WRITTEN EXERCISES. IN ADDITION AND SUBTRACTION. 1. An estate worth $35,000 has two mortgages upon its one for $15,000, and the other for $8000; what is it worth above the incombrances? Ans. $12,000. 2. A merchant's gross profits last year were $9000; he pays for rent $1200, insurance $150, salaries $3500, and incidental expenses, $225; what is bis net profit? Ans. $3925. 3. A clerk receives $800 a year; he pays $150 a year for hogse rent, bis butcher's bill is $177.50 and grocer's bill $145.45, and he has expended for clothes and other expenses $250; what does he save in the year ? Ans. $77.05. 4. Mr. Wainwright bought a farm which cost him $25,000; but afterwards getting into difficulties, he burdened the property with a mortgage for $7500; for what must be sell the farm to gain $3500? Ans. $21,000. 6. Mr. Hatton receives for goods sold a check for $15,495.25 on the Girard National Bank; he wishes to deposit $13,500 in the same bank; what will the bank return him when he presents the check? Ans. $1995.25. 6. I had in bank on Monday morning, Dec. 4, $11,275, I checked out Monday afternoon $745: Tuesday, I deposited $1500; Wednesday, I deposited $475 Thursday, I checked out $873.50; Friday, I again checkec out $563.75; Satur. day, I deposited $560; what is the amount of my deposit on Monday morning, Dec. 11? Ans. $11,627.75. 7. The day before Christmas I went into a fancy store and bought for Christmas presents, a writing-desk at $4.25, a work-box at $2.75, a glove-box at $1.50, a handkerchief. box at $1.75, a case of perfuniery at $2.25, and a gentle, man's dressing-case at $5.75; I banded the clerk a twenty. dollar bill; what change should I receive ? Ans. $1.75. 8. A farmer took to the store 2 dozen eggs, $0.70; 10 pounds of butter, $5; 2 barrels of apples, $11.50; he bougbt 25 pounds crushed sugar, $3.50; 2 gallons molasses, $0.60; 10 yards red flannel, $3.75, and one piece unbleached sheet ing, $10; how much cash must be pay? Ans. $0.65. INTRODUCTION TO MULTIPLICATION. MENTAL EXERCISES. 1. Repeat the table of 2 times; of 3 times; of 4 times; of 5 times of 6 times; of 7 times; of 8 times; etc. 2. If one barrel of flour costs 6 dollan, what will 5 barrel cost at the same rate ? SOLUTION.-If one barrel of flour costs 6 dollars, 5 barrels will cost s Ames 6 dollars, which are 30 dollars. 3. What will 7 gold pens cost at 3 dollars apiece ? 4. At 20 cents apiece what will 6 spelling-books cost ? 5. What is the cost of 11 yards of calico at 12 cents a yard? 6. George has 15 dollars and James has 6 times as much; how many dollars has James ? 7. A farmer bought 6 cows at 25 dollars apiece; how much did ho pay for them? 8. If 6 men can do a piece of work in 20 days, how long will it take 1 man to do it? 9. If 8 men mow a field of grass in 15 days, how long will it take 1 man to mow it? 10. In an orchard there are 16 rows of trees and 10 trees in each row; how many trees are there in the orchard ? 11. John borrowed 12 cents from a friend, and then earned 6 times as much as he borrowed; how many cents had he then? 12. Arnold earned 18 dollars a week, and paid 9 dollars a week for his board; how much could he save in 8 weeks? 13. How many are 3 times 5, plus 6? 5 times 6, plus 7? 6 times 7, plus 8 ? 7 times 8, plus 9? 9 times 10, plus 11 ? 12 times 10, plus 13? 14. How many are 4 times 6, minus 8? 6 times 7, minus 5? 8 times 9, minus 109 7 times 11, minus 9? 9 times 12, minus 139 15. How many are 6 and 6 times 7? 7 and 7 times 9? 8 and 8 times 109 9 and 9 times 8? 10 and 10 times 11? 11 and 11 times 12? 16. The process of taking one number as many times as there are units in another is called multiplication. The number multiplied is the multiplicand; the number by which we multiply is the multiplier; the result is the product. The sign of multiplication is X, and is read "multiplied by.” 17. Read the result of the following: 0x478 7x3+2 9x7+12 12x9_18 12x 12—24 BX074 6x45 8X6-11 10X8+16 13X 6–18 7x875 5x5+7 7 X 810 11x415 14x 7-27 8x7+8 4x68 8x4+12 13X39 9x877 3x7+5 9X3-10 14x4-12 16x 0-30 17 x 8-21 MULTIPLICATION. 71. Multiplication is the process of finding the product of two numbers. 72. The Product of two numbers is the result obtained by taking one number as many times as there are unite in Another. 73. The Multiplicand is the number to be multiplied. 74. The Multiplier is the number by which we multiply. 