MULTIPLICATION. MENTAL EXERCISES. 53. 1. What will 4 pounds of sugar cost, at 8 cents a pound? ANALYSIS. Four pounds will cost as much as the price, 8 cents taken 4 times; thus, 8+8+8+8=32. But instead of adding, we may say, since one pound costs 8 cents, 4 pounds will cost 4 times 8 cents, or 32 cents. 2. If a ream of paper cost 3 dollars, what will 2 reams cost? 3. At 7 cents a quart, what will 4 quarts of cherries cost? 4. At 12 dollars a ton, what will 3 tons of hay cost? 4 tons? 5 tons? 5. There are 7 days in 1 week; how many days in 6 weeks? in 8 weeks? 6. What will 9 chairs cost, at 10 shillings apiece? 7. If Henry earn 12 dollars in 1 month, how much can he earn in 5 months? in 7 months? in 9 months? 8. What will 11 dozen of eggs cost, at 9 cents a dozen? at 10 cents? at 12 cents? 9. When flour is 7 dollars a barrel, how much must be paid for 7 barrels ? for 9 barrels ? for 12 barrels ? 10. At 9 dollars a week, what will 4 weeks' board cost? 7 weeks'? 9 weeks'? 11. If I deposit 12 dollars in a savings bank every month, how many dollars will I deposit in 6 months? in 8 months? in 9 months? 12. At 9 cents a foot, what will 4 feet of lead pipe cost? 7 feet? 10 feet? 13. When hay is 8 dollars a ton, how much will 3 tons cost? 4 tons? 7 tons? 9 tons ? 11 tons? 14. What will be the cost of 11 barrels of apples, at 2 dol lars a barrel? at 3 dollars? 15. At 10 cents a pound, what will 9 pounds of 11 pounds? 12 pounds? sugar cost? 54. Multiplication is the process of taking one of two given numbers as many times as there are units in the other. 55. The Multiplicand is the number to be taken. 6. The Multiplier is the number which shows how many times the multiplicand is to be taken. 57. The Product is the result obtained by the process of multiplication. 58. The Factors are the multiplicand and multiplier. NOTES. 1. Factors are producers, and the multiplicand and multiplier are called factors because they produce the product. 2. Multiplication is a short method of performing addition when the numbers to be added are equal. 9. The sign, X, placed between two numbers, denotes that they are to be multiplied together; thus 9 × 6 = 54, is read 9 times 6 equals 54. Define multiplication. Multiplicand. Multiplier. Product. Fac. tors. Multiplication is a short method of what? What is the sign of multiplication? The operation in this example may be performed in another way, which is the one in common use. OPERATION. 374 6 2244 ANALYSIS. Writing the numbers as before, we begin at the right hand or unit figure, and say: 6 times 4 units are 24 units, which is 2 tens and 4 units; write the 4 units in the product in units' place, and reserve the 2 tens to add to the next product; 6 times 7 tens are 42 tens, and the two tens reserved in the last product added, are 44 tens, which is 4 hundreds and 4 tens; write the 4 tens in the product in tens' place, and reserve the 4 hundreds to add to the next product; 6 times 3 hundreds are 18 hundreds, and 4 hundreds added are 22 hundreds, which, being written in the product in the places of hundreds and thousands, gives, for the entire product, 2244. 61. The unit value of a number is not changed by repeating the number. As the multiplier always expresses times, the product must have the same unit value as the multiplicand. But, since the product of any two numbers will be the same, whichever factor is taken as a multiplier, either factor may be taken for the multiplier or multiplicand. NOTE. In multiplying, learn to pronounce the partial results, as in addition, without naming the numbers separately; thus, in the last example, instead of saying 6 times 4 are 24, 6 times 7 are 42 and 2 to carry are 44, 6 times are 18 and 4 to carry are 22, pronounce only the results, 24, 44, 22, performing the operations mentally. greatly facilitate the process of multiplying. EXAMPLES FOR PRACTICE. This will Second explanation. Repeating a number has what effect on the unit value? The product must be of the same kind as what? Ans. 6328476. 14. Multiply 703164 by 9. 15. What will be the cost of 344 cords of wood at 4 dolAns. 1376. lars a cord? 16. How much will an army of 7856 men receive in one week, if each man receive 6 dollars? Ans. 47136 dollars. 17. In one day are 86400 seconds; how many seconds in 7 days? Ans. 604800 seconds. 18. What will 7640 bushels of wheat cost, at 9 shillings a bushel? Ans. 68760 shillings. 19. At 5 dollars an acre, what will 2487 acres of land cost? Ans. 12435 dollars. 20. In one mile are 5280 feet; how many feet in 8 miles? Ans. 42240 feet. CASE II. 62. When the multiplier consists of two or more figures. 1. Multiply 746 by 23. OPERATION. Multiplicand, 746 Multiplier, 23 2238 3 1492 20 17158 23 Product, S times the mul- 5 times the mul- S times the mul- ANALYSIS. Writing the multiplicand and multiplier as in Case I, we first multiply each figure in the multiplicand by the unit figure of the multiplier, precisely as in Case I. We then multiply by the 2 tens. 2 tens times 6 units, or 6 times 2 tens, are 12 tens, equal to 1 hundred, and 2 tens; we place the 2 tens under the tens figure in the product already obtained, and add the 1 hundred to the next hundreds produced. 2 tens times 4 tens are 8 hundreds, and the 1 hundred of the last product added are 9 hundreds; we write the 9 in hundreds' place in the product. 2 tens Case II is what? Give explanation. |