2. When the solidity and two dimensions are given to find the other dimension, the product of three factors and two of the factors are given to find the other factor.

Problems.

Find the capacities of solids having the following dimensions, and change each result to higher denominations :— 4. 10 ft. 6 in. by 8 ft. by 7 ft. 5. 12.5 yd. by 9 yd. 2 ft. by 8 yd. 6. 20.4 rd. by 10 rd. by 8.5 rd.

1. 8 in. by 7 in. by 41⁄2 in. | 2.9 ft. by 8 ft. by 7 ft. 3. 12 ft. by 91 ft. by 8 ft. 7. Of a cellar 30.5 ft. long, 14 ft. wide, and 6 ft. deep. 8. Of a packing-box 6 ft. 8 in. long, 41⁄2 ft. deep, 3 ft. wide. 9. Of a bin 12 ft. 9 in. long, 7.5 ft. wide, and 43 ft. deep. 10. Of a thousand bricks, each 8 in., by 4 in., by 2 in. 11. How many cords are in a pile of wood 90 ft. 6 in. long, 8 ft. wide, and 51 ft. high?

Find the required dimension of the following solids:12. Solidity 459 cu. ft., length 8 ft., height 8 ft.

13. Solidity 1380 cu. yd., length 20.5 ft., depth 4 ft. 6 in. 14. If a packing-box 10 ft. 6 in. long and 51⁄2 ft. deep contains 462 cu. ft., how wide is it? If it contains 691 cu. ft.? 15. A mason used 768 cu. ft. of stone in building a wall 4 ft. high and 2 ft. thick. How long was it?

16. How many bricks 8 in. × 4 in. × 2 in. in a cart 8 ft. by 4 ft. by 2 ft.?

Review.

can be

put

1. Define Reduction of Denominate Numbers. How many kinds of reduction are there? What is Reduction Descending? State the principle of reduction descending. Repeat the rule. How are hundreds changed to tens? Tens to ones? What is the uniform multiplier in changing simple integers to lower orders? Are the multipliers in compound numbers uniform, or varying?

2. Define Reduction Ascending. State the principles of reduction ascending. Repeat the rule. How are ones changed to tens? Tens to hundreds? Hundreds to thousands? What is the uniform divisor in changing simple integers to higher orders of units? Are the divisors in compound numbers uniform, or varying?

3. What is meant by Addition of Compound Numbers? Subtraction of compound numbers? Multiplication of compound numbers? Division of compound numbers? Upon what general principles do operations upon compound numbers depend? Repeat each rule.

4. Define Rectangle. What dimensions has a rectangle? Define area, and explain how it may be found. State the principle. Repeat the rules to find the area and each dimension of a rectangle. Define Rectangular Solid. What dimensions has a rectangular solid? Define solidity, or capacity, and explain how it may be found. State the principle. Repeat the rules to find the solidity and each dimension of a rectangular solid.

General Review Problems.

1. Multiply (800+ 45 x 75) ÷ 167 by 750-11875 ÷ 95. 2. Divide 900 + 25 × 25 × 64 by 625 ÷ 25 + 84 × 75. 3. From 480 × 75 ÷ 90 take (125 ÷ 25) × 734 — 659. 4. Find the value of (913 +8,3%) x 36 (7511-54%).

15

5. How much is (951) 861) + 88 × 7,3 times §? 6. Find the result of (18.75 x 48.018) (125 x .004). 7. The minuend is $187.37, and the subtrahend $137.663. What is the remainder? If the subtrahend is $75.062?

8. The sum of three numbers is 875.0075. If two of them are 750 and .000075, what is the third?

9. What is the product of the three factors 14 of 13, 8 times 10, and 9918 times 8?

85

9

10. The product of three factors is 10 times 83, and two of them are 26 times 713 and 5 x 8. Find the third. 11. Find the quotient of of 1917 divided by the sum of 7 times 8+1 of 44. Of.0001 ÷ 100.0695 100.007.

