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Received payment, Jan. 15, 1896,

BURKE & WHITE,

By JOHN R. PIERCE.

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INDICATED OPERATIONS.

111. The Parenthesis, (), indicates that all the numbers contained therein are to be taken together.

112. Brackets, [ ], Braces, {}, and the Vinculum, have the same use as the parenthesis.

113. When the parenthesis is not used, operations indicated by or must be performed first. Thus,

1. 124 x 2 + 36 ÷ 4 − 2 x 4 = ?

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NOTE.- When one parenthesis, brace, or vinculum includes another, first remove the inner one.

114. Find the value of :

1. 153 × 6 + 10 ÷ 5.

2. (6+4) × (3 + 2) − (8 × 5).

3. 183 x 2 + 8 × 2 ÷ 4 6.

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8. 17+ 3 x 4 × 6+3 ÷ 3 + 3.

9. [39 +82 +7] × 6.

10. [615 x 3 (6+16+8+4)]÷8 +5.

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MISCELLANEOUS.

115. 1. I have four pieces of broadcloth. The first contains 13.7642 yd.; the second, 22.008 yd.; the third, 15.027 yd.; and the fourth, 19.255 yd. How many yards in all? 2. From a piece of ribbon containing 103ğ yd., 73a yd. were sold. How many yards were left?

3. How many yards of muslin at $.12 a yard will it take for 4 pair of curtains, if each curtain contains 3.375 yd.?

4. I have 14.735 yd. of lace, and desire to cut it into seven equal strips; how much will there be in each strip?

5. What will be the cost of a hat at $7.50, a pair of gloves at $1.13, a veil at $1.25, and a parasol at $3.375?

6. Arrange the following articles in the form of a bill: 7 qt. of molasses at $.15 a qt., 3 pk. of apples at $1.28 a bushel, 30 lb. of sugar at $.08} a pound, and 12 bu. of potatoes at $.29 a bushel.

7. A grocer bought three bunches of bananas at $1.54 a bunch. The first bunch contained 73 bananas, the second 54, and the third 97. He sold them all at 30g a dozen; did he gain or lose, and how much?

8. The first year in business a grocer made $2374.68, the second $1529.47, and in the third year he lost $300. His expense each year averaged $928.45; how much money had he gained at the end of three years?

9. What will 9 barrels of flour cost, if 28 barrels cost $173.60 ?

10. I bought 437 heads of lettuce at $5 a hundred, and sold them at $.08 a head; what was my gain?

Find the cost of:

11. 6824 lb. of coal at $4.68 a ton.

12. 2384 lb. of coal at $5.67 a ton.

13. 8972 ft. of lumber at $35.40 a thousand.

14. 6854 lb. of hay at $16.50 a ton.

15. 4836 bricks at $9.45 per M.

16. 895 ft. of lumber at $19.75 per M.

17. What part of 4.50 is 3.331 ?

18. What part of 3.625 is 1.5?

19. What part of 6.2 is 3.25?

20. 1.1 is what part of 7.4 ?

21. A father left his son $24000, which was .375 of his estate. What was the value of the estate?

22. Divide 26 by 21, and multiply the result by 17.345. 23. Divide of .375 by 1⁄2 of % of .298.

24. The product of three numbers is 167.7.

numbers are 3.25 and 5.16.

What is the other?

25. What number divided by 2.86 equals .34?

Two of the

26. What number diminished by 38.64 leaves .356 ?

27. A man bought 8.5 yd. of cloth at $3.331 a yard, 12.4 yd. at $2.75, 18 yd. at $4.375, and 24g yd. at $2.875. How many bushels of corn at 43 cents a bushel will pay for the cloth ?

28. .5 of a number exceeds .45 of it by 20. What is the number?

SOLUTION: .5

what? 20.05

.45.05. Now the question is, 20 is .05 of = € 400.

29. At 85 a yard, how many yards of cloth can be purchased for $29.75.

30. Divide $785 among A, B, and C, so that C will have $185 more than each of the others.

1

31.

.0045

.05 .4 × .005 + .002 × .125

32. What part of .876 is .31536 ?

= ?

33. If .375 of a ton of coal cost $1.25, what will 7.125 tons cost?

34. What is .3 of a number when .8 of it is 80 ?

35. How many thousandths in 3 units?

36. How many thousandths in .1?

37. Express of one hundredth as a decimal.

38. The salary of the President of the U. S. is $50,000 a year. How much does he receive per day?

116. Review of Factors, Multiples, Divisors, and Cancellation. 1. Define factor, composite number, prime number, and prime factor.

2. Find the prime factors of 5075; of 9576; of 3150; of 6006.

3. Find the sum of the prime factors of 34650.

4. Find the prime factors of 2310; of 17199; of 6840. 5. 81158 is the product of what prime factors?

6. Find the largest prime factor of 12600.

7. What is a common divisor of two or more numbers? 8. What is the greatest common divisor of two or more numbers?

9. When are numbers prime to each other.

Find the greatest common divisor of:

10. 672 and 960.

11. 616 and 1012. 12. 272 and 428.

13. 1650 and 1920.

14. 696, 1218, and 1160.

15. 450, 720, and 810.

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