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6. How many times 5 = 30? 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? 28 = 7? 24 = 6? 2. 56 • 7? 70 • 10 ? 40 ; 5? 32 + 8? 90 • 10? 3. 81 ; 9? 40 • 8? 30 – 6? 72 ; 8? 42 ; 7? 4. 64 • 8? 72 ; 9? 35 ; 5? 25 + 5? 63 ; 9? 5. 21 • 7? 56 • 8? 27 • 9? 70 • 7? 21 : 7? 6. 28 ; 4? 36 • 4? 45 • 9? 24 • 4? 27 • 3? 7. 45 • 5? 21 ; 3? 54 • 6? 36 • 9? 35 ; 7? 8. 30 ; 3? 63 ; 7? 100 • 10 ? 48 + 8? 32 - 4? 9. 54 ; 9? 50 • 10 ? 36 • 6 ? 30 – 5? 50 • 5? 10. 80 • 8? 42 • 6?

D. 1. Reduce 7 to fourths.

Solution. Since 1 = 4 fourths, 7 must equal 7 times 4 fourths, or 28 fourths. Therefore, 7=

2. Reduce 6 to fifths. 9 to thirds. 5 to sevenths. 3. 3 to ninths. 8 to sixths. 4 to sevenths. 3 to eighths. 4. 6 to sevenths. 4 to ninths. 8 to sevenths. 10 to ninths. 5. 9 to eighths. 8 to ninths. 7 to eighths. 6 to eighths. 6. 9 to ninths. 8 to thirds. 4 to eighths. 3 to sevenths. 7. 6 to sixths. 7 to sevenths. 8 to ninths. 10 to fifths.

8. Reduce 45 to ninths. Since 1 9 ninths, 4 must equal 4 times 9 ninths, or 36 ninths; and 5 ninths added are 41 ninths. Therefore, 43 =4 9. Reduce 3 to sevenths. 44 to sevenths.

81 to sixths. 10. 470 to tenths. 5to fifths. 93 to thirds. 7 to sixths. 11. 64 to ninths. 5$ to eighths. 64 to eighths. 12. 97 to ninths. 103 to thirds. 9f to sixths. 64 to sixths. 13. 98 to sevenths. 75 to ninths. 63 to ninths. 14. 9 to eighths. 10 to fourths. 37 to eighths. 15. 37 to ninths. 8 to fifths. 5$ to eighths, 73 to thirds

16. 83 to ninths. 46 to sevenths. 10$ to sevenths.
17. 9] to sixths. 74 to sevenths. 8f to ninths.
18. 8 to fourths. 45 to ninths. 8f to ninths.
19. 91 to fourths. 7 to ninths.

E. 1. Reduce 46 to ones.

Solution. Since 6 sixths 1, 48 sixths must equal as many ones as there are times 6 sixths in 48 sixths, which are 8 times. Therefore, the : 8 ones, or 8.

Reduce each of the following expressions to ones.
2. z 18. 3 Bit 7,2 18. 18. .
3. 8.924. 2. 78. 256 29,0. 1. *8.
4. 2. 7. 64.4 7. 2. 18. 4 4. es.
5. 4. 24. 20.
6. 42 43 Pe

F. 1. How many are 8 times f? Solution. 8 times 2*, which is equal to 6 ones. Therefore, 8 times 6.

2. How many are 6 X ? 9 X ? 8 X 9 X 3?
3. How many are 7 X 8? 9 X 41? 9 X 6%?
4. How many are 8 x 73? 9 X 83? 3 X 79?
5. How many are 6 X 93? 4 X 78? 10 X 8f?
6. How many are 9 X 74 ? 8 X 97?

7. 6 = how many times ? Solution. 6= *, and are contained in , 8 times. Therefore, 6 = 8 times 1.

8. 7} = how many times $? Solution. 7 = , and are contained in 36, 9 times. Therefore, 71 = 9 times .

