5. THE COTTON CROP OF THE UNITED STATES BY STATES Copy the above report, fill in the totals, and. see that the sum of the totals of the crop by years equals the sum of the totals of the crop by states. Subtraction 36. Subtraction is the process of finding by how many units one number exceeds another or how many are left after taking part of a number from it. The greater number is called the minuend, the smaller the subtrahend, and the result the difference or the remainder. NOTE. Similar amounts, and only such, may also be subtracted; the result is similar to the amounts subtracted. Exercise 7 Find the difference and check by seeing that the sum of the subtrahend and the difference equals the minuend : 37. Multiplication is the process of taking one number, called the multiplicand, additively as many times as there are units in another number called the multiplier. The result of multiplication is called the product. 38. The sign of multiplication (x) is read times when the multiplier is written before it and multiplied by when the multiplier is written after it. Thus, 4 × 7 da. is read 4 times 7 da.; 7 days × 4 is read 7 days multiplied by 4. 39. The multiplier is always a number, and if the multiplicand is an amount, the product must be a similar amount. REMARK. It is evident from Sec. 39 that such expressions as "2 ft. x 3 ft. 6 sq. ft.," "2 ft. x 5 sq. ft. = 10 cu. ft.," and "15° × 2 hr. 30°," cannot be justified and should not be employed. = = Exercise 8 Read the first nine examples; name the multiplicand, the multiplier, and give at sight the product: 10. State a short way of multiplying a whole number 12. State a short way of multiplying a whole number 14. State a short way of multiplying a whole number by 1000. 15. State at sight the product : 1000 × 7; 1000 × 17; 1000 × 25, Illustrative Examples 1. Multiply 5768 by 473. 5768 473 17304 40376 23072 2728264 What is omitted from the third partial product? What is the product? 2. Multiply 5768 by 3007: The multiplier is 3000 +7. 5768 3. Multiply 11826 by 11826. Notice that in Exercises 3-6 each product contains the nine digits. Division 40. 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. 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. 41. If in division there is an undivided part of the dividend less than the divisor, this undivided part is called the remainder. 42. 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. 43. 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 amounts similar to the dividend. REMARK. It is evident from Secs. 42 and 43 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. Exercise 10 Read the first ten examples and name at sight the quotient and the remainder in each: |