LESSON V. New Divisor Figure, 9. MENTAL EXERCISES. 1. How many times 9 in 18? 9 in 27? 9 in 36? 9 in 54? 9 in 72? 9 in 90? 2. How many 9's in 45? 5's in 45? 9's in 63? 7's in 63? 9's in 72? 8's in 72? 3. How long will it take a steamer to make a trip of 81 miles if it run 9 miles an hour? 4. If 9 words fill a line, how many lines will 72 words fill? 81 words? 5. If a man can do a piece of work in 90 days, how many men can do it in 9 days? 6. If a quantity of provisions will last 72 men one day, how long will it last 9 men? 7. How many sheep, at $9 a head, can be bought for $54? For $63? 8. A copy-book contains 100 lines, with 10 lines on each page: how many pages in the book? 9. If a man earn $10 a week, how long will it take him to earn $100? 10. How many tons of hay, at $10 a ton, can be bought for $90? TO THE TEACHER.-For additional examples see MANUAL OF ARITHMETIC, page 39. The Divisor ending in One or more Ciphers. WRITTEN EXERCISES. 1. Divide 350 by 10. FIRST PROCESS. 10)350(35 30 50 50 SECOND PROCESS. 1|0)35|0 35, Quotient. 2. Divide 2865 by 100. 28, Quotient. 3. Divide 45600 by 10. By comparing these two processes, it is seen that 350 is divided by 10, by cutting off the right-hand figure. The reason is obvious. The cutting off of the right-hand figure removes each of the other figures one place to the right, and thus decreases their value ten-fold. In like manner, it may be shown that cutting off the two right-hand figures divides a number by 100; cutting off three right-hand figures, by 1000, etc. By 100. 4. Divide 187000 by 1000. PROCESS. By 100. First divide both divisor 48 00)1968 00(41, Quotient. and dividend by 100, which 192 48 48 is done by cutting off the two right-hand figures. NOTE. The teacher can show that both divisor and dividend may be divided by any number without affecting the value of the quotient. NOTE.-The true remainder is found by annexing the first remainder to the second. The reason for this can be easily given by the teacher. 13. Divide 466384 by 3900. 14. Divide 99990 by 5400. 220345 by 940. 172800 by 14400. 15. A barrel of beef contains 200 pounds: how many barrels will contain 12800 pounds? 16. There are 480 sheets of paper in a ream: how many reams will 129600 sheets make? 17. There are 3600 seconds in an hour: how many hours in 172800 seconds? 18. How many city lots, at $1600 each, can be bought for $25600 ? 19. How many cars, each carrying 1800 pounds, will transport 79200 pounds of hay? 20. How many barrels, each holding 196 pounds, will hold 9016 pounds of flour? 21. How many regiments, averaging 750 men each, will make an army of 30000 men? 22. A peach orchard contains 6758 trees, and there are, on an average, 62 trees on each acre: how many acres in the orchard? 23. A pipe discharges 94 gallons in an hour: in how many hours will it empty a cistern holding 3384 gallons of water? 24. What number multiplied by 98 will produce 15288? 25. The dividend is 5292 and the divisor is 63: what is the quotient? 26. The divisor is $1500 and the dividend $564000: what is the quotient? DEFINITIONS, PRINCIPLES, AND RULES. Art. 38. Division is the process of finding how many times one number is contained in another. The Dividend is the number divided. The Divisor is the number by which the dividend is divided. The Quotient is the number of times the divisor is contained in the dividend. The Remainder is the part of the dividend which is left undivided. When the dividend contains the divisor an exact number of times, there is no remainder. Art. 39. The Sign of Division is, and is read divided by. When placed between two numbers, it shows that the number before it is to be divided by the number after it. Thus: 16 ÷ 4 4 is read 16 divided by 4 equals 4. Division is also expressed by writing the dividend above and the divisor below a short horizontal line. Thus: 18 is read 18 divided by 3. Art. 40. One number is contained in another number as many times as it can be taken from it. Hence division is a short method of finding how many times one number may be subtracted from another. A number is contained in another as many times as it must be taken to produce it. Hence division may be regarded as the reverse of multiplication. The divisor and quotient are factors of the dividend. Art. 41. There are two methods of division, called Short Division and Long Division. In Short Division, the partial products and partial dividends are not written, but are formed mentally. This method is generally used when the divisor does not exceed 12. In Long Division, the partial products and partial dividends are written. Art. 42. RULE FOR SHORT DIVISION.-1. Write the divisor at the left of the dividend, draw a curved line between them, and a straight line under the dividend. 2. Find how many times the divisor is contained in the left-hand term or terms of the dividend, taken as a partial dividend, and write the quotient under the last figure of the dividend used. 3. Multiply the divisor by the quotient term found, and subtract the product from the partial dividend used, performing each process mentally. 4. Prefix the remainder, if there be one, to the next term of the dividend for a second partial dividend, and divide, multiply, and subtract, as before. 5. Proceed in this manner until all the terms of the dividend have been used. PROOF-Multiply the divisor by the quotient, to the product add the remainder, if there be any, and if the result equals the dividend, the work is correct. |