Addition-Simple Numbers. 39. Find the sum of 275, 436, and 821. Operation. 275 436 821 1532. Explanation. The sum of the units of the first order is 12, this is equal to one unit of the second order and 2 units of the first order. Write the 2 units of the first order, and add the 1 unit of the second order to the other units of the second order. The sum of the units of the second order is 13; this is equal to 1 unit of the third order and 3 units of the second order. Write the 3 units of the second order, and add the 1 unit of the third order to the other units of the third order. The sum of the units of the third order is 15; this is equal to 1 unit of the fourth order and 5 units of the third order, each of which is written in its place. The sum of 275, 436, and 821 is 1532. (a) Find the sum of the eight sums. TO THE TEACHER.-Impress upon the pupil the fact that in arithmetic nothing short of accuracy is commendable. One figure wrong in one problem in ten is failure. The young man or the young woman who cannot solve ten problems like those on this page, without an error, is worthless as an accountant. 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 274.36, 21.37, 38.007, and .275 6. Add 85.997, 47.9994, 72, and 53.93 7. Find the sum of two hundred and six thousandths, and two hundred six thousandths. 8. 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 eight sums. TO THE PUPIL.-Can you solve these eight problems and find the sum of the eight sums on first trial without an error? Addition-United States Money. 43. Find the sum of the money represented in the follow 354.48 916.37 144.50 75.34 8.88 246.25 $3962.01 Observe that the 8 of the first sum is included in the 70 of the second sum; that the 7 of the second sum is included in the 82 of the third sum; that the 8 of the third sum is included in the 56 of the fourth sum, and that the 5 of the fourth sum is included in the 39 of the fifth sum. Hence, the sum of the five sums will be represented by the figures 396201. * TO THE PUPIL.-Remember that nothing short of absolute accu racy 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 4 ab, 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 bis 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: 8 a × 4 b + 5 a ÷ 6 b. 49. Positive terms are preceded by the plus 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: *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. |