Addition-Decimals.

41. Find the sum of 4.327, 8.29 and .836.

Operation. 4.327 8.29 .836 13.453

Explanation.

The sum of the units of the third decimal order is 13; this is equal to 1 unit of the second decimal order and 3 units of the third decimal order. Write the 3 units of the third decimal order and add the 1 unit of the second decimal order to the other units of that order.

The sum of the units of the second decimal order is 15; this is equal to 1 unit of the first decimal order and 5 units of the second decimal order. Write the 5 units of the second decimal order and add the 1 unit of the first decimal order to the other units of that order.

The sum of the units of the first decimal order is 14; this is equal to 1 unit of the first integral order and 4 units of the first decimal order. Write the 4 units of the first decimal order and add the 1 unit of the first integral order to the other units of that order.

The sum of the units of the first integral order is 13; this is equal to 1 unit of the second integral order and 3 units of the first integral order, each of which is written in its place.

The sum of 4.327, 8.29, and .836 is 13.453.

42. PROBLEMS.

1. Add 474.36, 21.37, 38.007, and 487. 2. Add 78.63, 61.993, .725, and 724.64. 3. Add .7, .84, .375, .0275, and 25326. 4. Add 85.997, 47.9994, 72, and 53.93.

5. Find the sum of seven hundred ninety-eight and nine hundred ninety-four thousandths, and seven hundred ninetyfour thousandths.

(a) Find the sum of the five sums.

TO THE PUPIL.-Can you solve these five problems and find the sum of the five sums on first trial without an error?

Addition-United States Money.

43. Find the sum of the money represented in the follow

354.48 Observe that the 8 of the first sum is included in the 916.37 70 of the second sum; that the 7 of the second sum is 144.50 included in the 82 of the third sum; that the 8 of the 75.34 third sum is included in the 56 of the fourth sum, and 8.88 that the 5 of the fourth sum is included in the 39 of 246.25 the fifth sum. Hence the sum of the five sums is represented by the figures 3962.01.

$3962.01

(a) Find the sum of the four sums.

*TO THE PUPIL -Remember that nothing short of absolute accuracy is of any value in such work as this.

Addition-Denominate Numbers.

45. Find the sum of 7 bu. 2 pk. 5 qt., 3 bu. 3 pk. 3 qt., 6 bu. 1 pk. 7 qt., and 9 bu. 3 pk. 5 qt.

Operation.

7 bu. 2 pk. 5 qt. 3 bu. 3 pk. 3 qt.

6 bu. 1 pk. 7 qt. 9 bu. 3 pk. 5 qt. 27 bu. 3 pk. 4 qt.

Explanation.

The sum of the number of quarts is 20; this is equal to 2 pecks and 4 quarts. Write the 4 quarts and add the 2 pecks to the pecks given in the second column.

The sum of the number of pecks is 11; this is equal to 2 bushels and 3 pecks. Write the 3 pecks, and add the 2 bushels to

the bushels given in the third column.

The sum of the number of bushels is 27, which is written in its place.

Algebraic Addition.

47. A coefficient is a number that indicates how many times a literal quantity* is to be taken; thus, in the expression 4ab, 4 is the coefficient of ab.†

When no coefficient is expressed, it is understood that 1 is the coefficient; thus, in the expression 4a+b, the coefficient of b is 1. 48. The terms of an algebraic expression are the parts that are separated by the sign + or -. There are three terms in the following: ab+3c+4abc. There are only two terms in the following: 8a × 4b+ 5a ÷ 6b.

49. Positive terms are usually preceded by the plus sign. 50. Negative terms are preceded by the minus sign.

If no sign is expressed, the term is understood to be positive.

51. When the literal part of two or more terms is the same, the terms are said to be similar.

52. PROBLEMS.

Unite the terms in each of the following algebraic expressions into one equivalent term:

Referring to the problems given above, use the following words in complete sentences: Coefficient, terms, positive, negative, similar, literal.

*The word quantity in algebra means number. The expression literal quantity means number expressed by letters.

The term coefficient is sometimes applied to the literal part of an expression; thus, in the expression abc, ab is the coefficient of c. Usually, however, the term coefficient has reference to the numerical coefficient.

Algebraic Addition.

54. Regarding the following positive numbers as representing gains and the negative numbers as representing losses, find the total gain (or loss) in each case; that is, find the algebraic sum of the numbers in each group:

NOTE. The positive sums of Nos. 1, 2, 4, and 5 indicate actual gain; the negative sums of Nos. 3 and 6 indicate actual loss.

55. Regarding each of the following positive numbers as representing a rise and each of the negative numbers as representing a fall of the mercury in a thermometer, find the total rise (or fall) in each case; that is, find the algebraic sum of the numbers in each group:

NOTE. The positive sums of Nos. 1, 2, 4, and 5 indicate actual rise; the negative sums of Nos. 3 and 6 indicate actual fall.