II. If I gave in payment for the following purchases a $2 bill, a quarter, a dime, and two nickels, how much change should I receive? 4 lb. of butter at $0.32 = $ 2 lb. of cheese at $0.16 = $ 1 qt. of molasses at $0.12 = $ Division 32. Division is the process of finding one of the equal parts of a number or an amount, or how many times one number or amount is contained in another. 33. The dividend is the number or amount divided. The divisor is the number or amount by which we divide. The quotient is the result of the division. 34. The sign of division is, read divided by. Thus, 24 ÷ 4 = 6, is read 24 divided by 4= 6. 35. If in the division there is an undivided part of the dividend less than the divisor, this undivided part is called the remainder. Thus, 27 ÷ 4 = 6, with a remainder of 3 undivided. If the division were completed, the quotient would be 63 with no remainder. 36. Finding one of the equal parts of a number is sometimes called partitive division, or partition. In this kind of division the divisor is always a number, and if the dividend is an amount, the quotient and the remainder must be amounts similar to the dividend. Thus, $60÷ 5 = $12. 37. Finding how many times one number or amount is contained in another is sometimes called comparative division. In this kind of division the quotient is always a number, and if the dividend is an amount, the divisor and the remainder must be similar amounts. Thus, 20 yd. ÷ 2 yd. = 10. In practice divide 20 by 2. REMARK. It is evident from Secs. 36 and 37 that such expressions as "45° ÷ 15 = 3 hr.," "6 sq. ft÷ by 2 ft. =3 ft.," and "12 cu. ft. ÷ 4 sq. ft. 3 ft." cannot be justified and should not be employed. = 38. I. Since 10 × 46 460, 4601046, or 460. Cutting one cipher from the right of a number divides the number by 10. 2. Since 100 × 46 = 4600, 4600 ÷ 100 = 46, or 4600. Cutting two ciphers from the right of a number divides the number by 100. 3. Since 1000 × 4646000, 46000100046, or 46000 Cutting three ciphers from the right of a number divides the number by 1000. 4. Since 30 × 7=210, 210+30=7; that is, 210 ÷ 30 = 7. In practice, cut off the same number of ciphers from the right of both dividend and divisor before dividing. 31. 485 by 10 33. 7568 by 1000 35. 789 by 30 37. 7568 by 200 39. 10,096 by 300 41. 9587 by 5000 32. 2675 by 100 34. 756 by 20 38. 986 by 300 40. 8642 by 400 Divide across; add upward; check by seeing that the sum of the quotients above the line is equal to the quotient obtained by dividing the sum of the dividends by the indicated divisor: 1. If 45 beams of equal weight weigh 16,200 lb., how much does each beam weigh? 40. To check the result in division, find the product of the divisor and quotient and to it add the remainder (if any); the result should be the dividend. NOTE. The method of dividing by expressing the successive partial dividends is called long division. The method of dividing without expressing the partial dividends is called short division. |