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6. How many times 530? 25? 50? 40? 35? 45? 20 ?

7. How many times 9 45? 36? 27? 81? 63? 90? 54? 72?

8. How many times 6 36? 48? 30? 24? 42? 54? 60?

C. 1. How many are 48÷6? 287? 24 ÷ 6? 2. 567? 70 10? 40 5? 328? 90 ÷ 10? 3. 819? 40 ÷ 8? 4. 648? 72 ÷ 9? 5. 217? 56 ÷ 8? 6. 284? 36 ÷ 4? 7. 455? 21 ÷ 3? 8. 303? 63 ÷ 7? 9. 549?

306?
355?

72÷8?

42 ÷ 7?

25 ÷ 5?

63 ÷ 9?

279?

70 7?

21 ÷ 7?

45 ÷ 9?

244?

27 ÷ 3?

546?

36 ÷ 9?

35 ÷ 7?

100

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2. Reduce 6 to fifths. 9 to thirds.

3. 3 to ninths. 8 to sixths. 4 to sevenths. 3 to eighths.

4. 6 to sevenths. 4 to ninths. 8 to sevenths.

5. 9 to eighths.

8 to ninths. 7 to eighths.

6. 9 to ninths.

8 to thirds. 4 to eighths.

7. 6 to sixths. 7 to sevenths. 8 to ninths.

8. Reduce 48 to ninths. Since 1

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10 to ninths.

6 to eighths.

3 to sevenths.

10 to fifths.

9 ninths, 4 must equal

4 times 9 ninths, or 36 ninths; and 5 ninths added are 41

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15. 37 to ninths. 8 to fifths. 5 to eighths. 7 to thirds

16. 83 to ninths. 4 to sevenths. 10 to sevenths.

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1, 48 sixths must equal as many

ones as there are times 6 sixths in 48 sixths, which are 8 times. Therefore, 48 8 ones, or 8.

Reduce each of the following expressions to ones.

2. 26. 48. 20, 30, 64, 72. 98. 78. 48,

36.

3. 80. 2. 28. 78. 21.
4. 27. 70. 63. 42. 72. 24. 08. 24.
5. 40. 21. 81, 54, 50, 63, 48, 30.
6. 42. 56. 36. 100.

56. 25. 90. 16. £8.

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F. 1. How many are 8 times ? Solution.

24, which is equal to 6 ones.

Therefore, 8 times

8 times ₹ =
= 6.
×??

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2. How many are 6 X?
3. How many are 7 X

4. How many are 8 X 72?
5. How many are 6 X 9
6. How many are 9 X 7?

7. 6 how many times

contained in 2, 8 times.

8.7

?

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Therefore, 6 = 8 times .

how many times ? Solution. 736, and

9. 4 how

many

=

are contained in 36, 9 times. Therefore, 7 = 9 times . times? 5 how many times 7? - how many times? 5 = how how many times ? 10% how many times 13? 7

10. 34

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many times ??

how many times 14?

how many times ? how many times 13?

11. 8

12. 9

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G. 1. How many are 7 x 3 +4, ÷ 5?

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2.9 X 4-6, +51 8X3+3, +3?

3. 486-4, X 9? 8x8 +6,÷7?

4. 324, X 6,8? 10 x 10 28,9? 5. 7x42,÷6? 9×8+9,÷9?

6. 599,÷4? 7x9 +1,÷8?

÷

7. 3 x 824, 6? 8. 7 × 36 × 4?

8

7 x 84, 10?

× 5 + 6 × 7?

9. 9 X 6408? 10 X 88, ÷ 9?

10. 7×7 +3 × 8? 6 × 6 + 4 × 7? 11. 6 x 97x8? 7X 918, 9?

12. 10 × 6+8×9? 7×9+8×8?

13. 6 x 109 x 9? 6 x 4+3x9+4X8? 14. 9 × 78×9+7×6?

15. 8 x 9-3X8+7x 9? 16. 5 × 36 × 6 + 7 × 7? 17. 9 x 34x8+7x 6? 18. 9 X 9 5 × 7+7× 8?

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19. 8 x86 x 6, 10? 5x9+6x4-7X 7? 20. 5 × 10 6 x 6 + 3 x 7, ÷ 5?

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7,÷

21. 7 x 57 x 6-4 x 8, ÷ 9? 22. 8 x 34 x 9-6 x 3, ÷ 7? 23. 5 x 109 x 959, ÷ 8?

H. 1. 6X4+9+9,÷7—1, X 8-4, 9, X6 ÷ = how

many times 6 ?

2. 7×5—3,÷8, × 9, ÷ 6 +17 +5,÷7, X 10= how many times 5?

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3. 8 × 7-2,÷6, × 8+ 9,÷9, × 3 + 27,÷6, X 4+36= how many times 8?

4. 9 X 9-17, 8, +8 x 9, 10, 4, X2, X2, ×7+3+9+4= how many times 9 ?

