multiplication table, being multiplied together will produce it, divide the given dividend by one of those figures, and the quotient thence arising by the other, and the last quotient will be the an swer. Note. The total remainder is found by multiplying the last remainder by the first divisor, and adding in the first remainder. SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number; that is a whole number joined with a fraction as 41, 53, 61, &c. RULE. Multiply by the whole number, and take,,,, 1, &c. of the multiplicand, and add it to the product;-Or multiply the upper number of the fraction, and divide its product by the under one, and the result will be the value of the fraction. APPLICATION TO DIVISION. 59. How many 4's are there in 320 ? Ans. 80. 60. A man intending to go a journey of 3264 miles would wish to perform it in 136 days, how many miles must he travel each 'day? Ans. 24 miles. 61. Ifa man's board cost him 72 shillings for a month, or 4 weeks, how much does he pay for each week ? Ans. 18s. 62. Several boys went to gather nuts, and collected 4275, which when shared among them, each had 855; how many boys were in company? Ans. 5 boys. 63. A farm of 375 acres is let for 1125 dollars, how much does it pay an acre? Ans. 3 dollars. 64. Suppose a man's income to be 2555 dollars a year; how much is that per day, there being 365 days in a year? Ans. 7 dollars. Questions to exercise the learner in Addition, Subtraction, Multiplication, and Division. 65. If I add 167, 394, and 447, and divide their amount by 12, what number will result? Ans. 84. 66. Deborah bought 24 peaches: she kept 14 of them herself, and divided the rest equally between her two little sisters: how many had each? Ans 5. 67. Admitting a man has a farm containing 200 acres, which is divided into plough land, pasture, meadow, and wood land; he has 50 acres of wood, 25 of meadow, 60 of pasture; how many acres were there left for plough land? Ans. 65. 68. Suppose 2072 apple trees be planted in 14 rows; how many will there be in each row, and how many bushels of apples will the orchard bear, admitting each tree to have 12 bushels on it? Ans. 148 trees, and 24864 bushels. 69. A man at his decease, left property, amounting to £12426. He directed in his will that £1000 should be given to his niece; and that the remainder of the property should be divided, equally, between his two nephews. What is the share of each nephew? Ans. £5713. 70. To find how many dollars are contained in any number of pounds, we multiply the pounds by 21. How many dollars are there in £846 ? Ans $2115. 71. There are 16 bags of coffee, weighing each 120 pounds, and 8 bags weighing each 343 pounds. What is the weight of the whole ? Ans. 4664. QUESTIONS IN NUMERATION. What is Arithmetic ? How many principal rules are there in Arithmetic ? What does numeration teach? Of what does it consist? When several figures are set down together, which are the units, which the tens, which the hundreds, &c. QUESTIONS IN ADDITION. What does addition teach? What is the amount or sum? How should we place figures to be added, and wherein is partiqular care necessary? Where do we begin to add a sum? When the sum or amount of each column does not exceed nine, what must be done with it? But if the sum or amount is more than nine, which of the figures is to be set down, and what is to be done with the other? What is to be observed in setting down the sum of the last column? How is addition proved? QUESTIONS IN SUBTRACTION. What does simple subtraction teach? In ubtraction, what are the greater number, the less one, and the difference called? How are numbers placed to be subtracted? Where do we begin to subtract, and how is subtraction performed? When the lower figure is larger than the one above, what is then to be done? When the lower figure is taken from 10, what do we do? QUESTIONS IN SIMPLE MULTIPLICATION. What is simple multiplication? What are the names of the terms in simple multiplication? Which is the multiplicand? What is the product? What are the multiplier and multiplicand generally called? Where must the multiplier be set under the multiplicand? After placing the multiplier in its proper place, what is to be' done with it? When the product does not exceed 9, what should be done with it? But if the product exceed 9, which figure must be set down; and what should be done with the other? What must be done with the last product? How is multiplication proved? When the multiplier exceeds 12, or consists of several figures,' how must it be placed? What must be done with each figure of the multiplier, and how must the product of each be placed? How is the total product found? When there are cyphers on the right hand of either or both the factors, what must be done with them? When the multiplier is the exact product of two figures in the multiplication table, how should we proceed to obtain the answer? QUESTIONS IN SIMPLE DIVISION. What is division? What does division teach? How many principal parts are there belonging to division, and what are they called? Which is the dividend? Which is the divisor? Which the quotient? Which is the remainder? What is always observed respecting the remainder? What is short division ? How are the divisor and dividend to be placed? ¿ What is the first step taken in short division? If there be any remainder, what is to be done with it? What is long division? Having placed the divisor and dividend in their proper places what is first to be considered? What is to be done with the figure or number that is placed in the quotient? What is to be done with the product found by multiplying the quotient and divisor together? What must be prefixed to the remainder? After having brought down a figure, and placed it in its proper place, what is then to be done? How is long division proved? When there are cyphers at the right hand of the divisor, how is the operation generally performed? What is to be done with those figures which are cut off in the dividend? When the divisor is the product of any two figures in the multiplication table, how do we proceed? When we divide thus, and there are remainders, how is the total remainder found? How do you multiply by a mixt number; that is, a whole number joined with a fraction? FEDERAL MONEY. The denominations of Federal money are, Eagle, Dollar, Dime, Cent, and Mill. The relative values of these denominations are precisely the game as those of units, tens, hundreds, &c. For this reason Federal money is added, subtracted, multiplied, and divided by the same rules that are given for Simple Addition, Subtraction, Multiplication, and Division. It is not customary in reading sums in Federal money to meneagles or dimes, as the following table will show : tion |