WRITTEN EXERCISES 77. Make out bills for the following, supplying the date and places of business of both debtor and creditor, find the footings, and receipt in due form : 1. H. H. Moore bought of Lackawanna Coal Co. 1343 tons of coal @ $3.40. 2. H. H. Moore sold to President of Board of Contract and Supply (your city), 1260 tons of coal @ $4.25. 3. Hayes & Reynolds sold to Empire Milling Co. 1000 bu. No. 1 hard Manitoba wheat @ 87, 1200 bu. No. 2 red wheat @ 85%, and 5000 bu. No. 2 corn @ 46. 4. George Saxe bought of John Stillman 2 brass bedsteads @ $36.50, 2 bureaus @ $28, 1 mahogany chiffonier @ $75, and 1 golden oak toilet table @ $42.50. 5. The Champlain Canning Co. is debtor to Stephen A. Dole, for carting and advancing freight charges, as follows: Jan. 6, 2 loads @ $1.50; freight charges $ 8.50 6. Albert Perkins bought of the Continental Hardware Co. 15 Excelsior ranges @ $38, 12 Alps ranges @ $32.25, 16 Jewel gas ranges @ $13.50, 42 cook stoves @ $23, 18 Safety oil stoves @ $7.75, 2 parlor stoves @ $35, 6 parlor stoves @ $31.50, 27 double boilers @ $.89, and 4 dozen razors @ $11.50. 7. Allen Bros. bought of Storrs & Stoneman 6 doz. blank books @$1.40, 4 doz. blank books @ $2.25, 72 pints ink @ 35, 64 steel rulers @ 39, 15 cameras @ $4.95, 3 doz. trays @ $1.50, 5 M clips @ $1.10, 16 doz. blotting pads @ 49, and 48 bottles library paste @ 19. DIVISION OF INTEGERS AND DECIMALS 78. How many 4's are there in 16? How many times is 4 contained in 16? Separate 24 cent-pieces into 4 equal piles. How many are there in each pile? 79. The process of finding how many times one number is contained in another is called division. Division is also the process of separating a number into equal parts. This kind of division is sometimes called partition. 80. The number divided is called the dividend. 81. The number by which we divide is called the divisor. 82. The result obtained by dividing is called the quotient. 83. When all the dividend is divided and the quotient is an integer, the division is exact. 84. The part of the dividend that is left when the division is not exact is called the remainder. 85. The sign indicates division. It is read divided by. Division is also indicated by writing the dividend above the divisor with a straight line between them; or by writing the dividend at the right of the divisor with a curved line between. Thus, or 6)24, indicates that 24 is to be divided by 6. 24 6 86. Complete and read: 1. $20÷$4= ? 2. 369 = ? 3. 18 rods ÷ 6 rods = ? 4. 56 feet ÷ 8 feet = ? If the dividend and divisor are like numbers, the quotient is an abstract number. If the dividend is concrete and the divisor is abstract, the dividend and quotient are like numbers. When the divisor is so small that the work may be done mentally, and only the figures of the quotient are written, the process is called short division. 89. Cutting off one figure from the right of an integer corresponds to moving each figure one place toward the right and, therefore (§ 20), changes the tens to units, the hundreds to tens, etc. Hence, To divide an integer by 10, cut off one figure from the right; by 100, two figures; by 1000, three figures; etc. When the figures cut off are all O's, the division is exact; when any are significant, the number represented by the figures cut off is the remainder. 3800 ÷ 100 = 38 0038; and 3827 ÷ 100 38|27 38, remainder 27, or 38.27. = = 90. In a decimal or a mixed number, every removal of the decimal point one place toward the left corresponds to removing each figure one place toward the right. Hence, To divide a decimal by 10 move the decimal point toward the left one place; by 100, two places; by 1000, three places, etc. If necessary, prefix 0's; thus, 5.6 100 = .056. EXERCISES 1. Divide by 10: 320; 46,000; 167; 4.67; 82.4; .775. 2. Divide by 100: 66,400; 3250; 4182; 62.81; 206; .089. 3. Divide by 1000: 4,360,000; 8720; 485; 37.61; .32; 6.25. 4. Divide by 1,000,000: 12,820,000; 422,300,000; 66.6. 13 476 827 times 68, plus 13 rem. = 56,249 Since 50,000 68 is less than any number of ten-thousands and 56,000 ÷ 68 is less than any number of thousands, but 56,200 ÷ 68 equals about 800, write 8 in the quotient over the hundreds of the dividend, multiply 68 by 800, and subtract the product from the dividend, leaving 1849 to be divided. 1849 contains 68 about 20 times. Subtract 20 times 68; then the part of the dividend still undivided is 489. This contains 68 about 7 times. Subtract 7 times 68; the remainder is 13. The quotient is 827. = = Since 827 times 68, plus 13 56,249 (the dividend) the work is correct. In practice we write the work in brief form as in the process on the right, dividing thus: 562 ÷ 68 about 8; write 8 in the quotient over 2, the last figure of the part of the dividend used; 8 times 68 544; subtract and bring down 4, the next figure of the dividend; 184 ÷ 68 = about 2; write 2 in the quotient; 2 times 68 = 136; subtract and bring down 9; 489 ÷ 68 = about 7; 7 times 68 476; subtract. Test. = = Multiply the divisor by the quotient and to the product add the remainder, if there is one. If the work is correct, the result will equal the dividend. |