With the divisor and remainder of each of the above examples make a fraction; thus (1) †, (2) }, (3) †, etc. Write the exact quotient of all the examples in the second column; thus (21) 6755. WRITTEN PROBLEMS. 1. How many 6-pound packages of buckwheat flour can be made from 1200 pounds of flour? 2. How many ploughs at $7 each can be bought for $1232? 3. How many tons of coal at $7 a ton can be bought for $1995? 4. There are 3 feet in one yard. How many yards are there in 63,360 feet? 5. There are 8 quarts in a peck. How many pecks in 525,232 quarts? 6. 4 pecks make 1 bushel. How many bushels do 249,024 pecks make? 7. If 9 cents will buy one pound of cotton, how many pounds will 507,285 cents buy? 8. If $4 will buy one yard of velvet and $1 will buy of a yard, how many yards and fourths of a yard can be bought for $23? 9. How many times must you take $7 to make $1134? How many times must you take $9? 10. A stage travelled 8 miles per hour. In how many hours would it travel, at the same rate, 4704 miles? 11. A bicycler rides at the rate of 12 miles per hour. How long would it take him to ride 1728 miles? 12. James Blair paid $37,504 for some Western land at $8 per acre. How many acres did he buy? 13. A man gave $36,755 in equal shares to his 5 children. How much did he give to each child? 14. If sound moves 10,080 feet in 9 seconds, how many feet does it move in 1 second? 15. 9 square feet make 1 square yard. How many square yards in 43,560 square feet? 16. 7 days equal 1 week. In 364 days how many weeks? 17. How many yards of cloth, at 9 cents per yard, can be bought for 58,878 cents? 18. How many $5 bills must be counted out to pay a bill of $1240. 19. How many pounds of sugar, at 8 cents a pound, must be given for 488 pounds of coffee, at 22 cents a pound? 20. Find the value of 240 bottles of wine at $3 a bottle, and find how many $4 bottles of wine must be given in exchange for the $3 bottles. 21. Prove that if we multiply a given number by 100 and divide the product by 4 we obtain the same result as when multiplying by 25. 22. Prove by the asterisks in the margin that 4 X 5 = 5 x 4. ***** * * * * The Divisor a Single Digit with Ciphers Annexed. ORAL EXERCISES. 1. If 50 cents be put in 10 equal packages, how many cents will each package contain? 2. When flour is worth $10 a barrel, how many barrels. can be bought for $110? 3. 120 divided by 10 gives what quotient? What remainder? Does not cutting off the cipher, thus 12/0, give you the same results? 4. How many times is 10 contained in 124? What remains? Does not cutting off the 4 thus, 12/4, give the same results? What is the exact quotient? 5. How, by cutting off, can you divide 124 by 100? What is the quotient? What is the remainder? What is the exact quotient? 6. How many figures will you cut off to divide by 1000? PRINCIPLES. 1. Cutting off one figure divides by 10. 2. Cutting off two figures divides by 100. 3. Cutting off three figures divides by 1000, and so on. WRITTEN EXERCISES. 1. Divide 365 by 10. Process. Divisor. Dividend. 10) 365 361, Quotient. 2. Divide 1728 by 300. Process. 300) 17|28 52 28. Explanation. In accordance with Principle 1, to divide by 10, we cut off one figure from the dividend, and obtain for quotient 36, with 5 as remainder. Hence, the exact quotient is 361. Explanation. In accordance with Principle 2, to divide by 100 we cut off two figures, and obtain for quotient 17, with 28 remaining. Since the entire divisor is 300, we must divide this quotient by three. One-third of 17 hundreds 5 hundreds, with two hundreds remaining; 2 hundreds 200 units; 200 units plus 28 units 228 units. Hence, the exact quotient is 5328. Hence, the following rule: 1. Cut off the ciphers from the divisor. 2. Cut off as many figures from the dividend. To apply the rule: 3. Divide 1898 by 400. Process. 400) 1898 4298 400 Explanation. Having cut off the two ciphers from 400 and two figures from the dividend, we obtain 18 for quotient and 98 for remainder Dividing now by the signifi cant figure 4, we obtain 4 for quotient and 200 + 98 for remainder. Making a fraction with the remainder and divisor, we have for the exact quotient 4288. 4. Divide: 1. 89 by 10. 3. 3422 by 100. 4. 5489 by 1000. 5. 6079 by 1000. 6. 71,560 by 100. 16. 96,704 by 3000. 14. 5097 by 500. 15. 90,798 by 2000. 30. 5,678,901 by 80,000. The Divisor Any Number of Digits. EXERCISES. 1. Divide 25,003 by 48. Process. 48) 25003 (5204 240 100 96 43 Explanation. Beginning at the left, we perceive that 48 will divide neither 2 nor 25. We therefore divide 48 into 250 hundreds, and obtain 5 hundreds for quotient. 48 × 5 hundreds 240 hundreds; 250 hundreds - 240 hundreds = 10 hundreds. Annexing 0 tens from the dividend, we have 100 tens; dividing 100 tens by 48, we obtain 2 tens. 48 x 2 tens 96 tens; 100 tens - 96 tens= 4 tens. Annexing 3 units from the dividend, we have 43; 48 is contained in 43 no times, and we write 0 in the quotient. 43 is the remainder, and the exact quotient is |