13. What is the value of (x) x, and what will be the remainder when is subtracted from the product so obtained?

17. Explain the principles by which the addition and subtraction of fractions is effected.

18. Prove the rule for division of vulgar fractions by each other.

19. Define the terms fraction, proper fraction, inproper fraction, mixed number, compound fraction, complex fraction.

(20) 2 of 5 bushels + 1 of 5 gallons.

(21) (1 of 3 of 1 − (1 − + 1)} of Is. 6d.

4. What is the value of the sum of 10 of a guinea, of a sovereign, and 21 of a crown?

5. If of an estate be worth 3003, what is the whole worth?

6. If I sell 1⁄2 of 4 of an estate, what portion of it have I left?

7. If a person pays away of his income, and invests of the remainder, what portion of the whole has he left?

8. A person, having sold of an estate, bequeaths of the remainder to his son, and leaves the rest to be divided equally between three charities: if each of the latter receives 1367. 5s. what was the value of the whole estate?

9. Two pipes together fill a cistern in 1 hour, and one of them alone fills it in 1 hour: how long will it take the other alone to fill it?

10. If one man can do a piece of work in 10 days which would take another man 15 days, in what time could they do it both working together?

11. A and B can do a piece of work in 7 days which B and C can do in 8 days, or all three together can do in 5 days: what portion of the whole can each do in one day?

12. Reduce

(1) 3 cwt. 2 qrs. 3 lbs. to the fraction of a ton.
(2) I rood 5 perches to the fraction of an acre.
(3) 12 gallons 2 quarts of wine to the fraction of
a hogshead.

(4) 5 furlongs 13 poles I yard 2 feet 6 inches to
the fraction of a mile.

(5) 2 weeks 2 days 19 hours to the fraction of a month.

(6) 12s. 9d. to the fraction of 15s. 6d.

(7) 8 cwt. 2 qrs. 2 lbs. to the fraction of 18 cwt. 3 qrs. 5 lbs.

(8) 14 hours 15 minutes to the fraction of 31 days. (9) 6s. 81d. to the fraction of 12d.

(10) 2 guineas to the fraction of 137

(11)

of a guinea + of a sixpence to the fraction of Il

(12) 21 of a groat +

of a crown + of a guinea

to the fraction of Il

13. Reduce

(1)

(2)

of a guinea to the fraction of a pound.

to the fraction of a penny.

(3) of a guinea to the fraction of 23s. 4d.

(+) 1⁄2 of 1⁄2 of 1 of 157. to the fraction of 2s. 8d.
cwt. to the fraction of a lb.

(5)

(6) ğ of lb. Troy to the fraction of lb. Avoir.

(7) of a cwt. to the fraction of a lb.

(8) 25 of a week to the fraction of an hour.

of 15s. 6d. to the fraction of 57.

of a guinea to the fraction of a sovereign. of a pint to the fraction of a gallon.

3. Find the value of 606 +005 — 6·0606.

(15) 026 by 3'3, by 33, by

(16) 223 by 23, by 2.3, by 023, and by 23 separately.

(1) 998-824392 by 018. (2) 160·68 by 3·9.

(5) 52 by 32. (6) 18 by 500. (7) 611 by 13.

(8) 07306 by 1'405.

(10) 85 by 00017.

(12) 2.961 by 007.

(14) 3 by OI.

(9) 119.18 by 059.

(11) 68 by '000017.

(13) 03 by 001.

(15) 2175.68 by 100.

(16) 736 by 02 and 736 by 2.

(17) 101 by 101, and '101 by 10'1.

(18) 486 by 18, and by 18; and 486 by 18, by 18, and by 0018.

(19) 352 by 2.2, by '22, and by 22; and 35°2 by •22, and by 022.

(20) 6978-6 by 3'24.
(22) 8727587 by 162.
(24) 76 by 01254.
(26) 0002 by '0163.

(21) 76 by 1254.

(23) 05625 by '0275. (25) 2 by 021.

(27) 211 by 15.

6. Which is the greatest and which the least of
25 × 075, 2.6257,5 x '05 ?

7. Find the value of 375 × 375-025 × 025

*375-025

23

(10) 16. (11) 580.

(14) 129. (15) 17.

55

9. Find the decimals equivalent to + -, and to

(12)

3

1

(13) 35.

4

44

125

10. Find the value of 134 + 12 +81-41 by decimals and by vulgar fractions.

11. When a fraction has been reduced to its lowest terms, and it is required to express it as a decimal, how