ARITHMETIC. ARITHMETIC is that science which treats of the properties, powers, and operations of numbers. It has five primary rules..........viz. Numeration......Addition...... Subtraction......Multiplication......and Division. NUMERATION. NUMERATION teaches how to read any number of figures which may be written; and also to express, by figures properly arranged, any number of figures which can be conceived. The characters used in calculations are 1 one.......2 two.......3 three......4 four......5 five......6 six ...... seven......8 eight......9 nine......O cipher. TABLE: 1........One 21........Twenty-one 2 1........Three hundred twenty-one 3 2 1........4 thousand 321 3 2 1........54 thousand 321 6 5 4 3 2 1........654 thousand 321 654 4.5 6 3 2 1........7 million 654 thousand 321 3 2 1........87 mill. 654 thousand 321 3 2 1........987 mill. 654 thous. 321 7 8 9........123 mill. 456 thous. 789 69 ........483 mill. 572 thous. 691 B The above table is thus briefly comprised and enlarged: Although the preceding table is sufficient in practice, yet the following may not be unnecessary : Nonillions. Octillions. Septillions. Sextillions. Quintillians. 654321 987654 3219.87 654321 987654 Quadrillions, Trillions. Billions. Millions. Units 321987 654321 98654 321987 654321 Billions are substituted for millions of millions.......Trillions for millions of millions of millions........Quadrillions for millions of millions of millions of millions, &c. EXAMPLES: Set down in figures the following numbers: Nine hundred and five. Twelve thousand and ninety. Two hundred eighty thousand, seven hundred. eight hundred and seventy-two. Seven hundred sixty-four thousand millions, eight hundred ninety-five millions, two hundred thirty-one thousand, eight hundred and seventy-nine. In words express these numbers: 478 3010 70904 4091875. 49163189.186 500098400700 Numbers are also thus denoted, and are called numeral 1....2.....3.......4......5......6......7........8........ 9....10....... 20.......30.......40....50...60......70.....80.......90...100 500.....1000........... 1798......... D A less numeral number, placed after a greater, augments ADDITION of integers is the collecting of several- Place the numbers so, that units be under units, tens under tens, &c. Then add the right-hand column, setting down the units of the result, carrying the left-hand figure EXPLANATION.-The sum of any two numbers in the top line and left-hand column, is found directly under the one of them opposite the other-as, 9 and 8 make 17. If young beginners would learn to repeat this table perfectly by memory, they would not stumble, as many do, at the very threshold of the science. PROOF. Add downwards: Or, set down the sum of the first column-likewise the sum of each other, the unit figure under, the tens to the left in the upper line-the sum of the whole will equal the first total. In all the succeeding examples, through the four primary rules, both simple and compound, the one at the right hand is intended, when wrought, to prove that on the left. PRACTICAL QUESTIONS.. 1. If £.7685. £.632. £.98. £.7642. £.28. and nine thousand and seventy-two pounds be added, what is the fum? Answer.........25157. 2. A person born in the year 1688, in what year will he be 112 years of age? Answer..........in 1800. 3. A bond is due for .8973. interest thereon £478. what is the amount? Answer...........9451 4. A person has due to him on bond, L.1084. in book accounts.9865.in sundry notes .107. and in cash .1794. what is the whole sum? Answer......12850.. week? 5. How many strokes does a regular clock strike in a Answer..........1092. 6. A draper bought six pieces of linen, three of which contained each 76 yards, the other three each 68 yards— the number of yards is required? Answer..........432. 7. If from the creation to the flood be 1650 years, from that time to the calling of Abraham 427, from that to the building of the temple 909, thence to the founding of ́• Rome 266, thence to the birth of Christ 752, and since 1801 the age of the world is required? Answer.........5805.. 8. A person left his widow .5850. his eldest son .4828.-to two other sons each £3500. to three daughters each 2565.and in charitable bequests.1086. the fum bequeathed is required? Answer......26459.. 9. The lesser of two numbers is 9087, their difference twice as many and 198-what is the greater number? Answer.........27459. · 10. A grocer bought 8 casks of sugar, No. 1 and 2 weighed each 1087 lbs. No. 3, 4, and 5, each 1278lbs. No.6, 7, and 8, each 1456lbs.-the whole weight is required? Answer......10376lbs. 11. Bought 10 bales of lines, in four of which were 65 pieces, which contained 1625 yards, the other 6 had 95 pieces and 2375 yards-how many pieces and yards were there? Answer......160 pieces, 4000 yards. 12. Borrowed a sum of money; paid £.389. £.576. L.1274. L.2488. and the residue unpaid is 273. query, the sum borrowed? Answer......5000.. |