2. Complete, explain, and prove the following: (3.) 6 (5.) 408 5 (6) 5 (7.) 8 (8.) 7 (9.) g (10.) 12 3. How many places in the product must be pointed off for cents ? 4. Multiply : 1. 8692 by 8. 6. 13,896 by 3. 2. 5328 by 7. 7. 52,209 by 5. 3. 10,318 by 5. 8. 68,387 by 7. 4. 7289 by 9. 9. 79,588 by 4. 5. 17,345 by 4. 10. 91,983 by 9. 5. Find the value of: 1. 420 X 9. 5. 40,527 X 4. 2. 9059 X 2. 6. 305,238 X 5. 3. 78,059 X 3. 7. 40,597 x 6. 4. 1,790,478 x 7. 8. 910,362 X 8. The parts of an equation, right and left of the sign of equality, are called its members. 6. Find a second member for each of the following: 1. 127 + (2 + 8) X 9 + 85 ( 2 PROBLEMS. Let the pupil indicate the solution of each problem by using the sign X. 1. If sound moves 1092 feet in a second, how far does it move in 5 seconds ? Process Indicated. 1092 x 5 how far it moves. Process. Explanation. 1092 feet Since sound moves 1092 feet in 1 second, in 5 seconds it 5 moves 5 times 1092 feet; 1092 feet x 5 = 5460 feet. 5460 feet What principles are involved ? 2. When wheat is worth $1.25 per bushel, what is the value of 9 bushels ? 3. What will 7 horses cost at $175.35 each? 4. Since in 1 mile there are 1760 yards, how many yards are there in 9 miles ? 5. Find the cost of 4886 sheep at $6 a head. 6. Each workman in an iron-foundry is paid $605 a year: what do 11 men receive at that rate ? 7. A bushel of corn weighs 56 pounds : find the weight of 12 bushels. 8. The distance to the moon is 240,000 miles : what is 10 times that distance ? 9. If the distance of the earth from the sun is about 91,430,000 miles, how many miles is 9 times that distance ? 10. If an army major receives monthly $208.33, what is the monthly pay of 12 majors ? 11. Mr. White owns 3 houses, and the first house is worth $3872; the second, 3 times as much ; and the third, 7 times as much. Find the cost of the 3 houses. : Process Indicated. 12. A farmer's wife took to a store 3 pounds of butter worth 33 cents a pound, and bought 12 yards of calico at $.08 a yard. Find the balance due her. 13. Which are worth more, 7 cows at $35 apiece or 3 horses at $75 apiece ? 14. A lady bought a bicycle for $100; she rented it to a friend for 5 months at $3 a month, and finally sold it for $75. Did she gain or lose, and how much ? 15. A man sold three houses ; for the first he received 3575 dollars; for the second, $950 less; for the third, three times the difference between the price of the first and second. What did he receive for the three? CHIEF DIFFICULTY OF MULTIPLICATION. 1. Multiply 438 by 234. 1st 2d Process. Process. Explanation. 438 438 1st PROCESS.- 4 units - 4 units. 30 units. 12 hundreds 200 units. 13140 1314 Therefore, we are to multiply 438 firstly 87600 876 by 4 units, secondly by 30 units, thirdly by 200 units, and then find the sum of the 102,492 102,492 three partial products. Multiplying by 4 we have 1752 units ; Proof. multiplying by 30 we have 13140 units; 234 multiplying by 200 we have 87600 units. The sum of these products is 102,492 units. 438 2D PROCESS.—Since 13,140 units=1314 1872 tens, and since 87,600 units 876 hundreds, we omit the ciphers, and, writ 1314 as 702 tens, and 876 as hundreds, the significant 936 figures keep their relative positions, and the result of the addition is the same as 102,492 before. PROOF.-State the principle on which the proof depends. 2. Find the product, explain the process, and show proof of accuracy : (1.) (2.) (3.) (4.) (5.) 657 343 37 (6.) 33 (7.) 43 (8.) 72 (9.) 81 (10.) 29 Put a decimal point in each product. 11. 619 by 96. 12. 777 by 86. 3. 405 by 53. 13. 910 by 52. 4. 534 by 37. 14. 732 by 62. 5. 645 by 73. 15. 839 by 93. 6. 843 by 54. 16. 327 by 67. 7. 917 by 46. 17. 931 by 95. 8. 903 by 74. 18. 733 by 123. 9. 593 by 91. 19. 981 by 234. 20. 891 by 345. ? 7. 5386 x 65 = how many ? 8. 4860 X 9574 : ? 9. $357.63 x 47 = ? 10. Find the second member of the following unfinished expressions : 1. $9.672 x 635 3. 51,526 X 527 4. 97,601 x 987 : 11. Multiply five thousand nine hundred sixty-five by six thousand nine. 12. Multiply four hundred sixty-two thousand six hundred nine by itself. 13. Multiply eight hundred forty-nine million six hundred seven thousand three hundred six by nine hundred thousand two hundred four. 14. Multiply 704 million 130 thousand 496 by three thousand three hundred one. 15. Multiply one hundred twenty-three and 45 hundredths by 804. 16. Multiply 415 and 5 hundredths by 367. 21. Find the value of (3467 X 7004) — (3467 x 704), and form an equation. PROBLEMS. 1. Find the cost of a farm of 202 acres at $102 per acre. Process Indicated. $102 x 202 2. A farmer had 105 rows of trees, each row containing 105 trees. How many trees had he? 3. If horses are worth $117 each, and oxen $85.50 a pair, what must I pay for 18 horses and 5 pairs of oxen ? 4. If 786 yards of cloth can be made in one day, how many yards can be made in 1252 days? 5. A grocer's sales average $19 a day for the month of March ; leaving out 5 days for Sundays, how much money did he receive during the month? 6. John takes 1434 steps in going to school ; if he goes and returns twice a day, how many steps will he take in 24 days? cost. |