9. 4= how many times ? 5$ = how many times f? 10. 34 = how many times $? 54 how

many

times it? 11. 8= how many times ? 10% = how many times 17 ? 12. 9

how

many times 17 ? 75 = how many times f? 13. 5% = how many times 14? 6% = how many times 14? 14. 10 = how many times 1f ? 91 how

many

times 21? 15. 9

how
many
times 18? 7}

times 11? G. 1. How many are 7 x 3 + 4, +5? 2.9 X 4-6, +5? 8 X 3+8, +3?

how many

SA

3. 48 + 6-4, X 9? 8 X 8 +6, +7? 4. 32 : 4, X6, 8? 10 X 10 - 28, • 9? 5.7 X 4+2, + 6? 9 X 8+9, +9? 6. 5 X 9-9, •4? 7 X 9+1, + 8? 7. 3 X 8+ 24, + 6? 7 X 8+4, + 10? 8.7 X3 +6X4? 8 X 5+6 X 7? 9. 9 X 6 + 40 - 8? 10 X8_8, +9? 10.7 X 7+3 X 8? 6 X 6+4 X 7? 11. 6 X 9+7 X 8? 7 x 9 + 18, +9? 12. 10 X 6+8 x 9? 7 X9+8 X 8? 13. 6 X 10+9 X 9? 6 X 4+3 x 9 +4 X 8? 14. 9 X 7+8 X 9+7 X 6? 15. 8 X 9 -3 X 8+7 x 9? 16. 5 X 3 + 6 x 6+7 X7? 17.9 X 3+4 X8+7 x 6? 18. 9 X 9-5 X 7+7 X 8? 19. 8 X 8+6 X6, 10? 5 X 9+6 X 4-7X7? 20. 5 X 10 — 6 X 6+3 X 7, +5? 21. 7 X 5+7 X 6-4 X 8, +9? 22. 8 X 3+4 X 9–6 X 3,- 7? 23. 5 X 10 +9 X 9 — 59, + 8?

4+ 36

H. 1. 6 X 4+9+9, +7—1, X 8–4, • 9, X 6 = how many

times 6 ? 2.7 x 5—3, +8, X 9, • 6+ 17 + 5, 7, X 105 how many

times 5 ? 3. 8 X7–2, -6, X 8+9,:9, X3+27,6, X

how many times 8? 4. 9 X 9 – 17, •8, + 8x 9, • 10, •4, X 2, X 2, X7+3+9+4= how many times 9 ?

5. 50 • 10, X 9-5, + 8, X 7 - 5, -6, X 5 5, = how many times 5 ?

6. 6 X 8 -6, -6, X7-1, +6+2, X 3+2, ; = how many times 4 ?

7.9 X 7+5+4, +8+7+9+8+7 +9, 7, X 10 +6 +5, +9, X 4 = how many times 6?

8. 8 X 5-4, +9+3, X 3 +6, +9+4 X5+7 = how many times 6 ?

9. 2 x 10 +7X4,-8, X6-3X7+21, –4, X 5 - 13 how many times 8 ?

10. 5 X 9+9 X 3, • 8-3, X 8+6 X 4, 9, X 7—9—5, +6, X 10 +2= how many times 9?

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I. 1. What will 6 barrels of four 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. What was the cost of the whole ?

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 ?

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.

10. 9 gal. how many quarts ? 8 weeks days?

11. 8 gal. = how many quarts ? 93= how many 3? 12. 9 bu. = how many pecks ?

how many quarts ? 13. 8 quarters = how many nails ? 6 weeks = how many days?

14. 6 w. 4 d. 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. - 15. 8 gal. 3 qt. = how many qt. ? 5 pk. 7 qt. = how many 16. 9 yd. 2 ft. how many ft. ? 4 3 6 3 how many 3?

17. 4 m. 3 fur. = how many fur. ? 8 C. 5 cd. ft. = how many cord feet ?

how many

S

5 pk.

qt. ?

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

10. 56 fur. how many miles ? 24 ft. = how many yd.? 11. 32 nails = how many qr. ? 49 da. how many weeks ?

12. 40 pk. = how many bushels ? 28 qt. = how many gallons ?

how many qt. ? 24 3 = how many = ? 14. 28 farthings

how many pence? 35 dollars = how many half eagles 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. 17. 28 gills

how many pt. ? 28 da. how many weeks ? 18. 81 sq. ft. = how many sq. yd. ? 80 pk. = how many bushels ?

13. 18 pt.

yd.?

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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