75. The Sign of Multiplication is x, and is read mul tiplied by, times, or into. When placed between two rumbers it denotes that one is to be multiplied by the other. NOTES.—1. The Sign of Multiplication consists of two short lines of oqual length, bisecting each other at an angle of 45 degrees with the line of writing. 2. The symbol X was introduced by Wm. Oughtred an English matho matician, born in 1574. PRINCIPLES. 1. The multiplier is always an abstract number. 2. The multiplicand may be abstract or concrete. 3. The product is always similar to the multiplicand. CASE I. OPERATION. 76. When the multiplier is not greater than twelve. 1. Multiply 353 by 8. SOLUTION.—We write the multiplier under the multiplicand, draw a line beneath, and Multiplicand, 854 begin at the right to multiply. 8 times 4 Multiplier, 8 units are 32 units, or 2 units and 3 tens; we write the units in units place, and reserve the Product, 2832 tens to add to the next product: 8 times 5 tens are 40 tens, plus the 3 tens equal 43 tens, or 3 tens and 4 hundreds; we write the 3 tens in tens place, and reserve the 4 hundreds ro add to the next product: 8 times 3 hundreds are 24 hundreds, plus che 4 hundreds equal 28 hundreds, or 8 hundreds and 2 thousands, which we write in their proper places, and we have 2832. Hence the following Rule.-I. Write the multiplier under the multiplicand, and draw a line beneath. II. Begin at the right, and multiply each term of the multiplicand by the multiplier, carrying as in addition. 567 3 1701 WRITTEN EXERCISEB. (4) 795 4 2 2728 1590 (6) 821 7 5747 (6) (9) $25.08 9 $62.90 $225.72 Multipl 10. 5708 by 8. Ans. 45664. 16. 32187 by 3. Ans. 96561. 11. 3218 by 7. Ans. 22526. 17. 58799 by 6. Ans. 352794. 12. 2107 by 6. Ans. 12642. 18. 25767 by 5. Ans. 128835. 13. 5189 by 7. Ans. 36323. 19. 41937 by 4. Ans. 167748. 14. 12076 by 4. Ans. 48304. 20. 82709 by 8. Ans. 661672. 15. 21876 by 5. Ans. 109380. / 21. 70095 by 9. Ans. 630855. 22. Multiply 97548 by 9. Ans. 877932. 23. Multiply 847946 by 9. Ans. 7631514. 24. If one acre of land is worth 275 dollars, what are 7 acres worth at the same rate ? SOLUTION.- If one acre of land is worth 275 dollars, 7 acres are worth 7 times 275 dollars, which we find 275 by multiplying is 1925 dollars. Therefore, etc. 7 1925 Ans. 25. Sound moves 1120 feet in a second; how far will it move in six seconds ? Ans. 6720 feet. 26. If a horse cost $150, what will 8 horses cost at the game rate ? Ans. $1200. 27. If there are 1375 letters on one page of a book, how many letters on 7 pages at the same rate ? Ans. 9625. 28. If there are 231 cubic inches in one gallon, how many cabic inches in five gallons? Ans, 1155. 29. Light moves about 192,500 miles & second; how far will it move in four seconds ? Ans. 770,000. 30. The distance of the moon from the earth is about 240,000 miles; what is nine times the distance ? Ans. 2,160,000. OPERATION. CASE II. 77. When the multiplier is greater than twelve. 1. Multiply 465 by 37. SOLUTION.–We write the multiplier under the OPERATION. multiplicand, units under units, tens under tens, etc. 465 Since 37 equals 7 units and 3 tens, it is evident that 37 37 times a number equals 7 times the number plus 3 3255 tens times the number. Seven times 465 equals 13953255; 3 times 465 equals 1395, hence 3 tens times 17205 465 equals 1395 tens. "Taking the sum of the partial products we have 17205. Hence, etc. Rule.-I. Write the multiplier under the multiplicand, placing terms of the same order in the same column, and draw a line beneath. II. Begin at the right, and multiply the multiplicand by each term of the multiplier, writing the first term of each product under the term of the multiplier which produces it. III. Add the partial products, and their sum will be the entire product. Proof.-Multiply the multiplier by the multiplicand; if the work is correct this product will equal the first product. Notes.—1. When there are ciphers between the significant terms of the multiplier, pass over them and multiply by the significant terms alone. 2. We begin at the right to multiply, so that when any product exceeds nine we may add the number expressed by the left hand figure to the nex product. 2. Multiply 247 by 24; also by 204. OPERATION. OPERATION. 247 247 24 204 988 988 494 494 5928 50388 (6) 321 18 5778 (10) $2.18 5024 (9) (8) 21 $87.36 25 $54.50 24 $58.80 23 $95.91 |