Numbers are either Concrete or Abstract. A Concrete Number is applied to a particular thing or quantity; as, 4 pears, 7 hours, 30 steps. An Abstract Number is not applied to any particular thing or quantity; as, 4, 7, 30. Fourteen balls and 13 balls are numbers of the same kind; and 6 tens and 3 tens are numbers of the same order. Numbers of the same kind or order are called Like Numbers. Only like numbers can be added. Art. 27. The Sign of Addition is +. It is called plus meaning more. When placed between two numbers, it shows that they are to be added. Thus, 85 is read 8 plus 5, and it shows that 5 is to be added to 8. The Sign of Equality is =. It is read equals or is equal to. Thus 7+ 8 = 15 is read 7 plus 8 equals 15. Art. 28. RULE FOR ADDITION.-1. Write the numbers to be added so that figures denoting units of the same order shall be in the same column, and draw a line underneath. 2. Beginning with units, add each column, and write the sum, when less than ten, underneath. 3. When the sum of any column exceeds nine, write the right-hand figure under the column added, and add the number denoted by the left-hand figure or figures with the next column. 4. Write the entire sum of the left-hand column. PROOF.-Add the columns downward. SECTION III. SUBTRACTION LESSON I. Subtrahend Figures, 1, 2, 3. 1. How many is 4 less 3? 6 less 3? 10 less 3? 12 less 3? 11 less 3? 2. How many is 11 less 2? 2? 19 less 2? 29 less 2? 8 less 3? 21 less 2? 41 less 49 less 2? 3. Three from 12 leaves how many? 3 from 22? 3 from 42? 3 from 52? 3 from 32? 3 from 20? 3 from 40? 3 from 50? 4. Begin with 50 and 50 and count back to 0 by subtracting 2 successively, thus: 50, 48, 46, 44, 42, etc. 5. Begin with 40 and count back to 1 by subtracting 3 successively. 6. Charles bought 12 sticks of candy and ate 3 of them how many sticks were left? 7. The teacher pronounced 21 words to Henry, and he misspelled 2 of them: how many words did he spell correctly? 8. A lesson in arithmetic consists of 15 examples, and Charles has solved all but 3 of them: how many examples has he solved? 9. James is 11 years old and his brother Henry is 3 years younger: how old is Henry? WRITTEN EXAMPLES. 1. From 345 take 123. PROCESS. Minuend, 345 Write 123 under 345, placing units under units, tens under tens, and hundreds under hundreds. Subtract 3 units from 5 units, and write 2 units, the difference, below; subtract 2 tens from 4 tens, and write 2 tens, the difference, below; subtract 1 hundred from 3 hundreds, and write 2 hundreds, the difference below. The difference, or remainder, is 222. 16. From four thousand and sixty-five take two thousand and thirty-one. 17. A grocer bought 585 pounds of sugar and sold 231 pounds: how many pounds had he left? 18. In a graded school, there are 345 boys and 321 girls: how many more boys than girls in the school? 4? LESSON II. MENTAL EXERCISES. New Subtrahend Figures, 4 and 5. 1. How many is 7 less 4? 6 less 4? 9 less 8 less 4? 10 less 4? 11 less 4? 9 less 5? 8 less 15 less 5? 2. How many is 7 less 5? 5? 10 less 5? 12 less 5? 3. How many is 13 less 4? less 4? 63 less 4? 83 less 93 less 4? 4. How many is 14 less 5? less 5? 54 less 5? 54 less 5? 64 less 5? less 5? 23 less 4? 43 4? 53 less 4? 34 44 less 5? 5. Begin with 60 and count back to 0 by subtracting 4 successively. 6. Begin with 53 and count back to 1 by subtracting 4 successively. 7. A man gave $12 for a saddle and $4 for a bridle how much did the saddle cost more than the bridle? 8. Charles earned 21 cents by selling papers and gave 4 cents for a comb: how many cents had he left? 9. Kate is 15 years old and her sister is 4 years younger what is her sister's age? 10. There are 21 passengers in a car: if 5 of them leave at a station, how many will remain ? 11. There are 13 men in one coach and 5 men in another how many men in the first coach more than in the second? 7. From five thousand and seventy-six take three thousand and fifty. 8. A farm contains 358 acres of land: if 155 acres should be sold, how many would be left? 9. A man bought a house for $4320 and sold it for $6450: how much did he gain? 10. A man bought 3487 bushels of wheat and sold 1425 bushels: how many bushels had he left? 11. A ship-builder sold a vessel for $24350 : if the vessel cost him $27585, how much did he lose? 12. The number of school-houses in Ohio, in 1867, was 11353; in Pennsylvania, 11453: how many more school-houses in Pennsylvania than in Ohio? 13. A wool dealer having bought 23437 fleeces of wool, shipped 12322 fleeces to Boston: how many fleeces had he left? LESSON III. MENTAL EXERCISES. New Subtrahend Figures, 6 and 7. 1. How many is 8 less 6? less 6? 13 less 6? 15 less 6? 2. How many is 12 less 7? less 7? 16 less 7? 18 less 7? 3. How many is 14 less 6? less 6? 64 less 6? 34 less 6? 4. How many is 14 less 7? less 7? 16 less 7? 36 less 7? 10 less 6? 12 14 less 6? 13 less 7? 15 22 less 7? 24 less 6? 44 74 less 6? 24 less 7? 44 46 less 7? |
