I. (1) What weight may be bought for £3 14s. 4d. when 5 cwt. 3 qrs. 16 lbs. cost £1.

(2) If I be given for 8 cwt. 2 qrs. 8 lbs., what weight may be bought for £2 13s. 81d. ?

(3) If 5 cwt. I qr. 12 lbs. be bought for £1, what weight may be bought for £1 13s. 2d. ?

(4) If I ton 5 cwt. 2 qrs. 24 lbs. cost £1, what weight may be bought for £3 17s. 41d. ?

(5) What weight may be bought for 12s. 2 d., when I is paid for 5 tons II cwt. I qr. 20 lbs. ? (6) If 6 lbs. 2 oz troy cost £1, what weight may be bought for £1 16s. 101d. ?

(7) If I worth of fuel be consumed in 43 hrs. 28 min., how long would £2 13s. 5d. worth last? (8) If the railway fare be 1s. for 3 m. 4 fur. 32 p., how far may a person travel for IIS. 10d.?

(9) If a yard of silk be woven in 3 hrs. 39 min. 12 sec., how long would it take to weave a piece 3 yds. 2 qrs. 3 nls. long?

(10) How much calico worth is. a yard should be given for 10 yds. 2 nls. of cloth worth 15s. 8d. per yard?

CHAPTER VII.

EXACT DIVISORS.

29. An exact divisor of a number is one that is contained in it a certain number of times without remainder. Thus 3 is an exact divisor of 12; 5 of 15; 6 of 42, &c.

30. An exact divisor of a number is sometimes called a measure of the number.

31. A prime number is one whose only exact divisors are itself and unity. Thus 2, 3, 5, 7, II, 13 are prime numbers.

32. Numbers are prime to each other when the only exact divisor of each of them is unity. Thus 8 and 9 are prime to each other.

33. All other than prime numbers are called composite numbers, and prime numbers which measure them are called their prime factors.

34. Test of divisibility :

Every even number is divisible by 2.

A number is divisible by 3 if the sum of its digits be so divisible.

A number is divisible by 4 if the number composed of the last two digits be so divisible. Every number ending with oor 5 is divisible by 5.