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MULTIPLICATION AND DIVISION.

1. The two factors are 341 and 257; what is the product?

Ans. 87637. 2. The divisor is 15, the quotient 31, and the remainder 5; what is the dividend ?

Ans. 470. 3. One factor of a number is 12 and the other factor is 2602 ; what is the number?

Ans. 31224. 4. The remainder is 14, the quotient 407, and the dividend 61878; what is the divisor ? Ans. 152.

5. If a ship sail 185 miles in a day, how far will it sail in 51 days ?

Ans. 9435 miles. 6. If the earth moves in its orbit 68000 miles in an hour, how far will it move in 24 hours ?

Ans. 1632000 miles. 7. James earned $15 in a week and paid $5 for his board ; how much did he save in 52 weeks ? Ans. $520.

8. A drover bought 45 horses at $84 each, 72 cows at $25 each, 315 sheep at $6 each ; what did they all cost?

Ans. $7470. 9. Two men start from the same place and travel in opposite directions; the one goes 5 miles an hour and the other 3 ; how far apart will they be in 12 hours ?

Ans. 96 miles. 10. If the men mentioned in the last example had traveled the same direction for 12 hours, how far apart would they be ?

Ans. 24 miles. 11. The divisor is 8, and the quotient 1142; what is the dividend ?

Ans. 9136. 12. If one sheep cost $5, how many sheep can be bought for $2315 ?

Ans. 463 sheep.

13. The salary of the President of the United States is $50000; what is it per day?

Ans. $137. 14. There are 3150 gallons in 50 hogsheads; how many gallons are there in one hogshead ?

15. The dividend is 582, the divisor 15, and the remainder 12 ; what is the quotient ?

Ans. 38. 16. The three factors of a certain number are 35, 43, and 57; what is the number?

17. What is the cost of 554 acres of land, at $65 an

acre ?

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18. The wine gallon contains 231 cubic inches; how many cubic inches are in a hogshead of 63 gallons ? .

19. A drover bought 53 horses at $75 each, 25 cows at $21 each, 3458 sheep at $6 each : be sold them for $251 less than he paid; for how much did he sell them?

Ans. 24997. 20. What number multiplied by 11 gives 638 ?

REDUCTION OF FRACTIONS.

63

90

48

100

4 5

Reduce to the least common denominator, 1. $,$$.

Ans. 16, , 14 2. }, 4, .

Ans. 295, 315, 17%. 3. , %,

Ans. 19% M, 188, 4. t of , f off, and 3 of %. Ans. 44, 42, 44. 5. 1 of 2), f of 3), and of 54. Ans. 18, 15.0, 6. 6. 1, 1, and .

Ans. $ Ž, ŽE 7. 3, 4, and Post

Ans. , 1l, 8. 4, 5, , and

Ans. , 13, 14,

용 9. }, s, 1, $, , and %

Ans. 188, 18, 36, 385, 344, 388. 10. 17, 31, 41.

Ans. 15, 2009

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1. What is of f? of? 1 of 4 ? } of ? ; of #? of ?

2. One-third of 6 is 4 of what number? ? ? ? ? ? ? ? ? ?

3. One-third of 9 is of what number? 1? 1? 1 ? ? 3? 3? 10 ? 1? ?

4. Two-thirds of 9 is of what number? į? ? ?? 7 ? ? $? to? 11 ? 1g?

5. One-third of 12 is of what number? 1? *? ? +? ? ? ? ? 1?

6. Two-thirds of 12 is of what number? 1 ? ? ? ? 1? 1? 1? *? 12? #

10 11? 9. One-fourth of 12 is 1 of what number? 3? 1? 1? ? ? ? 10 ? ? ?

11 8. One-half of 12 is } of what number? 1 ? ? ? 7 ? ? ? to? It? 1?

9. Three-fourths of 12 is of what number? 1? 1? 3? *? *? $? 1? 11? 11? 11?

10. One-fourth of 16 is of what number? j? ? 1 ? ? ? ? ? 1 ? ?

itth 11. One-half of 16 is of what number? 1? 1? * ? 4? 1? ? to? t ? 1?

12. Three-fourths of 16 is of what number? 3? 1 ? *? ? ? ? ? ? ? ? 13. One-third of 18 is of what number? 7? }? 1?

을 7 ? ? ? ? ? 1g?

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14. Two-thirds of 18 is 1 of what number? 1? 1? 1? ? ?? ? ? ? ? ? 15. What part of 1 is ? ? ? ?

*$ 16. What part of 2 is f ? ? ? ?

Ans. £, £, , to 17. What part of 3 is 1 ? 1 ? ? ? ?

$ $*$

Ans. 5, 1, $, te, to. 18. What part of 4 is } ? ? ? ?

Ans. $,$,, %. 19. What part of $ is 1 ? 1 ? ? ? ?

Ans. , , , , 20. What part of 4 is 1 ? } ? f ? ? ?

Ans. , is, }, {1, 14. 21. What part of 5 is 1 ? 1 ? ? ? ?

$.

Ans. to, 15, i, o, 22. What part of 20 is 4? 5? 6? 102 15 ?

Ans. *, 4, }, }, &. 23. What part of 25 is 4 ? 5? 67?10? 121 ?

Ans. , }, }, }, J. 24. What part of 100 is 4? 5? 6? 10 ? 121 ?

Ans. to, zbo, be to, š. 25. What part of 54 is j ? 11 ? 21 ? 31 ? 41 ?

Ans. t, it, I', 1, . 26. What part of 61 is 1 ? ? 11? 11 ? 11?

Ans. zł, , , , 27. 1 is of what number ? ? ? ? ? +

Ans. 7, 3, 2, 11, 13.
28. 5 is of what number ? ? ? ? ?
4

导? ? 导
Ans. 35, 171, 119, 81,7.

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29. 6 is of what number ? ? ? ? ?

Ans. 42, 21, 14, 101, 8%. 30. 7 is 4 of what number ? ? ? ? ?

Ans. 49, 241, 163, 124, 94. 31. 4 of 14 is of what number ? $? 4? ? *.?

Ans. 4, 6, 8, 10, 12. 32. of 14 is 4 of what number ? ? ? ? ? ?

Ans. 8, 12, 16, 20, 24. 33. $ of 14 is of what number? $? ? *? 1?

Ans. 12, 18, 24, 30, 36. 34. of 15 is of what number? } ? ? ? 3?

Ans. 18, 27, 36, 45, 54. 35. 4 of 15 is of what number ? ? ? ? ?

Ans. 24, 36, 48, 60, 72.

MULTIPLICATION OF FRACTIONS.

PROBLEMS,

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1. Multiply } by 1.

x1= t; and by alternating, 1 x }= t. 2. Multiply } by 1.

* x1 = $; and by alternating, 1 x } = f. 3. Multiply 4 by 1.

1 x1= 4; and by alternating, 1 x t= 1 4. Multiply } by 2.

* x 2 = ; and by alternating, 2 x t = . 5. Multiply f by 2. * x2 = $; and by alternating, 2 x f = f.

} 6. Multiply by 2. x 2 = 4; and by alternating, 2 x j = 4.

$ 7. Multiply by 2. * x 2 = 4; and by alternating, 2 x * = *.

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