93. Written. 38. Find the product of 1 thousand by one thousandth. 1 million by one millionth. 39. Multiply 700 thousandths by 7 hundred-thousandths. 40. Multiply the sum of 2 millionths and 10 thousandths by their difference. 41. Multiply together .35, 18.5, 28.004. DIVISION. 94. Since in multiplication there are as many decimal places in the product as in both multiplier and multiplicand, in division the quotient must have as many places as the number of places in the dividend exceeds those in the divisor. 1. Divide 12.685 by .5. SOLUTION. - Since there are three decimal places in the dividend and one in the divisor, there must be two in the quotient. .5/12.685 25.37 Rule I. In all cases divide as in integers, then place the decimal point. 2. Divide 399.552 by 192. Rule II. When the divisor is an integer, place the point in the quotient directly over the point in the dividend in long division (directly under in short division). Prove by multiplying divisor by quotient. 2.081 192/399.552 384 1555 1536 192 192 PRINCIPLE. — Multiplying both dividend and divisor by the same number does not change the quotient. 3. Divide 28.78884 by 1.25. Rule III. When the divisor contains 23.031+ decimal figures, move the point in 1.25' / 28.78'884 both divisor and dividend as many mal places in the divisor (this, in 250 378 375 388 375 134 125 9 NOTE 1. The new points may be placed on a line with the tops of the figures, and the original point may stand to preserve the reading of the decimals. NOTE 2. - If the quotient does not have a sufficient number of figures, prefix ciphers. NOTE 3. Before commencing to divide, see that there are at least as many decimal places in the dividend as in the divisor. NOTE 4. — If there is a remainder after all the figures of the dividend are used, annex decimal ciphers and continue the division. NOTE 5. It is not usually necessary to have more than four decimal figures in the quotient. 95. To divide by 10, 100, 1000, etc., remove the point one place to the left for each cipher in the divisor. NOTE. - To divide by 200, remove the point to the left, and divide 96. 1. What part of 100 is 12? 25? 331? What part of 1000 is 125? 2. 250? 3331? 97. To multiply by 25, annex two ciphers, and take of the result. 7. Tell how to multiply by 331; by 121; by 250; by 125; by 3331. 17. What cost 650 oysters at 50 cents a hundred ? 18. What will be the cost of 3850 laths at 40 cents a hundred? 19. What is the freight on 685 pounds of baggage at $1.10 per 100 lb. NOTE.-C. means 100; M., 1000. 20. What is the cost of 4862 ft. of pine lumber at $30 per M.? 21. Find the cost of 38,586 bricks at $8.25 a thousand. 22. What will 583 heads of cabbage cost at $3.50 a hundred? 23. At $3.50 a thousand, what will be the cost of 7800 shingles ? 24. At $8.25 per C., what will be the cost of 2864 lb. of dried fish? 25. At $50 per M., what will be the cost of 3865 feet of cherry lumber? 26. What is the cost of laying 5890 bricks at $9.00 a thousand? To find the cost of merchandise sold by the ton, divide the price by 2 and proceed as above. 27. Three loads of hay weigh 7894 lb. What will the hay bring at $12 a ton? NOTE. 1000 lb. will cost of $12 $6. $6 x 7.984 ? 28. What cost 48986 lb. of railroad iron at $35 a ton ? 29. Four loads of coal weigh respectively 3896 lb., 3524 lb., 4106 lb., and 3123 lb. What is the cost of the coal at $4.82 a ton. ALIQUOT PARTS OF $1.00. 98. The Aliquot Parts of a number are the numbers which are exactly contained in it. The aliquot parts of 100 are 5, 20, 12, 163, 333, etc. |