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7. Copy upon your slates and read the following: 8)8 8)16 8)24 8)32 8)40 8)48 8)56 8)64 8)72

1 2

4

5

6

7

8

9

3 Read thus: 8 in 8, once; 8 in 16, 2 times, etc. 8. Copy upon your slates and read the following:

9)9 918 927 936 9)45 9)54 9)63 9)72 9)81

3

4

5

6

7

1 2
Read thus: 9 in 9, once; 9 in 18, 2 times, etc.

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REMARK.-The above examples constitute the DIVISION TABLE. They must be thoroughly committed to memory, unless this has already been done in reading the PRIMARY ARITHMETIC.

PROBLEMS.

1. A boy picks 2 apples from a tree every day. In how many days will he have picked 6 apples? 12 apples? 16 apples? 10 apples? 4 apples? 8 apples? 14. apples? 18 apples?

2. Since there are 2 pints in a quart, how many quarts in 18 pints? 14 pints? 10 pints? 6 pints? 4 pints? 12 pints? 16 pints? 8 pints? 2 pints?

3. If a boy gives 3 marbles to each boy, among how many boys can he distribute 12 marbles? 21 marbles? 15 marbles? 27 marbles? 24 marbles? 18 marbles? 9 marbles? 6 marbles?

4. 3 times what other number make 24? 21? 27? 18? 12? 15? 9? 6? 3?

5. If you subtract 4 from 20, and then 4 from the remainder, and so on, how many subtractions do you make before 0 is left? Then 4 in 20 how many times? 4 in 36? 4 in 16? 4 in 24? 4 in 28? 4 in 12? 4 in 8?

6. Since 5 cents make a half-dime, how many halfdimes in 30 cents? 45 cents? 35 cents? 10 cents? 40 cents? 25 cents? 15 cents? 20 cents?

7. If you subtract 6 from 54, and then 6 from the remainder, and so on till 0 is left, how many subtractions are made? (See 30, ex. 25.) Then 6 in 54 how many times? 6 in 24? 6 in 30? 6 in 48? 6 in 18? 6 in 36? 6 in 12? 6 in 42?

8. A boy has 21 oranges, and gives 7 oranges to each of his sisters. How many sisters has he? How many times 7 in 49? 63? 56? 14? 28? 7? 42?

9. Write the number 72 upon your slate, and from it subtract 8, and then 8 from the remainder, till 0 is left. How many subtractions are made? Then 8 in 72 how many times? 8 in 64? 8 in 56? 8 in 48? 8 in 40? 8 in 32? 8 in 24? 8 in 16? 8 in 8?

10. Write the number 81 upon your slates, and from it subtract 9, and then 9 from the remainder, and so on till 0 is left? 9 in 81 how many times? Count the subtractions and see. 9 in 72? 9 in 63? 9 in 54? 9 in 45? 9 in 36? 9 in 27? 9 in 18? 9 in 9?

11. Copy upon your slates and read the following: 2)19 2)17 215 2)13 2)11 2)9 2)7 2)5 2)3

9-1 8-1 7-1 6-1 5-1 4-1 3-1 2-1 1-1 Read thus: 2 in 19, 9 times and 1 over, etc.

12. Divide 5; 6; 7; 8; 9; 10; etc., to 39 by 4.
13. Divide 6; 7; 8; 9; 11; etc., to 49 by 5.
14. Divide 7; 8; 9; 10; 11; 13; etc., to 59 by 6.
15. Divide 8; 9; 10;
16. Divide 9; 10; 11;
17. Divide 10; 11; 12;

...

...

...

15; 16; etc., to 69 by 7.

17; 18; etc., to 79 by 8. 19; 20; etc., to 89 by 9.

18. A boy has 89 marbles. To each of how many boys can he give 9 marbles? How many marbles has he left?

19. Write 89 upon your slates, and from it subtract 9, and then 9 from the remainder, and so on till 8 is

left. How

many

subtractions do

you

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in 89 how many times, and how many over? 9 in 80 how many times, and how many over? 9 in 64? 9 in 57? 9 in 53?

SHORT DIVISION.

40. To divide a whole number by any of the nine digits.

EXAMPLES.

