ROMAN NOTATION. 32. The method of expressing numbers by means of letters is called Roman Notation. It is called Roman Notation because it was originally used by the ancient Romans. 33. In this system, seven capital letters are used to express numbers, viz.: LETTERS: VALUES: M. I, V, X, L, C, D, By combining these letters according to certain principles, any number can be expressed. 34. PRINCIPLES. is repeated. 1. When a letter is repeated, its value Thus, X represents ten; XX, twenty; XXX, thirty; CC, two hun. dred; MM, two thousand. 2. When a letter is placed before another of greater value, its value is to be taken from that of the greater. Thus, I represents one, V, five, and X, ten. But IV represents four; IX, nine; XL, forty; XC, ninety. 3. When a letter is placed after another of greater value, their values are to be united. Thus, XV represents fifteen; LXX, seventy; LXXX, eighty; MC, one thousand, one hundred. 4. When a letter is placed between two letters, each of greater value than itself, its value is to be taken from the sum of the other two. Thus, XIV represents fourteen; XIX, nineteen; CIV, one hundred four. 5. A bar placed over a letter increases its value a thousand fold. Thus, V represents five; V, five thousand; LXX represents seventy; LXX, seventy thousand. ADDITION. 35. 1. How many blocks are 5 blocks, 3 blocks, and 7 blocks? 2. How many splints are 3 splints, 2 splints, and 8 splints? 3. How many oranges are 7 oranges, 2 oranges, and 5 oranges? 4. How many are 5 and 6 and 7 ? 5. How many are 7 and 8 and 6? 6. How many are 5 and 9 and 2 and 6? 7. How many are 3 and 7 and 4 and 8? 8. How many are 4 and 8 and 5 and 9? 9. What have you been doing with the numbers given above? 36. The process of finding a number that is equal to two or more given numbers is called Addition. 37. The result obtained by adding is the Sum, or Amount. 38. The Sign of Addition is a small upright cross (+). It is read plus, and is placed between the numbers to be added. Thus, 4+2 is read 4 plus 2, and means that 4 and 2 are to be added. 39. The Sign of Equality is two short parallel horizontal lines (=). It is read equals, or is equal to. Thus, 3 + 2 = 5 is read 3 plus 2 equals 5. WRITTEN EXERCISES. 40. 1. Add 13, 12, 24, 30, and 14. EXPLANATION. -- - In adding, the numbers are written in 13 columns, units under units, tens under tens, and it is more 12 convenient to begin with the units' column. Adding, we find there are 13 units. 13 means 1 ten and 3 units; therefore the 3 is written in the units' column, and the 1 ten is added to the tens. Adding the tens, we find that there are 9 tens. Therefore the result is 93. 24 30 14 93 In adding, do not say 4 and 4 are eight and 2 are ten, etc., simply name results, thus: 4, 8, 10, 13. 26. Two birds fly in opposite directions, one 19 miles, and the other 27 miles. How far apart are they? 27. Max earned 24 dollars, and John earned 9 dollars more than Max. How many dollars did both earn? 28. Baby is 4 years old; mamma is seven times as old as baby; grandma is twice as old as mamma. What is the sum of their ages? 29. In a store window I saw 38 books, 25 toys, 17 slates, and 20 globes. How many articles did I see? 30. In one class in our school there are 11 boys and 9 girls; in another, 17 boys and 18 girls; in another, 10 boys and 14 girls. How many boys are there in all? How many girls? How many children? 31. A fisherman caught 46 trout, 75 bass, and 13 bluefish. How many fishes did he catch? 32. Fred weighs 83 pounds, and Nathan weighs 97 pounds. How much do they both weigh? 33. In one book there are 98 pages, in another 89, and in a third 75. How many pages are there in all the books? 34. A certain tract of land was divided into 4 farms; one containing 13 acres, another 37 acres, the third 70 acres, and the fourth 48 acres. How many acres did the original tract contain? 35. The distance from Alburn to Grade is 6 miles, from Grade to Newton 8 miles, from Newton to Arnold 9 miles, and from Arnold to Houston 8 miles. How far is it from Alburn to Houston? 36. Elsie solved 18 examples on Monday, 14 on Tuesday, and 12 on Wednesday. How many examples did she solve in all ? 37. If I buy a collar for 25 cents, some gloves for 37 cents, some ribbon for 8 cents, and a paper of needles for 9 cents, what do they all cost? · 38. A farmer has in one bin 28 bushels of oats, in another |
