The words at the head of the numeration table, units, tens, hundreds, &c., are equally applicable to all numbers, and must be committed to memory, after which, the pupil may read the Table. *NOTE. This Table is formed according to the French method of numeration. The English method gives six places to thousands, &c. 327, 826 To make the reading of figures easy, they are often separated into periods of three figures each, counting from the right hand. EXAMPLES IN EXPRESSING NUMBERS BY FIGURES. Ans. 6. Write four hundred thousand. 7. Write four millions. These examples show us very clearly that the same significant figure will have different values according to the place which it occupies. 8. Write seven. Write six units of the 2d order. Write nine units of the 3d order. Write six units of the 4th order. Write eight units of the 2d order. Write one unit of the third order. Write nine units of the 6th arder. Write two units of the 8th order. 9. Write six hundred and seventy-nine. 10. Write six thousand and twenty-one. 11. Write two thousand and forty. Ans. 679. 12. Write one hundred and five thousand and seven. 13. Write three billions. 14. Write ninety-five quadrillions. 15. Write one hundred and six trillions, four thousand and two. 16. Write fifty-nine trillions, fifty-nine billions, fiftynine millions, fifty-nine thousands, fifty-nine hundreds, and fifty-nine. 17. Write eleven thousand, eleven hundred and eleven. 18. Write nine billions and sixty-five. 19. Write three hundred and four trillions, one million, three hundred and twenty-one thousand, nine hundred and forty-one. § 10. There is yet another method of expressing numbers, called the Roman. In this method the numbers are represented by letters. The letter I stands for one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred, &c. § 11. John has three apples and Charles has two; how many apples have they between them. Every boy will answer, five. Here a single apple is the unit, and the number five contains as many units as the two numbers three and two. The operation by which this result is obtained is called addition. Hence, ADDITION is the uniting together of several numbers, in such a way, that all the units which they contain may be expressed by a single number. Such single number is called the sum or sum total of the other numbers. Thus, 5 is the sum of the apples possessed by John and Charles. What is the sum of 2 and 4? of 3 and 5? of 6 and 3? of 4, 3 and 1? of 2, 3 and 4? of 1, 2, 3 and 4? of 5 and 7? How many units in 4 and 6? How many units in 9 and 4? Q. What is addition ? What is the single number called which expresses all the units of the numbers added? What is the sum of 2 and 4? What is six called? OF THE SIGNS. § 12. The sign +, is called plus, which signifies more When placed between two numbers it denotes that they are to be added together. Thus, 3+2 denotes that 3 and 2 are to be added together. The sign, is called the sign of equality. When placed between two numbers it denotes that they are equal to each other. Thus, 3+2=5. When the numbers are small we generally read them, by saying, 3 and 2 are 5. Q. What is the sign of addition? What is it called? What does it signify? When placed between two numbers what does it express? Express the sign of equality. When placed between two numbers what does it show? Give an example. § 13. Before adding large numbers the pupil should be able to add, in his mind, any two of the ten figures. Let him commit to memory the following table, which is read, two and 0 are two; two and one are three; two and two are four, &c. 3. What is the sum of 4, 5, and 4 tens? Ans. 89. Ans. 4. What is the sum of 1, 2, 3, 4, and 9 tens? Ans. 100. 5. What is the sum of 1, 2, 3, 4, 5, and 6 tens ? Ans. 6. What is the sum of 1, 4, 9, and 5 tens? Ans. 64. 7. What is the sum of 4, 8, 3, and 7 tens? Ans. 8. What is the sum of 1, 2, 4, and one hundred. 9. What is the sum of 1, 3, 4, and 4 units of the second order. 10. What is the sum of 4 and 5, and 4 units of the third order. 11. What is the sum of 6 and 2, and 5 units of the third order. 12. James has 14 cents, and John gives him 21: how many will he then have? Having written the numbers, as at the right of the page, draw a line beneath them. 14 21 35 The first number contains 1 ten and 4 units, the second 2 tens and 1 unit. We write the units under the units, and the tens under the tens. We then begin at the right hand, and say 1 and 4 are 5, which we set down below the line in the units' place. We then proceed to the next column, and add the tens, by saying 2 and 1 are 3, which we write in the tens' place. Hence, the sum is 35: that is, James will have 35 cents. 13. John has 24 cents, and William 62: how many have both of them? |