succeed millions, billions, &c., to each of which, as to units and to thousands, are appropriated three places, as exhibited in the following examples: co Units of Quadrillions. → Tens ✩ Units Or Hundreds Hundreds • Tens co Units Hundreds EXAMPLE 1st. EXAMPLE 2d. 3 1 7 4 5 9 2 8 3 7 4 6 3 5 1 2 3, 1 7 4, 5 9 2, 8 3 7, 4 6 3, 5 1 2 To facilitate the reading of large numbers, it is frequently practised to point them off into periods of three figures each, as in the 2d example. The names and the order of the periods being known, this division enables us to read numbers consisting of many figures as easily as we can read three figures only. Thus, the above examples are read 3 (three) Quadrillions, 174 (one hundred seventy-four) Trillions, 592 (five hundred ninety-two) Billions, 837 (eight hundred thirty-seven) Millions, 463 (four hundred sixtythree) Thousands, 512 (five hundred and twelve.) After the same manner are read the numbers contained in the following *This is according to the French method of counting. The English, after hundreds of millions, instead of proceeding to billions, reckon thousands, tens and hundreds of thousands of millions, appropriating six places, instead of three, to millions, billions, &c NUMERATION TABLE. Hundreds of Millions. Hundreds of Thousands. Tens of Thousands. Tens. Units. Those words at the head of the table are applicable to any sum or number, and must be committed perfectly to memory, so as to be readily applied on any occasion. 8 6 4 3 2 7054 Of these characters, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, the nine first are sometimes called significant figures, or digits, in distinction from the last, which, of itself, is of no value, yet, placed at the right hand of another figure, it increases the value of that figure in the same tenfold pro0 3 0 2 0 7 0 portion as if it had been followed by any one of the significant figures. 86200 90037 1 5086000 1 02070 806 105409 Note. Should the pupil find any difficulty in reading the following numbers, let him first transcribe them, and point them off into periods. The expressing of numbers, (as now shown,) by figures, is called Notation. The reading of any number set down in figures, is called Numeration. After being able to read correctly all the numbers in the foregoing table, the pupil may proceed to express the following numbers by figures: 1. Seventy-six. 2. Eight hundred and seven. 3. Twelve hundred, (that is, one thousand and two hun dred.) 4. Eighteen hundred. 5. Twenty-seven hundred and nineteen. 7. Ninety-two thousand and forty-five. 9. Two millions, eighty thousands, and seven hundreds. 10. One hundred millions, one hundred thousand, one hundred and one. 11. Fifty-two millions, six thousand, and twenty. 12. Six billions, seven millions, eight thousand, and nine hundred. 13. Ninety-four billions, eighteen thousand, one hundred and seventeen. 14. One hundred thirty-two billions, two hundred millions, and nine. 15. Five trillions, sixty billions, twelve millions, and ten thousand. 16. Seven hundred trillions, eighty-six billions, and seven millions. ADDITION OF SIMPLE NUMBERS. 4. 1. James had 5 peaches, his mother gave him 3 peaches more; how many peaches had he then? 2. John bought a slate for 25 cents, and a book for eight cents; how many cents did he give for both? 3. Peter bought a waggon for 36 cents, and sold it so as to gain 9 cents; how many cents did he get for it? 4. Frank gave 15 walnuts to one boy, 8 to another, and had 7 left; how many walnuts had he at first? 5. A man bought a chaise for 54 dollars; he expended 8 dollars in repairs, and then sold it so as to gain 5 dollars; how many dollars did he get for the chaise? 6. A man bought 3 cows; for the first he gave 9 dollars, for the second he gave 12 dollars, and for the other he gave 10 dollars; how many dollars did he give for all the cows? 7. Samuel bought an orange for 8 cents, a book for 17 cents, a knife for 20 cents, and some walnuts for 4 cents; how many cents did he spend ' 8. A man had 3 calves worth 2 dollars each, 4 calves worth 3 dollars each, and 7 calves worth 5 dollars each how many calves had he? 9. A man sold a cow for 16 dollars, some corn for 20 dollars, wheat for 25 dollars, and butter for 5 dollars; how many dollars must he receive? The putting together two or more numbers, (as in the foregoing examples,) so as to make one whole number, is called Addition, and the whole number is called the sum, or amount. 3 10. One man owes me 5 dollars, another owes me 6 dollars, another 8 dollars, another 14 dollars, and another dollars; what is the amount due to me? 11. What is the amount of 4, 3, 7, 2, 8, and 9 dollars? 12. In a certain school 9 study grammar, 15 study arithmetic, 20 attend to writing, and 12 study geography; what is the whole number of scholars? SIGNS. A cross, +, ce line horizontal and the other perpendicular, is the sign of addition. It shows that numbers, with this sign between them, are to be added together. It is sometimes read plus, which is a Latin word signifying more. Two parallel, horizontal lines,=, are the sign of equality. It signifies that the number before it is equal to the number after it. Thus, 5 + 3 = 8 is read 5 and 3 are 8; or, 5 plus (that is, more) 3 is equal to 8. In this manner let the pupil be instructed to commit the following 3+7=10 4+7=11 5+7=12 2+8=10 3+8 =11 4+8=12 5+8=13 2+9=11 3+912 | 4+ 9 = 13 5+9=14 B 6+1 = 6+2= 7 ADDITION TABLE-CONTINUED. 6+0= 617+0= 78+0=8 9+0= 9 7+1= 8 8+1 9 9+1=10 8 7+2 9 8+2=10 9+2=11 5. When the numbers to be added are small, the addition is readily performed in the mind; but it will frequently be more convenient, and even necessary, to write the numbers down before adding them. 3. Harry had 43 cents, his father gave him 25 cents more; how many cents had he then? One of these numbers contains 4 tens and 3 units. The other number contains 2 tens and 5 units. To unite these two numbers together into one, write them down one under the other, placing the units of one number directly under units of the other, and the tens of one number directly under tens of the other, thus: 43 cents. Having written the numbers in this man. 25 cents. ner, draw a line underneath. |