SHORT DIVISION. 67. When the divisor is so small that the work can be performed mentally, the process is called Short Division, and will be understood from the following examples: (1) Divide 697,425 by 3. The divisor is written at the left of the dividend, as in the margin. Wording. 3 in 6, 2; in 9, 3; in 7, 2; in 14, 4; in 3)697425 22, 7; in 15, 5. 232475 Here the divisor is contained in 6 twice, in 9 three times, and in 7 twice with remainder 1; this 1 is equal to 10 of the next lower order, and with the 4, the next order of the dividend, makes 14. Then 14 is divided by 3; the quotient is 4 with remainder 2; this 2 is equal to 20 of the next lower order, and with the 2 makes 22. Then 22 is divided by 3; the quotient is 7 with remainder 1. Then 15 is divided by 3, and the quotient is 5. (2) Divide 4,236,158 by 7. 7) 4236158 605165 with remainder 3. In this example, 7 is not contained in 3, so 0 is the second figure of the quotient: then the next figure 6 of the dividend is joined to the 3, making 36, and the division is continued. When the division is finished, there is a remainder 3. (3) Divide 54,123 by 9. 9)54123 6013 with remainder 6. Each quotient figure is of the same order of units as the right-hand figure of that part of the dividend used in obtaining it. Thus, 54 in this example are 54 thousands, and the first figure of the quotient is 6 thousands. (4) Divide $23,087 by 5. 5)$23087 $4617 with $2 remaining. In this example, we are required to divide 23087 dollars into five equal parts, and find the number of dollars in each part. The answer is 4617 dollars, with 2 dollars over. The complete quotient may be written $46173. (5) Divide $23,087 by $5. $5)$23087 4617 with $2 remaining. In this example, we are required to find the number of times we can take away $5 from $23,087, and the answer is 4617 times, with $2 left over. The complete quotient may be written 4617; and the meaning is, that we can take $5 away 4617 times from $23,087, and the next time have $2 to take away. 68. The last two examples illustrate the different meanings of division. When the divisor corresponds to the multiplier in multiplication the quotient corresponds to the multiplicand, and denotes the same kind of units as the dividend; when the divisor corresponds to the multiplicand the quotient corresponds to the multiplier, and denotes the number of times the divisor must be taken to obtain a quantity equal to the dividend. 69. A number, when divided by 10, will have a quotient consisting of the same series of figures, the last one being cut off for the remainder. Thus, 35764÷10=3576 with remainder 4. In this case, the value of each figure in the result is diminished ten-fold, the tens becoming units, the hundreds becoming tens, and so on. A number, when divided by 100, 1000, etc., will have the same series of figures in the quotient, the last two, three, etc., figures being cut off for the remainder. Hence, When a divisor ends in one or more zeros, cut off the zeros and an equal number of figures from the right of the dividend, perform the division with the numbers left, and for the total remainder annex the figures cut off from the dividend to the remainder from the division. Divide 5,786,342 by 200. 200) 5786342 28931 with remainder 142. In this example, we cut off the two zeros at the right of the divisor and two figures at the right of the dividend; then we divide, putting the first figure of the quotient under the figure 8, which is the righthand figure of the first partial dividend when the entire divisor 200 is used. 70. The product of the divisor and quotient increased by the remainder is equal to the dividend. Hence, To test the accuracy of the work of division, find the product of the divisor and quotient, and to this product add the remainder; this result will be equal to the dividend if the work is correct. Thus, in the last example, and 200 × 28,931 = 5,786,200, 5,786,200+ 142 = 5,786,342 (the dividend). |