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5. Divide 1£ by lj. Multiply the same.

6. Divide £ of f of 2\ by %

7. Write and 2T^ in a decimal form. Give the division in decimals of the first by the second.

8. Divide .09 by .0016. Multiply them.

9. Divide 876.196 by 2.12. If the decimal point were moved, in the first, two places to the left, and, in the second, one place to the right, how many times greater or less would the quotient be?

10. Find the square root of 49.2804.

11. What is the fourth power of 2 ? of 0.2? of .02?

12. If a man travels 64 rods in .05 of an hour, how many minutes will it take him to go a mile?

13. Find the simple interest on $1,000 for 1 yr. 2 mos. and 12 ds.

14 How many feet, board measure, in a plank 12 ft. 4 in. long, 2 ft. 3 in. wide, and 4 in. thick? (Multiplication of Duodecimals.)

III.

1. What is the Least Common Multiple of 20, 24, and 36?

2. Add f, I 2^, and 3-&.

3. Multiply 48 by Divide Ah by

4. Eeduce - ~fgjo ^ to its simplest form.

5. Reduce J of a bushel to the fraction of a pint.

6. Reduce 5 yds. 2 ft. 6 in. to the decimal of a rod, long measure.

7. Multiply 34.27 by 60,000. Divide 10634.16 by .4506.

8. At what rate per cent must $ 370 be put on interest to gain $ 55.50 in three years?

9. What is the amount of $25 for 3 yrs& 5 mos. at compound interest?

10. What is the third power of 30? of .03?

11. What is the square root of 104.8576?

12. What are the contents of a granite block that is 8 ft. 9 in. long, 3 ft. 2 in. wide, and 2 ft. 5 in. thick? (Multiplication of Duodecimals.)

IV.

1. What is the Greatest Common Divisor of 1181 and 2741?

2. Eeduce f, h, and fa to a Common Denominator.

3. Divide £ of ^ by ^ of §$.

4. Add §, f and of f

5. Reduce of a gallon to quarts, pints, etc.

6. Multiply 4 lbs. 8 oz. 16 dwt. 20 gr. by 72.

7. Find the interest on $76.72 from April 18, 1852, to January 26, 1855, at 6 per cent.

8. What principal at 6 per cent will amount to $ 360,585 in 16 months?

9. Multiply .427 by 345.

10. Divide 87.69 by 47, also by .47.

11. What is the square root of 747.4756?

12. Give an example of a Continued Fraction.

V.

1. Name all the Prime numbers in the series of numbers between 1 and 30 inclusive; resolve all the Composite numbers into their Prime Factors; and name all the perfect squares, cubes, and other powers in the same series.

2. From £ of £ take \ of §.

3. Divide j| X 72£ by f of £ of 9|.

4. Reduce 9 rds. 1 ft. and 6 in. to the fraction of a furlong.

5. Multiply 8.764 by 40.015.

6. What is the square of 11 ? of .11?

7. Divide 769.428 by 200; by .00002.

'8. Transform the Infinite Decimal .2i6 into its equivalent Vulgar Fraction.

9. What quantity of boards will be required to lay a floor 14 ft. 8' 3" in length and 13 ft. 6' 9" in width? (Multiplication of Duodecimals.)

10. Find the square root of 4.190209.

11. Find the interest on $76.72 from April 18, 1852, to January 26, 1855, at 6 per cent.

12. If $ 50 gaih $ 5.60 in 3 yrs. 6 mos., at simple interest, what is the rate per cent?

13. Give an example of a Continued Fraction.

VI.

1. What are the Prime Factors of 360?

2. What part of a mile is one inch?

3. Eeduce ^ to a Simple Fraction.

4. Add | of a pound, f of a shilling, and £ of a penny together.

5. What is the product of $ of A of 15, and i| of llf?

6. Divide 100 by 4£

7. What is the square of 10.01?

8. Divide .1 by .0001. Divide 10 by .1.

9. Reduce A to a decimal. Eeduce yf^ to a Circulating Decimal.

10. What is the interest on $ 1461.75 for 4 yrs. 9 mos. at 8 per cent?

11. The interest on 8437.21 for 9 yrs. 9 mos. is $127,884 : what is the rate of interest?

12. Find the square root of 4.426816.

VII.

1. What is the Least Common Multiple of 21, 36, 50, and 64?

2. Add together f, £f, and and from their sum subtract

3. Multiply by & of 2\.

4. Eeduce of a furlong to inches.

5. Multiply 200.043 by 2.021.

6. Divide 9.00081 by 900; 4004004 by .002; .000624 by 324.

7. What are the contents of a granite block 12 ft. 2' 3' long, 6 ft. 8' 9" wide, and 4 ft. 9' 2" thick?

8. What is the amount of $5216.75 from January 21, 1860, to July 3, 1863, at 8 per cent, compound interest?

9. Find the cube of 10.1; of 1.01.

10. Find the square root of 49.87604.

11. Define a Circulating Decimal and give an example. What is a Continued Fraction?

12. What is the difference between an Arithmetical and a Geometrical Progression?

VIII.

1. What is a Prime Number? Find the Prime Factors of 4800.

2. "What Prime Factors compose the Greatest Common Divisor and the Least Common Multiple of several numbers? Find the Greatest Common Divisor and the Least Common Multiple of 84, 126, and 140.

3. From |- of subtract -fo of 11.

4. Divide A of ¥of3iby^L

5. Give the rule for pointing off in the multiplication of decimals, and explain the reason.

6. Multiply 0.0400268 by 0.260075.

7. Divide 0.011825369 by 5.884. What is the quotient of 118253690 by the same divisor?

8. Reduce jf^ to a Circulating Decimal. Verify the result by reducing it back to a Vulgar Fraction.

9. Reduce 0.845 of a mile to furlongs, rods, feet, and inches.

10. The interest on $ 127.50 from June 26, 1798, to May 8, 1802, was $36,975: calculate the rate of interest.

11. Find the square root of 7.333264

12. Find the cube root of 96702.579.

13. If 6 men can build 20 feet of a stone-wall in 10 days, how many men can build 360 feet of the same wall in 90 days?

IX.

1. Reduce 10917 to the product of its Prime Factors.

2. Find the Greatest Common Divisor of 720, 336, and 1736; Least Common Denominator of ff,

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