5,

4

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5. 5010, X 9-5, 8, X 7-5, ÷ 6, × 5 — X how many times 5?

6. 6 x 8-6, ÷ 6, × 7-1, +6 +2, x3 + 2,÷

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7.9 × 7+ 5+ 4,÷8+7+9+8+7+9,÷7, x 1065, +9, × 4 how many times 6?

8. 8X5-4, ÷ 9 + 3, × 3 +6,÷9+4×5+7 = how

many times 6?

9. 2 x 107X4,

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8, X 6-3 × 7+21, ÷ 4, X

times 8?

10. 5 x 99 x 3,÷8—3, x 8+6x4, ÷ 9, X 7. 9 — 5, 6, × 10 + 2 = how many times 9?

I. 1. What will 6 barrels of flour cost at 8 dollars per barrel? Solution. If one barrel cost 8 dollars, 6 barrels will cost 6 times 8 dollars, which are 48 dollars. Therefore, 48 dollars is the cost of 6 barrels of flour at 8 dollars per barrel.

2. What will 9 hats cost at 4 dollars apiece?

3. What will 8 pounds of rice cost at 5 cents per pound? 4. What will 7 drums of figs weigh if each drum weighs 6 pounds?

5. How many quarts will 5 jugs hold if each jug holds 5 qt. ? 6. Sold 8 ploughs at 9 dollars apiece and 7 cultivators at 8 dollars apiece. How much did they come to?

7. Bought 8 primers at 9 cents apiece, 7 small slates at 10 cents apiece, and 9 writing books at 7 cents apiece.

the cost of the whole ?

What was

8. Rode on Monday 8 hours at the rate of 7 miles per hour, on Tuesday 6 hours at the rate of 9 miles per hour, and on Wednesday 8 hours at the rate of 8 miles per hour. How far did I ride in all ?

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9. 7 gallons = how many quarts? Solution. Since 1 gal. 4 qts., 7 gal. must equal 7 times 4 quarts, or 28 quarts. Therefore, 7 gal. = 28 qt. how many quarts?

10. 9 gal. days? 11. 8 gal.

12. 9 bu.

=

=

8 weeks

how many quarts? 93 how many pecks? 5 pk.

13. 8 quarters

days?

14. 6 w. 4 d.

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how many

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how many

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nails? 6 weeks

how many days?

Solution. Since 1 week:

7 days, 6 weeks must equal 6 times 7 days, or 42 days, and 4 da. added are 46 days. Therefore, 6 w. 4 da. = 46 da.

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how many qt.? 5 pk. 7 qt. = how many

= how

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many ft.? 4363 how many 3? how many fur.? 8 C. 5 cd. ft.

how

J. 1. How many yards of cloth at 5 dollars per yard can be bought for 35 dollars?

Solution. If for 5 dollars 1 yard of cloth can be bought, for 35 dollars as many yards can be bought as there are times 5 in 35, which are 7 times. Therefore, 7 yards of cloth at 5 dollars per yard can be bought for 35 dollars.

2. How many bunches of crackers at 7 cents per bunch can be bought for 49 cents?

3. How many pounds of chalk at 4 cents per lb. can be bought for 24 cents?

4. If 3 cents will buy one roll of lozenges, how many rolls will 27 cents buy ?

5. If 4 dollars will buy 1 pair of boots, how many pairs will 36 dollars buy?

6. If it takes a man 1 hour to walk 4 miles, how many hours will it take him to walk 28 miles?

7. If it takes a horse 1 hour to travel 9 miles, how many hours will it take to travel 72 miles ?

8. If 1 hack will hold only 6 persons, how many hacks will it take to hold 54 persons?

=

9. 48 furlongs how many miles? Solution. Since 8 furlongs

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1 mile, 48 furlongs must equal as many miles as there are times 8 in 48, which are 6 times.

Therefore, 48 furlongs

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13. 18 pt. =

= 6 miles.

how many miles? 24 ft. =
how

many qr.? 49 da.
how many bushels?

how many qt.? 24 3

14. 28 farthings

many half eagles?

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how many yd.?

28 qt. =

how many weeks? how many

how many

?

how many pence? 35 dollars = how

15. 21 cents = how many three-cent pieces? 63 days = how many weeks?

16. 32 R.= how many acres? 27 sq. ft. how many sq.

yd.?

17. 28 gills

18. 81 sq. ft. bushels ?

how many pt.? 28 da. = how many weeks? how many sq. yd.? 80 pk.

how many

K. 1. How many jugs, each capable of containing 3 quarts, can be filled from 7 gal. 2 qt. of molasses?

Solution. Since 1 gal. 4 qt., 7 gal. must equal 7 times 4 quarts, or 28 qt., and 2 quarts added are 30 quarts. Now, since each jug holds 3 quarts, as many jugs can be filled as

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