! By the foregoing table it appears that any figure in the units place, represents only its simple value, or so many ones, but by being placed in the tens place, represents ten times as much as though it stood in the units place, by being placed in the hundreds place a hundred times as much as it would if placed in the units place, and ten times as much as it would if placed in the tens place, and so on. Though it is seldom necessary to make use of more than nine places as in the table, yet it may be extended to a greater number by making places for thousands of millions, tens of thousands of millions, hundreds of thousands of millions, &c. To know the value expressed by any given number of figures, Rule. 1. Read the figures from right to left, units, tens, hundreds, thousands, &c. as in the Numeration table. 2. To the value of each figure when it stands single, add the name of its place and read the figures from the left to the right. Example, 321, three hundred and twenty-one. What is Arithmetic? Questions. By what means are operations in Arithmetic performed? When numbers are expressed by more than one figure, how is the value of each figure determined? Recite the Numeration table. Is it usually necessary to make use of more than nine places to express numbers, when necessary, how is the number of places increased? Repeat the Rule to know the value expressed by any num ber of figures? To write down a proposed number. Rule. Begin at the right hand and proceed towards the left, writing units in the units place, tens in the tens place, hundreds in the hundreds place, and so on, Des Write down in figures sixty-five. Write down three hundred and fifty-one. Write down three hundred and ninety-six. Write down one thousand two hundred and fifty-six. Write down seventy-six thousand five hundred and ninety seven. Write down one hundred and fifty-two thousand two hundred and sixty-five. Write down two hundred and ninety-one thousand seven hundred and fifty-one. Write down four hundred and eighty-nine thousand two hundred and ninety-six. Write down nine hundred and fifty-six thousand two hundred and seventy-five. Write down one million eight hundred and fifty-six thousand seven hundred and eighty-six. Write down twelve million four hundred and ninety-three thousand two hundred and twenty-one. There are two primary rules by which all operations in Arithmetic are performed, namely, Addition and Subtraction. ADDITION. The use of Addition is to ascertain the amount of two or more numbers when put together. Rule. 1. Set down any one of the numbers, and place under it all the rest in such a manner that units may stand under units, tens under tens, hundreds under hundreds, and so on, and draw a line under the last. 2. Begin at the right hand or units column, and add together all the figures contained in that column. 3. Consider all the figures contained in the amount of the column and set down under it all above an even number of tens, and carry one for every ten to the next column, proceeding in the same manner until all the columns have been added up, setting down the whole amount of the last column. Proof-Perform the addition downwards, and if the amount is the same as when added upwards the work is right. Questions. How many primary rules are there in Arithmetic, and what are they called? For what is Addition used? How do you set down numbers which you intend to add logether? Do you commence at the right or left hand column of numbers which you wish to add together? When you have found the amount of all the figures contained in a column how do you proceed? How do you prove Addition? Addition Table. To use the table, look in the outside left hand column for one of the numbers to be added and in the top column for the other number, then in the square opposite the one, and under the other, their sum will be found. Note. If the pupil is required to commit the foregoing table to memory his progress will be thereby very much fa cilitated. 17. Add 14, 16, 23, 29, 80, 31, and 100 together, and tell the amount. 18. What is the amount of 36, 97, 125, 384, 1176? Ans, 293. Ans. 1818. 19. What is the amount of 3797, 95, 2, 75, 876, and 9750? Ans. 14595. 20. What is the amount of 205, 20, 840, 970, 367, and 1001? Ans. 3403. 21. What is the amount of three hundred and sixty-five, eight hundred and seven, five hundred and sixty, twenty-five, thirty-seven, and one hundred and one? Ans. 1895. 22. What is the amount of three hundred, seventy-five, two, forty-seven, thirty-three, nine thousand seven hundred and eighty-four, twenty thousand one hundred and fifty, seven hundred and sixty-five thousand and ninety-one, and one million seventy-five thousand and forty-seven? Ans. 1870529. 23. Add Seventy-five millions nine hundred and sixty thousand eight hundred, two hundred and twenty-five thousand, and one hundred and forty together. Ans. 76185940. Practical Exercises. 24. In one pocket I have thirty-five marbles and in anather 21, how many have I in all? Ans. 56. 25. John and Charles went to collect nuts, and when they had collected a quantity they sat down to count them, when John found he had collected 275, and Charles 196, how many nuts did both of them gather? Ans. 471. 26. Having a mind to buy a suit of new clothes, I went to the tailor's to see how much money would be necessary for that purpose, when I found he would charge for a coat 30 dollars, for a pair of pantaloons 12 dollars, and for a waistcoat 5 dollars, what will the suit cost at that rate? Ans. 47dols. |