Questions for Exercise. Ist. A man was born, A. D. he be 65 years of age? 1741, in what year will 2d. A man has paid $327 $643 remain unpaid; how much was the note at first? Ans. $970. 3d. From A's house to B's is 46 miles, from B's to C's is 78 miles in the same direction; how far is it from A's house to C's? Ans. 124 miles. 4th. A merchant sold an invoice of goods, for which he received in money $ 798, and a note for the remainder, which was $2750; how much was the whole value? Ans. $3548. 5th. A man being asked his age, said he was 23 years old when his eldest son: was born, who was then 25 yrs. old; what was the age of the father? Ans. 48 yrs. 6th. A tree was broken off by the wind, 16 feet from the ground, the top part broken off was 79 feet long; how high was the tree before it was broken? Ans. 95 feet. 7th. What number is that from which, if 750 be taken, 1268 will remain? Ans. 2018. 8th. A farm consists of 40 acres of plough land, 60 of pasture, 48 of mowing, 20 of orchard and garden, and 52 of wood land; how many acres in the whole ? Ans. 220. 9th. A man at his death left an estate, which, after paying debts and charges to the amount of $2643, there remained to divide among seven children, $ 5648 each; how much was the whole estate? Ans. $ 42179. SIMPLE SUBTRACTION Teaches to take a less number from a greater, of the same denomination, to find their difference. RULE. Place the less number under the greater, with units under units, tens under tens, &c. Begin with the units, take the lower figure from the upper, and set down the remainder under them; but, if the lower figure be greater than the upper, take it from ten, and add the remainder to the upper figure, set down their sum, and carry (or add) one to the next lower figure, with which proceed in the same manner, and thus through the whole. To prove Subtraction, add the remainder (or difference) to the less number, their sum will be equal to the greater number, if the work be right. In the first example I begin with the unit figure of the lower line, saying, 8 from 1 I cannot take, therefore I must take it from 10, and 2 will remain, which 2 added to the upper figure 1 make 3, which three I set down under the 8, and carry 1 to the next lower figure 5, makes 6; which 6 taken out of the figure over it (7) there remains 1, which 1 I set down under the 5; then say, 7 from 3 I cannot take, but 7 from 10 there remains 3, which added to the upper figure 3, makes 6, to set down under the 7; then I carry to the next figure 1, makes 2, which taken from 6, there remains 4, which I set down under the one; then say 3 from 9, there remains 6, which I set down under the 3, and find the whole difference (or remainder) to be 64613. To prove the work, I add the difference found, and the less of the given numbers together; and find their sum equal to the greater given number. 1st. A man was 65 years old, A. D. 1806; in what year was he born? Ans. A. D. 1741. 2d. From A's house to B's is 46 miles, from A's to C's 124 miles, in the same direction; how far is it from B's house to C's? Ans. 78 miles: 3d. A man has paid $ 327 on a note of $ 970, how much remains unpaid? Ans. 643. 4th. A merchant sold an invoice of goods valued at 3548, received a part of the value in money, and a note for the balance, which was $789, how much money did he receive ? Ans. 2759. 5th. A man being asked the age of his son replied, I was 23 years old when he was born, I am now 48; what was the son's age ? Ans. 25 years.. 6th. A tree 95 feet high was broken off by the wind, the top part which fell was 79 feet long; how high was the stump left? Ans. 16 feet. 7th. If $1564 be taken from $3620, how many will be left? Ans. $2056. 8th. From the vernal to the autumnal equinox is 186 days; how many days are there from the autumnal to the vernal equinox, allowing the year to be 365 days? Ans. 179 days. 9th. Said Jack to Tom, my purse and money together are worth twenty dollars, and the purse is worth 50 cents; how much inoney was in it? Ans. $19,50. SIMPLE MULTIPLICATION Teaches to find the amount of a simple number repeated a certain number of times. Before the Pupil proceeds to multiply numbers, it is necessary for him to learn perfectly the following To learn this table, begin with the upper line and left hand column you will find 1; and by following that line you will find twice 1 are 2, and three times 1 are 3, &c. By taking the second line, and proceeding as before, you will find twice 2 are 4, three times 2 are 6, &c. CASE I. When the multiplier does not exceed 12. RULE. Place the multiplier under the multiplicand, with units under units, &c. Begin with the unit figure, in the multiplicand, involve or multiply it, and also each figure in the multiplicand, into the multiplier, setting down the right hand figure of each product, and carrying what the others will make to the product of the next, as in Simple Addition. Multiplication may be proved by casting out the nines from the multiplicand, setting the remainder at the right of a cross; cast the nines out of the multiplier, setting the remainder at the left of the cross; multiply these remainders together, and set the excess over nines, over the cross; lastly, cast the nines out of the product, and set the remainder under the cross, which will be the same as that over it, if the work be right. In this first example, I say twice 2 are 4, which I set down directly under the multiplier; then say twice 8 are 16, I set down the right hand figure 6, in the ten's place of the product, and carry the left hand figure 1, to the product of the next figure, saying twice 3 are 6, and 1 I carry makes 7, which I set down at the left of the 6 in the product; then say twice 4 are 8, which I set down at the left of the 7; then say twice 6 are 12, I set down the 2 at the left of the 8 in the product, and carry the 1 to the product of the next figure, saying twice 7 are 14, and I carry makes 15; this being the product of the left hand figure of the multiplicand, I set the whole down |