1. Copy, complete, and recite the following exercises:

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2)2864

4321

(1) PROBLEM.-How many times are 2 contained in

4268?

(2) DIVISION.-2 in 4 thousands, 2 thousands; 2 in 2 hundreds, 1 hundred; 2 in 6 tens, 3 tens; 2 in 8 units, 4 units.

(3) RESULT.-Hence, 2 in 4268, 2134 times. 2. Copy, complete, and recite the following: 4)4884 2)2006 5)5505

3)3069

1023

3. Divide 2; 20; 200; 2000; 20000 by 2.
4. Divide 3; 33; 303; 3333; 30303 by 3.
5. Divide 2; 24; 242; 4260;
6. Divide 4; 40; 480; 8440;
7. Divide 5; 55; 555; 5555;
8. Divide 6; 60; 606; 6060;

28642 by 2.
84848 by 4.
50505 by 5.
66666 by 6.
70007 by 7.

9. Divide 7; 77; 707; 7707; 10. Divide 8; 88; 800; 8008; 80808 by 8. 11. Divide 9; 99; 999; 9999; 99999 by 9.

9)9999

12. Copy, complete, and recite the following exer cises:

8)96 7)91 6)84 5)75 4)64 3)51 2)36 9)99

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(1) PROBLEM.-How many times are 8 contained in 96?

87 by 3.

(2) DIVISION.-8 in 9 tens, 1 ten and 1 ten over; (1 ten and 6 units are 16 units), 8 in 16 units, 2 units. (3) RESULT.-Hence, 8 in 96, 12 times. 13. Divide 38; 34; 52; 58; 74; 78; 96; 98 by 2. 14. Divide 42; 45; 54; 57; 72; 75; 84; 15. Divide 52; 56; 60; 68; 72; 76; 92; 16. Divide 65; 60; 75; 70; 85; 80; 95; 17. Divide 72; 78; 90; 84; 96; 60; 66; 18. Copy, complete, and recite the following exercises:

96 by 4.

90 by 5.

12 by 6.

2)102 2)126 2)148 2)162 2)184 3)123 3)216 3)249

51

63

RECITATION.

41

(1) PROBLEM.-How many times are 2 contained in 102?

(2) DIVISION.-2 in 10 tens, 5 tens; 2 in 2 units, 1

unit.

(3) RESULT.-Hence, 2 in 102, 51 times.

19. Divide 126; 153; 189; 216; 249; 276 by 3.
20. Divide 128; 164; 248; 324; 368; 208 by 4.
21. Divide 155; 250; 355; 105; 405; 450 by 5.
22. Divide 186; 246; 306; 426; 480;
23. Divide 147; 217; 287; 350; 427;

24. Divide 168; 240; 328; 408; 568;
25. Divide 189; 279; 360; 459; 540;

546 by 6.

637 by 7.

720 by 8.

819 by 9.

26. Copy and recite the following exercises: 2)4538 3)4323 4)5124 9)3655

2)3654

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(1) Problem.—How many times are 2 contained in 3654?

(2) DIVISION.-2 in 3 thousands, 1 thousand and 1 thousand over: (1 thousand and 6 hundreds are 16 hundreds); 2 in 16 hundreds, 8 hundreds; 2 in 5 tens, 2 tens and 1 ten over; (1 ten and 4 units are 14 units); 2 in 14 units, 7 units.

(3) RESULT.-Hence, 2 in 3654, 1827 times.

RULE.

(1.) Arrange the numbers so that the DIVISOR may stand at the left of the DIVIDEND, or number to be divided (placing a curved line between them as in the foregoing operations).

(2.) See how many times the divisor is contained in the left-hand figure, or (if that figure is smaller than the divisor) in the number represented by the two left-hand figures of the dividend.

(3.) Place this figure under that part of the dividend just used.

(4.) Prefix the digit that remains over (if there be a REMAINDER) to the next figure on the right, and divide as before, continuing the work till all the figures have been used.

REMARK 1.-If there is a REMAINDER after the final figure is used, write it as in the last operation, example 26.

REMARK 2.-The sign is known as the sign of division, and when placed between two numbers it signifies that the former is to be divided by the latter. Thus: 32÷-8=4 is read, thirty-two divided by eight equal four, or eight in thirty-two, four times.

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