12. A farmer bought a farm for $3625, and sold it for $4986; how much did he gain? Ans. $1361. 13. In 1860 the population of Maine was 628276, and that of New Hamsphire was 326072; how many more people were there in Maine than in New Hampshire? 11. To subtract when any figure in the subtrahend is greater than the figure over it. 14. From 982 take 137. OPERATION. Min. 982 Sub. 137 Rem. 845 As we cannot take 7 units from 2 units, one of the tens is put with the two units, making 12 units; and then 7 units from 12 units leave 5 units. Now as one of the 8 tens has been put with the 2 units, only 7 tens remain in the minuend, and 3 tens from 7 tens leave 4 tens; and, finally, 1 hundred from 9 hundreds leaves 8 hundreds; therefore, the entire remainder is 845. 12. In the same manner solve the following examples, taking each lower number from the one over it in each example; also subtract in the manner indicated by the signs. 5384 8078 2184 1528 23. Washington was born in 1732, and died in 1799; at what age did he die? 24. Methuselah died at the age of 969 years, and Washington at 67; what was the difference of their ages? 6849 5468 8234 6845 25. A merchant sold goods for $3427, and thereby gained $1224; what did the goods cost him? 26. In a certain battle 27345 men were engaged on one side, and 23598 on the other; how many more were engaged on one side than on the other? 27. The distance round the earth is about 24856 miles, and the distance through it is about 7912 miles; how much further round it than through it? 28. How many years have passed since the discovery of America in 1492? MULTIPLICATION. 13. BY MULTIPLICATION we find how many units there are in any number of times a given number. The number to be repeated is called the MULTIPLICAND; the number which shows how many times the multiplicand is to be taken is called the MULTIPLIER; the result of the multiplication is called the PRODUCT. The Multiplicand and Multiplier are called FACTORS. 14. To multiply by a single figure. Ex. 1. In 1 bushel there are 32 quarts; how many quarts are there in 9 bushels ? OPERATION. 9 Product, 288 Having set the factors as in the marMultiplicand, 32 gin, we say, 9 times 2 units are 18 units Multiplier, 1 ten and 8 units; write the 8 units in units' place, and then say, 9 times 3 tens are 27 tens, which, increased by the 1 ten previously obtained, make 28 tens 2 hundreds and 8 tens, and these, written in the place of hundreds and tens respectively, give the true product, 288qt. 13. If 1 horse is worth $125, what are 7 horses worth? 14. In 1 year there are 365 days; how many days are there in 3 years? 15. If the President of the United States saves $5648 in 1 year, how much, at the same rate, will he save in 4 years? 16. How many yards of cloth are there in 9 bales, each bale containing 625 yards? 17. Multiply 356 by 7. 18. Multiply 874 by 3. 19. Multiply 368 bỷ 5. 20. Multiply 759 by 4. 21. 3742 X 8: ? ? 22. 6536 X 6 : 15. To multiply by two or more figures. OPERATION. Multiplicand, 32 Multiplier, Partial Products, First multiply by 9, as though 9 were the only figure in the multi49 plier; then multiply by 4, and set the first figure of this product under the 4; finally, add the partial products together, and the sum will be the true product. 288 128 True product, 1568 16. In the same manner solve the following examples, multiplying each upper number by the one under it in each example; also multiply in the manner indicated by the signs. 32. If a steamboat sails 288 miles per day, how far will she sail in 27 days? DIVISION. .17. BY DIVISION we find how many times one number is contained in another. The number to be divided, is called the DIVIDEND ; the number by which to divide is called the DIVISOR; the number of times the dividend contains the divisor is called the QUOTIENT. If anything is left after dividing, it is called the REMAINDER. 18. To perform Short Division. Ex. 1. How many weeks are there in 364 days? OPERATION.. Divisor, 7)364 Dividend. In dividing we first say, 7 in 36, 5 times and 1 remainder; set the quotient, 5, under the 6 of the dividend, and then, imagining the remainder, 1, placed before the 4, say, 7 in 14, 2 times; set the 2 under the 4, and thus we find the quotient, 52. This process is called Short Division. 16. How much sugar, at 9 cents a pound, can be bought for 342 cents, or $3.42 ? Ans. 38lb. 17. How many pigs, at $5 each, can be bought for $285 ? 18. If a horse travels 7 miles per hour, in how many hours will he travel 1001 miles? 19. Divide 161 by 7. 22. Divide 345 by 3. 24. 9732 25. 1768 2 28. 37629: 19. To perform Long Division. Ex. 29. Paid $4932 for 9 acres of land; what was the price per acre? OPERATION. 45 43 36 72 Having set the divisor and dividend as in 9)4932(548 Short Division, draw a curve at the right of the dividend, and then say, 9 in 49, 5 times, and set the 5 at the right of the dividend. Then multiply the divisior by the quotient, 5, and set the product, 45, under the 49 of the dividend, and substract the 45 from the 49. To the remainder, 4, annex 3, the next figure of the dividend, so forming a new partial dividend, and then say, 9 in 43, 4 times, and set the 4 as the next figure of the quotient. Multiply the divisor by this new quotient-figure, and substract the product from the partial dividend. Proceed in this manner until the whole dividend has been divided. This is called Long Division. 72 0 20. In the same manner solve the following examples; also divide in the manner indicated by the signs. 37. How much tea, at 35 cents per pound, can be bought for $8.75? |