13

12. The remainder is $1.37, the divisor 975, and the quotient $100.50. Find the dividend. If the divisor is .0975.

13. The divisor is 78, the quotient 325, and the remainder 88. What is 15 times the dividend?

14. The sum of four numbers is 132833, and three of them are 237, 456, and 10. What is the fourth?

40

3

15. The product of four factors is 1219, and three of them are 8 times 136, 49 of 3%, and 14+2. Find the fourth. 16. What is 7.007 + (700 × .075)? 800 + (.00088 x 80)? 400 + 10.0002300.00003.

17. From 131913 take 20,5 times. Find the sum. 18. To 5000 times .0004 add 25000 ÷ 5 times .00005. 19. Multiply 21% by 7 times 10, take 1911 from the product, and to the remainder add 192.

20. Multiply the sum of 65 and 894 by the quotient of 121 122. Divide the product by 113.

21. Divide the product of 25 thousand times 25 thousandths by the quotient of 25 thousand ÷ 25 thousandths.

ΤΣ

39

24. Change of 3 of 55 to 72ds, and change 36500, 17550, and 14455 to their lowest terms.

56160

25. Find the least common multiple of the first five prime odd numbers. The first five composite odd numbers.

26. Find the greatest number that exactly divides 21296 and 33528, and the smallest that exactly contains each.

27. Four partners put in business $3750.75, $5000.37, $4000.50, and $6250.183. At the end of the year the firm was worth $22000. What were the average profits?

28. How many pieces of stone flagging, each 71⁄2 feet square, are required to make a sidewalk 120 ft. long 3 ft. 9 in. wide?

30. Find the prime factors of 51968, 73008, and 86625. 31. Find the cost of 53 bales of cotton, each weighing 4.75 cwt., at $.131 per pound.

32. .00625 is of what number? % of what?

33. How many cu. in. are in 37.5 bu.? How many bushels in 212730.025 cu. in.?

34. How many cubic feet of lumber are in a load of 25 planks, each 15 ft. long, 10 in. wide, 2 in. thick?

35. From a 63-gallon cask, full of wine, there were drawn 20 gall. What was the balance worth at $2.75 per gallon?

36. At $.5625 per yard, how much delaine can be bought for $54, and how many dresses each 135 yd. can be made from it?

37. A farmer raised 343.75 bu. of corn from 11 acres, and 437.5 bu. from 14 acres. What was the average yield per acre?

38. At $75 an acre, what is the cost of a piece of land 150 rd. wide and 225 rd. long? And at $.75 a yard, how much will it cost to make a fence around it?

39. At $10 a hundred, how much will 225 cherry-trees cost? 40. A person who had 23 times $500, spent of it, and earned 23 times as much as remained. What had he then? 41. Divide 6125 by 5456875, and prove the result.

42. How many square yards in the walls of a room 30 ft. long, 18 ft. 4 in. wide, 10 ft. high? In the ceiling?

43. At $7 per cord, what is the value of the wood that can be put in a shed 16 ft. 8 in. long, 8 ft. 9 in. wide, 10 ft. high?

44. How many bushels of oats at $.663 a bushel will pay for 371⁄2 bu. of corn at 913 cents a bushel?

THE END.

Brooks' Elocution and Reading.

Chase & Stuart's Classical Series.

Crittenden Commercial Arithmetic.

Edward's Hand-Book of Mythology.

Gregory's Practical Logic.

Gregory's Christian Ethics.

Groesbeck's Practical Bookkeeping.
Kellerman's Elementary Botany.

Mills' Physiology and Hygiene.

Smyth's American Literature.

Thorpe's Civil Government.

Trimble's Hand-Book of Literature.

Trimble's Short Course in Literature.

Webb's Word Analysis.

Westlake's 3000 Practice Words.

Wilson's Elementary Algebra.