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11. 30, 34; 36, 40; 24, 36; 48, 80; 40, 65; 144, 168.

Write the prime factors of:

12. 15, 40, 48, 54, 60, 77, 92, 84, 120, 96, 140, 210.

Find the L. C. M. of:

13. 4, 9, and 12; 3, 9, and 7; 6, 12, and 14; 6, 8, and 10; 3, 5, and 7; 2, 9, and 5.

MISCELLANEOUS WORK

LESSON 30

1. Why are 9 and 17 prime to each other?

2. If of a barrel of oil equals 30 gallons, how many gallons equal of a barrel?

3. Find the cost of 21 cwt. of sugar at 6¢ a pound.

4. Change,,, and to 12ths; 24ths.

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5. At 121 each, how many articles can be bought for $1?

6. Find the cost of 2 dozen plates at 5 apiece.
7. What is subtraction? Division? Quotient?
What does the denominator of a fraction show?
9. What is a decimal fraction?

8.

10. In .444, the second 4 is what part of the value of the first 4? How many times the value of the third 4? In changing yards to rods, what is your divisor?

11.

12. In changing to 9ths, by what number do you. divide both numerator and denominator?

13. When 12ths are changed to 3ds, are the fractional parts larger or smaller?

14. If you divide both terms of by 3, will the value of the fraction be changed?

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30. A man has a piece of land 18 rods long and 15 rods wide. How many square yards does it contain? How many rods of fence will be needed to inclose it? How much will the fence cost at 18¢ per foot?

LESSON 31

Write as common fractions, and change to their lowest

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19. At $.08 a yard, how many yards of muslin can I

buy for $8? $80?

20. If it takes 9.4 yards of cloth to make one suit of clothes, how many suits can be made from 564 yards?

21. If 21 oranges cost $3, how many oranges can be bought for $11?

22. Find the L. C. M. of 8, 12, and 16.

23. If 9 bottles of chowchow cost $21, how much will a dozen bottles cost?

24. Change to 15ths; to 28ths; to 24ths.

25. Change to lowest terms: 26. Divide by 4; 19 by 5;

27. If of a ton of straw is ton can you buy for $1?

4, 18, 18, 18, 38.

14

by 3; 13 by 4; 18 by 6. worth $4, what part of a

28. At $g a day, how many dollars will a boy earn in 10 days?

29. How many pieces 4 inches long can be cut from a yard of ribbon? From 12 yards?

30. A farmer sold of his chickens and had 12 left. How many chickens had he at first?

31. At a peck, how many bushels of wheat can you buy for $6?

32. How many bottles holding of a pint each will be required to hold 23 gallons of ink?

33. What part of $1 is 10 cents? 20 cents? 25 cents? 50 cents? 75 cents? 12 cents? 33 cents? 16 cents? 663 cents?

LESSON 32

1. How many rods of wire fencing will be required to go round a rectangular field 462 feet long and 330 feet wide? How much will the wire cost at $1.60 per rod?

2. If 1 lb. 7 oz. of butter cost 46%, how much will 5 lb. 14 oz. cost?

3. Divide 42 mi. 160 rd. 5 yd. by 5.

4. How many years, months (30 da.), and days are there from April 29, 1759, to July 4, 1832?

5. If .25 of a yard of cloth cost $1.60, how much will 78 yards cost?

6. Find the sum of four hundred thirty-three thousand six hundred thirty-four dollars and twenty-nine cents; eighty-nine thousand three hundred dollars and seventytwo cents; forty-six thousand three hundred fifty-two dollars and thirty-six cents; sixty-five thousand seven hundred nine dollars and forty-five cents.

7. From 3 billion 444 million 236 thousand 164 dollars and 93 cents take 2 billion 542 million 370 thousand dollars and 98 cents.

8. How many miles are there in 52,800 feet?

9. How many yards of Brussels carpet yd. wide will cover the floor of a room 36 ft. long and 27 ft. wide? 10. If a boy steps 2 ft. 9 in., how many steps will he take in going from his home to school, a distance of 1 miles?

11. Divide 853.24 by 102.8; 2088.48 by 15.2.

12. Multiply 845 by .25; by .07; by .006.

13. How many dozen are there in 60 score? 14. Change 12 gross to dozens.

15. Change 133 quires to sheets.

16. Find the cost of 9480 ft. of hemlock boards at $18

per M.

CANCELLATION

LESSON 33

Cancellation is an operation to shorten work in division by striking out common factors from both dividend and divisor.

Striking out a factor from any number divides the number by that factor. Thus, to strike out, or to cancel, 7 from 21, is to divide 21 by 7.

Striking out equal factors from both dividend and divisor simply divides both dividend and divisor by those numbers. 1. Divide 210 by 30.

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It will be seen from the preceding operation that equal factors may be rejected from both dividend and divisor without altering the quotient.

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3. Divide 24 × 28 × 32 by 12 × 14 × 16.

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4. Divide 48 x 18 x 20 by 12 x 8 x 10. 5. Divide 40 × 64 × 70 by 8 x 10 × 32.

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