58. The four steps of long division are:

1. See how many times the divisor is contained by the first part of the dividend.

2. Write the number of times directly over the last figure of the part of the dividend used.

3. Multiply the divisor by this number, and subtract the product from the part of the dividend used. 4. Annex the next figure of the dividend and proceed with the division.

Note. By writing the quotient figure directly over the last figure of the part of the dividend used we maintain the place value of the figures used. In long division the chief difficulty rests with the determination of the number of times the dividend contains the divisor.

Exercises in Division of Integers, "Short" and "Long" Forms

59. 1. Divide by 3: 4524; 60459; 7401; 76452; 876321; 603245.

2. Divide by 4: 67824; 42396; 457863; 456780; 3002.

45286; 43210;

3. Divide by 5: 6730; 57865; 43215; 67890; 45762; 432106; 896043.

4. Divide by 6: 6780; 7860; 453218; 423569; 4576321; 43895624.

5. Divide by 7: 6742; 45321; 43256; 4578932; 436275; 8764524.

6. Divide by 8: 678042; 45760; 45326; 478954; 4578632; 45768934.

7. Divide by 9: 678213; 453267; 43789; 452301; 426015; 768324.

8. Divide by 21: 6784; 45320; 43268; 45326; 43789; 43268.

9. Divide by 51: 6780; 768420; 453789; 43216; 423567; 476324.

10. Divide by 72: 67840; 432678; 457869; 43216; 425368; 423165.

11. Divide by 812: 4325678; 4326750; 456897324; 456782; 4002438.

12. Divide by 29: 36748; 45326; 43286; 45326; 43876; 4235601.

13. Divide by 729: 347625; 452367; 43876; 487632; 4532106.

61. The process of division in U, S. money and in decimals is the same as in whole numbers. The location of the decimal point in the quotient may be determined in either of two ways, as follows:

1. Remembering that division is the converse operation of multiplication, we may make the number of decimal places in the divisor and the quotient equal those in the dividend.

2. If the divisor is an integer, we may locate the decimal point directly over the decimal point of the dividend.

When the divisor is not given in integral form, we may change both dividend and divisor so that the divisor will be an integer, by moving the decimal point the same number of places in both divisor and dividend. This will not change their relative values, nor the value of the quotient. Select the rule which you understand, and use it.

an integer, the point in the quotient must be directly over that in the dividend.

2. Divide 7.8125 by 31.25.

.25

31.25)7.8125

Ans. .25.

1st plan. Four places in the divi

the point two places to the right in both dividend and divisor makes the divisor a whole number and locates the point in the dividend between the 1 and the 2 of the dividend. The point in the quotient is placed directly over this.

an integer demands the writing of the three ciphers.

By the first plan, we remember that the number of decimal places in the dividend, corresponding to the product in multiplication, must be equal to the number of decimal places in both factors; and as there are three places in one of the factors,

the dividend must have at least three places, which we form by annexing the three ciphers.

Exercises in division of decimals

(Prove your answers.)

63. 1. Divide .00335 by 6.7.

2. Divide 335 by .067.

3. Divide 3.35 by 67.
4. Divide .0255 by .051.
5. Divide 255 by .051.
6. Divide 2.55 by 0.51.

7. Divide 25.5 by 0.51.

8. Divide 25.5 by .051. 9. Divide .00255 by 51. 10. Divide .014532 by .0692. 11. Divide .04905 by .327. 12. Divide 6.2512 by .37.

13. Divide 75 by .0125.

14. Divide 105.70 by 3.5.

Short process, where there are terminal ciphers in the

divisor

64. 1. Divide 50 by 10. (Change 50. to 5.0.)

Ans. 5.

2. Divide 500 by 100.

(Change 500. to 5.00.)

Ans. 5.