PROCESS. 196 8 1568 EXPLANATION.-For convenience the mul tiplier is written under the multiplicand. Beginning at the right each figure of the multiplicand is multiplied by the multiplier. Thus, 8 times 6 units are 48 units. 48 units are equal to 4 tens and 8 units. The 8 is written in units' place in the product, and the 4 is reserved to add with the tens. 8 times 9 tens are 72 tens, plus the 4 tens reserved, are 76 tens. 76 tens are equal to 7 hundreds and 6 tens. The 6 is written in tens' place in the product, and the 7 is reserved to add with the hundreds. 8 times 1 hundred are 8 hundreds, plus 7 hundreds reserved, are 15 hundreds. 15 hundreds are equal to 1 thousand and 5 hundreds, which are written in hundreds' and thousands' places in the product. Hence the product is 1568. The accuracy of the work may be tested by reviewing it. 10. If a ship sails 368 miles in one week, how many miles will she sail in 7 weeks? 11. There are 5280 feet in a mile. How many feet are there in 9 miles? 12. What will 6 yoke of cattle cost at 184 dollars a yoke? 13. If 1 horse is valued at 275 dollars, what is the value of 6 such horses? 14. If a ship sails 895 miles in 1 week, how far will she sail in 9 weeks? 15. What is the product of 457 multiplied by 7? 16. What is the product of 784 multiplied by 4? 17. If a clerk receives a salary of 972 dollars a year, how much will he receive in 5 years? 18. Since there are 365 days in 1 year, how many days are there in 9 years? 19. Multiply 3452 by 3. 20. Multiply 6841 by 6. 21. Multiply 7186 by 3. 22. Multiply 2041 by 8. Multiply 1472 by 5. 23. Multiply 4926 by 6. 24. Multiply 3624 by 4. Multiply 4829 by 7. 25. If it takes 5428 shingles for the roof of a house, how many shingles will it take for 5 such houses? FIRST PROCESS. 425 7 X 425 2975 = 30 X 42512750 37 × 425 = 15725 EXPLANATION.-The numbers are written as before. Since in multiplying we multiply by the parts of a number, to multiply by 37 we multiply by 30 and by 7, and add the results. 7 times 425 are 2975, the first partial product; 30 or 3 tens times 425 are 1275 tens or 12750, the second partial product. The sum of these partial products will be the entire product. Hence the entire product is 15725. SECOND PROCESS. 7X425 3 X 425 = 425 2975 EXPLANATION.-In this process the cipher at the right of the partial product is omitted and the significant figures placed in their proper places. Thus, in multiplying by 3 tens, the product is 1275 tens or 12 thousands 7 hundreds and 5 tens, which are written in their proper places in the partial product. In multiplying by tens the lowest denomination of the product is tens, in multiplying by hundreds it is hundreds, by thousands it is thousands. Hence, The first figure of each product should be placed under the figure by which we multiply. 1. How many barrels of flour at 8 dollars a barrel, can be bought for 72 dollars? 2. If there are 3 feet in a yard, how many yards are there in 27 feet? 3. At 4 dollars a cord, how many cords of wood can be bought for 40 dollars? 4. If a man can walk 4 miles per hour, how long will it take him to walk 36 miles? 5. If 5 paces are a rod of distance, what is the length in rods of a piece of land which is 30 paces long? 6. If paper is put in packages containing 6 sheets each, how many packages can be made out of 48 sheets? 7. If 5 bushels of wheat make a barrel of flour, how many barrels of flour can be made from 40 bushels of wheat? 8. At 6 dollars a ton, how many tons of hay can be bought for 54 dollars? 9. If a man can build 7 rods of fence in one day, in how many days can he build 35 rods? 10. If a teacher earns 9 dollars a week, in how many weeks can she earn 90 dollars? |