27. The money used in the United States is reckoned on a scale of tens, and thus applies the decimal system. TABLE 10 mills 10 dollars 1 eagle. = The sign for cent or cents is for ct.; the sign for dollar or dollars is $; the sign for eagle or eagles is E. Since United States money is reckoned decimally, a unit of one order being 1 tenth of a unit of the next higher order, it is written in figures, with dollars as integers or whole numbers, dimes as tenths of a dollar, cents as hundredths of a dollar, and mills as thousandths of a dollar. We reckon and express eagles as dollars, and dimes as cents. Thus, the number, 2 eagles, 1 dollar, 43 cents, 8 mills is written $21.438. It is read 21 dollars, 43 cents, 8 mills. 21 dollars, 3 cents is written $21.03. Read as dollars, cents, and mills: 19. $2.532, $61.013, $602.503, $24.003, $5204.209. 29. The Roman notation employs seven letters: I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, M for 1000. By combining these letters any number can be expressed. Thus, III = 3; IV=4; VIII = 8; IX = 9; XIV = 14. Principles to be observed in writing by letters are: 1. When a given letter is preceded by a letter representing a value less than the number to be written, the difference of the values of the letters is expressed. Thus, IV = 4; IX= 9; XL = 40; XC90. 2. When a given letter is followed by a letter or a combination of letters representing equal or less value than the given letter, the sum of the values of the letters is expressed. Thus, XX= 20; CC= 200; XXXIV = 34; LXIX = 69. 3. A bar placed over any letter multiplies it by a thousand. Thus, V 5, V = 5000. = 31. A book rack has 5 red books on the first shelf, 3 red books on another shelf, and 4 red books on a third shelf. To find the whole number of red books on the three shelves we combine or unite the numbers 5 and 3 and 4 and find that there are 12 red books on all the shelves. The process of combining or uniting two or more numbers in one number is called addition. The numbers to be united (or added) are called addends. The result obtained by adding two or more numbers is called the sum. 32. Illustrative Example. In a common year the months of 31 da. contain 217 da., the months of 30 da. contain 120 da., and the remaining month has 28 da. Find the number of days. in the year. 217) WORK 120, addends 28 EXPLANATION. For convenience in combining the numbers, we write the units of the same order in the same column. We put together first the units (ones); 8 and 7 are 15. We write 5 in the units' (ones') place below the line and reserve one ten to add with the tens. 1, 2, 2, and 1 (tens), are six tens. We write 6 at the left of the 5. 1 hundred and 2 hundreds are 3 hundreds. We write 3 at the left of the 6. In practice, to combine these numbers, we say or think, "8, 15" and write 5: "1, 3, 5, 6" and write 6: "1,3" and write 3. The last result, 365, is called the sum. 365, sum Ans. 365 days. The addition of 217, 120, and 28 may be expressed as in the columns above, or thus, 217 +120 + 28 365. The sign+means and or with, and is called plus. The sign means equal or equals. = Only numbers of the same kind and units of the same order can be added together. Numbers of the same kind are called like numbers. Thus, $8 and $3 are like numbers; also 5 pounds and 7 pounds; also 6 and 4; but $8 and 5 pounds are unlike numbers. Oral and Sight Exercise 33. 1. Add 2 to each of the following numbers, giving only sums; 2, 5, 7, 9, 1, 0, 3, 4, 6, 8. Add each of the other eight digits to each of the above numbers. Add the following till the sum is 70 or more: 2. By 2's beginning with 2; with 1. 3. By 10's beginning with 3; by 5's beginning with 4; with 3. 4. By 4's beginning with 3; with 2; with 1. 5. By 8's beginning with 7; with 6; with 5; with 4: with 3. Add till the sum is 60 or more: 6. By 3's beginning with 2; with 1. 7. By 6's beginning with 5; with 0. 8. By 9's beginning with 8; with 7; with 6; with 5; with 4. Add till the sum is 90 or more: 9. By 7's beginning with 6; with 5; with 4; with 3; with 2; with 1. Extend each of the following combinations: 34. WORK 1824 2571 278 3636 8309, Written Exercise Illustrative Example. Add 1824, 2571, 278, 3636. EXPLANATION. For convenience, we write the numbers with units of the same order in the same column. We add first the units; thus, 6, 14, 15, 19. We write 9 under the units' column, and add the 1 (ten) with the tens; thus, 1, 4, 11, 18, 20 (tens). We write 0 under the tens' column, and add 2 (hundreds) with the hundreds; thus, 2, 8, 10, 15, 23 (hundreds). We write 3 under the hundreds' column, and add 2 (thousands) with the thousands; thus, 2, 5, 7, 8 (thousands). We write 8 under the thousands' column. Ans. 8309. sum To prove the work in addition, we add downwards and compare the results. = = 36. EXPLANATION. In units, the groups 15 and 13 28, with 8 Carrying 3 (0), we have in tens the groups 14 and 15, 29 (0). Carrying 2 (00), we have in hundreds the groups 16 and 14 = 30 (00). |