55. How many miles from the southern extremity of Lake Michigan to the Gulf of St. Lawrence, passing through Lake Michigan, 330 miles; Lake Huron, 260 miles; River St. Clair, 24 miles; Lake St. Clair, 20 miles; Detroit River, 23 miles; Lake Erie, 260 miles; Niagara River, 34 miles; Lake Ontario, 180 miles; and the River St. Lawrence, 750 miles?

56. The estimated area of Lake Superior is 31400 square miles; Huron, 23800; Michigan, 25600; Great Bear, 9300; Great Slave, 12000; Winnipeg, 8900; Erie, 10000; Ontario, 7300. What is the area or surface of all these lakes?

57. What is the sum of 5736 dollars and 45 cents, 1000 dollars and 80 cents, 405 dollars and 15 cents, 50 dollars and 9 cents, and 79 cents?

58. Find the sum of twenty-five hundred dollars, 420 dollars and 47 cents, $23 and fifty cents, $600, and ten dollars and eight cents.

59. 1 million 400 thousand and 50 + 15 hundred 4 25 thousand +120 thousand 6 hundred and 14 = ?

60. Paid $3456 for a house, $426.75 for painting it, $2809.48 for the furniture. What was the cost of the whole ?

61. North America has an area of 8825537 square miles, South America 6954131 square miles, and the West Indies 93810 square miles. What is the area of the entire American continent?

62. A man owns farms valued at $62500, city lots worth $10260, a house worth $21300, and other property to the amount of $10500. What is the total value of his property?

A great variety of examples may be made from the following Ledger Columns by copying and adding the numbers in the first line of the four columns, then, the second line, etc., until all have been used in the same manner.

Then copy and add four numbers in first column, then five numbers, then six, and so on up to ten numbers. Do the same with all the columns.

SUBTRACTION.

143. Subtraction is the process of finding the difference between two numbers.

144. The Minuend is the greater of the two num bers compared to find their difference.

145. The Subtrahend is the smaller of the two numbers.

146. The Difference or Remainder is the result obtained by subtracting. (16.)

For the sign of subtraction, etc., see Page 21.

147. Parentheses () denote that the numbers within them are to be considered together. (Page 36.) A Vinculum has the same signification. Thus, 15+ (127), or 15+ 127, signifies that to 15 is to be added the difference between 12 and 7.

148. PRINCIPLES.-1. Only like numbers and units of the same order can be subtracted.

2. The minuend must be equal to the sum of the subtrahend and remainder.

Similar dictation exercises may be given by the teacher.

ORAL EXERCISES.

149. 1. From a cask containing 52 gallons, 27 gal lons were drawn out. How many gallons remained?

ANALYSIS.-The difference between 52 gallons and 27 gallons. 27 is 2 tens and 7 units. 2 tens or 20 from 52 leaves 32, and 7 from 32 leaves 25. Hence 25 gallons remained in the cask.

2. From a piece of cloth containing 46 yards, 24 yards were cut. How many yards were left?

3. A man bought a watch for $40, and a chain for $15, and sold both for $63. How much did he gain?

4. How many are 6 and 40, less 5 and 20 ?

5. How many are 7 and 30, taken from 5 and 50? 6. Eighteen plus 12 equals 40 minus how many? 7. Twenty-two plus 15 equals how many plus 10? 8. William having 75 cents, gave 25 cents for a book and 20 cents for a slate. How many cents had he left?

9. A farmer sold a horse for $96, which was $23 more than the horse cost. What did he cost?

Find the omitted term in the following equations:

WRITTEN EXERCISES.

150. 1. From 953 subtract 674.

OPERATION.
8 14 13

953

Minuend,
Subtrahend, 674

Remainder, 279

ANALYSIS.-Write the less number under the greater, so that units of the same order stand in the same column.

Since 4 units cannot be subtracted from 3 units, increase the 3 units by a unit from the next higher order, or 10 units, making 13 units. 4 units from 13 units leave 9 units, which write in the units' place. Since 1 of the tens was united with the units, there are 4 tens left. As 7 tens cannot be subtracted from 4 tens, increase the 4 tens by a unit from the next higher order, or 10 tens, making 14 tens. 7 tens from 14 tens leave 7 tens, which write in the tens' place.

Since 1 of the hundreds was united with the tens, there are 8 hundreds left. 6 hundreds from 8 hundreds leave 2 hundreds, which write in the hundreds' place. Hence the remainder is 279. PROOF.-The remainder 279 added to the subtrahend 674, equals 953 the minuend. Hence the work is correct.

When one of the given numbers contains cents, and the other does not, fill the vacant places with two ciphers.