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When the divisor is abstract and the dividend concrete, the quotient has the same name as the dividend. Thus: $21 - 7 = $3, or of $21 = $3.

When we consider that $7 is contained 3 times in $21, the problem differs from the separation of $21 into 7 equal parts. The latter kind of division is called partition.

4. Divide the following first by 10; then by 100; then by 1000: 5000; 35000; 42000; 63,000; 78,000. How does the removal of one naught from the right of a number affect its value ? the removal of two naughts ? three naughts ? etc. 5. Find of 120; 160; 200; 400; 480 ; 960. 6. How do you prove division? Illustrate.

Give the quotients at sight: 7. 160 : 4 12. 720 : 24 17. 750 : 15 22. 880 = 4 8. 280

7 13. 900 - 15 18. 400 : 4 23. 1200 20 9. 960 : 8 14. 500 : 2 19. 360 : 6 24. 7200 60 10. 1080 ; 12 15. 900 = 45 20. 360 : 5 25. 9000 = 60 11. 900 : 5 16. 100 ; 25 21. 900 : 3 26. 3600 - 30

27. Divide the number 4,294,967,296 by 4; divide the quotient by 4, and continue to write successive quotients by 4 as divisor for two minutes without writing divisors. Change the dividend and the divisor until rapidity and accuracy have been attained.

Find quotients and test : 28. 23021 - 49 34. 97009 : 69 40. 367047 734 29. 72012 - 85 35. 78007 : 89 41. 908006 - 906 30. 70057 - 91 36. 52475 : 62 42. 780980 ; 694 31. 77818 ; 67 37. 70601 - 96 43. 600809 ; 710 32. 75349 78 38. 70075 : 56 44. 740096 - 897 33. 77445 ; 86 39. 42882 - 74 45. 873401; 732

46. Find the average of 465 bu., 373 bu., 914 bu., and 762 bu.

47. Find the average of 613 ft., 724 ft., 484 ft., and 465 ft.

48. How many hats, at $1.25 each, can be purchased for $57.50 ?

49. $108.75 was received from a sale of china plates at $0.75 each. Find the number of plates that were sold.

50. A Reading Circle purchased copies of Longfellow's Poems at $1.35 each. The entire amount paid was $25.65. How many copies were bought ?

51. Find the number of dozen eggs at 127 cents a dozen that can be bought for $32.25.

52. Bicycles were sold at $ 22.50 each. A check for $1012.50 was given in settlement. Find the number bought.

REVIEW OF DENOMINATE NUMBERS

1. Change 12 gallons 1 pint to pints. 2. How many inches are there in 14 feet 10 inches? 3. How many feet and inches are there in 1020 inches? 4. Compare in length 6 inches and 2 yards. 5. Compare 24 yards and 2 rods. 6. How many yards are there in 2700 inches ? 7. Change 3 T. 6 cwt. 12 lb. to pounds. 8. How many seconds are there in 51 hours?

9. How many 8-ounce packages of soda can be put up from 1 ton 300 pounds of soda ?

10. A field is 80 rods long and 320 feet wide. How many yards is it around the field?

11. James is in school 51 hours each day for 180 days. How many days of 24 hours each would this equal ?

12. How many miles does William walk in going to and coming from school, in a term of 140 days, if he lives 600 yards from school and attends every day ?

13. Mr. Hosack feeds his horse 4 quarts of oats 3 times a day. How many

How many bushels of oats does he feed the horse during November, December, and January?

MISCELLANEOUS REVIEW 1. Compare 64 and 8; 21 and 7; 90 and 15. 2. 3 square feet is what part of a square yard? 3. Compare 36 inches and 6 inches. Compare: 4. 4 rods and 3 feet. 5. A yard and a rod. 6. A cube 1 foot on an edge and one 6 inches on an edge. 7. A pint and a gallon. 8. 3 pecks and 3 bushels. 9. What part of a square yard are 2 square feet? 10. What part of a bushel are 8 quarts ? 11. What part of a rod are 84 feet? 12. What part of a mile are 528 feet? 13. What part of 2 bushels are 2 pecks? 14. What part of a gross are 2 dozen? Make problems and solve them: 15. A floor is 16 feet long and 12 feet wide. 16. A floor is 8 yards long and 6 yards wide.

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17. A grocer bought 8 bushels 2 pecks of onions.
18. How many pint bottles can be filled from —?

19. A room 12 feet long, 10 feet wide, and 9 feet high is to be painted.

20. A square contains 36 square feet. 21. Find the number of cubic inches in a rectangular solid X

X 22. A wall is 25 ft. long. 23. g of the cost of a house is $1200. Announce the products : 24. 60 x 70 27. 50 x 70

30. 125 x 40 25. 80 x 90 28. 200 x 60

31. 150 x 50 26. 90 x 60 29. 250 x 40

32. 160 x 60 Announce the quotients : 33. 840 · 120 35. 240 120 37. 7200 + 120 34. 960 : 80 36. 6400 ; 80

38. 8100 ; 90 39. What two factors will produce 60 ? 722 95 ? 40. What two equal factors will produce 9? 16? 144 ? 41. Square 60; 90; 25; 15; 40. 42. What two equal factors will produce 3600 ? 8100 ? Find the value of : 43. (60 + 40) 10

46. 44 +90 + za 44. (3 x 80) + 6

47. (4 x 6) + (15 = 5) 48.

6 x 8 x 10 x 100 45. 8+ (4 x 3) = 5

3 x 5 x 25 49. How does annexing a naught to a number affect its value?

50. How does removing a naught from the right of a number affect its value ?

FACTORING

1. What are the factors of 4 ? of 6 ? of 8 ?

The factors of a number are the integers that, multiplied together, will produce that number. They are exact divisors of the number since they will divide it an integral number of times.

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Thus the factors of 4 are 2 and 2, since 2 x 2 4; the factors of 6 are 2 and 3, since 2 x 3 = 6; the factors of 8 are 4 and 2, since 4 x 2 = 8, or 2, 2, and 2, since 2 x 2 x 2 = 8. .

2. What two factors will produce 9 ? 15? 25 ? 32 ?

3. If 3 is one of the factors of 36, 'what is the other factor ? if 4 is one of the factors ?

4. Name two factors that will produce 16; 24; 28; 38; 46; 52.

5. What three factors will produce 8? 12? 20 ? 42 ?

6. What number will divide 13, giving a whole number as quotient? Observe that 13 has no factors except itself and 1.

A prime number is an integer that has no other factors except itself and 1.

All other integers are called composite numbers.

Thus, 5 5 x 1; 7 = 7 x 1. 5 and 7 are prime numbers. 2, 4, 6, 8, 9, etc., are composite numbers.

7. What numbers between 0 and 30 are prime numbers ? between 30 and 60 ?

Prime factors are factors that are prime numbers.
Thus, 3 and 7 are the prime factors of 21.

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