parts, called hundredths; the hundredth into ten equal parts, called thousandths; the thousandth into ten equal parts, called ten-thousandths, etc. By comparing these different decimal fractions, we see that the formation of decimal fractions depends, like that of whole numbers, upon the following principle: Ten units of any order are equal in value to one unit of the next higher order; and one unit of any order is equal in value to tcn units of the next lower order. Notation is a system of writing numbers. The common system of notation employs ten figures, or digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The first nine figures represent the first nine numbers; the last, which is called zero, or naught, is used to denote the absence of units of the order in which it stands. These ten figures express all numbers by the artifice of making the value of each figure increase tenfold for every place that it is moved to the left. To write a number in figures, we write successively the number of units of each order from left to right, beginning at the highest order, taking care, if the number contain a decimal fraction, to put a full point at the right of the units' figure, and to supply by zero the units of any order that may be lacking. If the number contain no whole number, we put a zero in the units' place, and the decimal point to the right of the zero. To read a number written in figures, we divide the number into periods of three figures each, from right to left. This done, we begin to read at the last period on the left, and read as if the figures of that period stood alone, adding the name of the period. Then the next period to the right is read, with the name of that period, and so on. 'If the number contain a decimal fraction, we first read the whole number; then the decimal as a whole number, taking care to add the fractional name of the lowest place. CHAPTER III. ADDITION. 36. ADDITION means putting together. The Saint George's Cross (+) is read plus, and means that the numbers between which it stands are to be added together. The result obtained by adding together two or more numbers is called their sum. The sign of equality (=) stands for the words "equals, or "equal." Thus, 8+1 = 9 is read, eight plus one equals nine. 37. Add 2 to each number from 0 to 9; add 3 to each I number from 3 to 9. Add 4 to each number from 4 to 9; add 5 to each number from 5 to 9. Add 6 to each number from 6 to 9; 7 to 7, to 8, and to 9; 8 to 8, and to 9; 9 to 9. Repeat these additions until thoroughly familiar with them. 38. Name, as fast as you can talk, the even numbers, 2, 4, 6, etc., up to 102. Name the odd numbers, 1, 3, 5, etc., up to 101. 39. Name every third number, 0, 3, 6, etc., up to 102. Name every third number, 1, 4, 7, etc., up to 103. Name every third number, 2, 5, 8, etc., up to 101. 40. Name every alternate even number, 0, 4, 8, 12, etc., up to 100. Name every alternate even number, 2, 6, 10, etc., up to 102. 41. Name every fifth number under 100, beginning 5, 10, 15, etc.; beginning 1, 6, 11; beginning 2, 7, 12; beginning 3, 8, 13; and beginning 4, 9, 14. 42. In like manner, add by sixes up to a number exceeding a hundred, beginning 0, 6, 12; beginning 1, 7, 13; beginning 2, 8, 14; and so on. 43. Add by sevens up to a number exceeding 100, beginning 0, 7, 14; 1, 8, 15; and so on; by eights, beginning 0, 8, 16; 1, 9, 17; and so on; by nines, beginning 0, 9, 18; 1, 10, 19; and so on. * 44. For the addition of numbers in general, the following mode has been found most convenient. Write the numbers in columns, units under units, tens under tens, tenths under tenths, etc. Add the digits in the right-hand place; set the units of the sum in that place, but carry the tens mentally to the next place to the left, to be added to the digits there, and so proceed. The study of three or four examples will make the process understood. The teacher may take ten small cards. On each side of the first write 0; of the second, 1; etc. Shuffle, and dictate the numbers on all but one for the class to add. Subtract the reserved number from 45; the remainder is the sum. With two sets of cards at once, subtract the reserved number from 90. For advanced classes, use cards with larger numbers; and complemental cards, which may be obtained of the publishers, furnishing unlimited examples, with the answers to all. 4128 3789 2667 The following wording, and no more, is to be used: 18, 17, 25 (emphasize 5, and write it down while pronouncing it), carry 2; 4, 10, 18, 5821 20, carry 2; 10, 16, 23, 24, carry 2; 7, 9, 16405 12, 16. 45. Find the following sums: 231+764; 341 + 57.8; 430.31+ 58.61; 512.87 + 36.84 +12.78+711.56 +415.86. 46. Add 1543.1 to 164.7; to 1728; to 402.56; to 1897.3; to 475.34; to 6897.65. 47. Add 1897.3 to 475.34; to 6897.65; to 1728; to 402.56; to 164.7; to .5236; to 2.71828. 48. Find the following sums: .7854 +3.1416+ 2.71828; 2.71828+402.56+1897.3; .78543.1416+30,103; 2.7113+27.53+341.586. 49. Add 737.87 to each of the following numbers: 111; 1011; 2304; 222; 263; 373; 262.13; 561.2; 32.35; 604.3. 50. Find the five sums: 230.8+223 +2.63 + 373.8+56.123; 32.358821.9 + 23.0473.7; 202.3031 + 71.575 + 65.813 + .0078 + 7.377; 653.03 +65.303 +6.5033; 939.303 +65.746 + 8.2794+681.28. 51. In this article are given 24 decimal fractions, arbitrarily numbered, for convenience in referring to them. 52. Add together numbers 2, 3, 4, from the last article; numbers 6, 8, 9; numbers 12, 9, 8; numbers 13, 18, 15; numbers 11, 24, and 14; numbers 10, 22, and 6. 53. Add the numbers marked 24, 23, 22; 23, 21, 20; 22, 20, 19; 21, 19, 18; 18, 17, 16; 15, 14, 13; 14, 12, 11; 13, 12, 10; 11, 10, 9; 10, 12, 8; 11, 6, 5; 2, 3, 5. 54. Add the numbers marked 2, 3, 4, 5, 6; 3, 5, 8, 9, 10; 4, 6, 8, 10, 11; 10, 12, 13, 6, 8; 13, 11, 10, 5, 6; 13, 14, 15, 16, 18; 14, 16, 18, 10, 12; 15, 16, 18, 19, 20; 18, 19, 21, 22, 23. 55. Add the numbers marked 1, 7, 13, 17, 22, 23, 24; 2, 3, 4, 6, 8, 9, 10; 24, 23, 22, 21, 20, 19, 18; 13, 14, 15, 16, 18, 19, 20; 10, 11, 12, 13, 14, 15, 16; 15, 18, 14, 19, 12, 11, 8. |