed north are here represented by positive numbers, and distances sailed south by negative numbers. Find how far the first boat is from the second.

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Note.—The positive differences in Nos. 1, 2, 4, and 5 indicate that the first boat is north of the second boat. The negative differences in Nos. 3 and 6 indicate that the first boat is south of the second boat.

91. Rule for algebraic subtraction: Conceive the sign {or signs) of the subtrahend to be changed (— to 4- and + to —), then proceed as in addition.

*Seepage 168, Art. 54.' "••

Algebraic Subtraction.

1. A gained $1200 and lost $250; B gained $500 and lost $350. How much more was A's wealth increased by the two transactions than B's?

$1200-$250 12a-56 Ua-Sb

$500 - $350 5a-7b 6a-5b

$700+ $100

2. C gained $1500 and $650; D gained $600 and lost $250. How much more was C's wealth increased by the two transactions than D's?

$1500+$650 15 a+ 13 J 13a + 5 6

$600 - $250 6a- 5b 4a-3&

$900 + $900

3. E gained $1300 and lost $450; F gained $400 and $250. How much more was E's wealth increased by the two transactions than F's?

$1300-$450 13a-95 17a-8b

$400 + $250 4a + 56 4a + 66

$900 - $700

4. G gained $1200 and lost $500; H gained $900 and lost $100. How much more was G's wealth increased by the two transactions than H's?

$1200-$500 12a-56 16 a-8b

$900-$100 9a- b 4a-2b

$300 - $400 ~ ~"

5. Review the foregoing and observe that in every instance subtracting a positive number is equivalent to adding an equal negative number, and subtracting a negative number is equivalent to adding an equal positive number.

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1. When one straight line meets another straight line in such a manner that two right angles are formed by the lines, the two lines are said to be perpendicular to each other.

2. Two lines side by side extending in the same direction are said to be parallel.

3. Of the lines given above:

AC is to BD.

BD is to AC.

MN is to OP.

4. A line extending in the direction of the horizon is said to be horizontal. A line on the floor of the room is horizontal; a line on the ceiling is horizontal; a line on the blackboard, every point in which is equally distant from the floor, is horizontal. For convenience, lines drawn upon paper, that are parallel with the top and bottom of the paper, may be regarded as representing horizontal lines.

5. A line suspending a piece of lead (plumbum) is called a plumb-line. A line in the direction of a plumb-line is said to be vertical. A vertical line is perpendicular to a horizontal line. Lines on the blackboard may or may not be vertical or horizontal. For convenience, lines drawn upon paper that are parallel with the sides of the paper may be regarded as vertical.

A

D

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93. Miscellaneous Reviews.

1. An angle that is equal to one half of a right angle, is an angle of degrees.

2. The angle ABB is an angle of . degrees.

3. If from a right angle, an angle of 30 degrees be taken, the remaining angle is an angle of degrees.

4. The angle FHG is an angle of degrees.

5. During the month of November, 1897, there were consumed at the Illinois Institution for the Education of the Blind, 64 loads of coal. The weight of each load in pounds

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