PROMISCUOUS EXAMPLES.

1. If 4 men in 5 days eat 7lb. of bread, how much will suffice 16 men 15 days? Ans. 84lb. 2. If 100dols. gain $3.50 interest in one year, what sum will gain $38.50 in 1 year and three months? Ans. 880dols. 3. If it take 5 men to make 150 pair of shoes in 20 days, how many men can make 1350 pair in 60 days?

Ans. 15.

4. If the wages of 6 men for 21 weeks be 120L. what will be the wages of 14 men for 46 weeks?

Ans. 613L. 6s. 8d. 5. If 333L. 6s. 8d. gain 15L. interest in 9 months, what sum will gain 6L. in 12 months?

Ans. 100L. 6. A wall which is to be built to the height of 21 feet, has been raised 9 feet in 6 days, by 12 men: hov many men must be employed to finish the work in days? Ans. 36 men

PRACTICE.

Practice is a short method of ascertaining the value cf any number of articles, or of pounds, yards, &c. by the given price of one article, one pound, or one yard, &. Practice may be proved by Compound Multiplication, or by the Single Rule of Three Direct.

An aliquot part of a number, is any number that will divide it without a remainder; thus, 4 is an aliquot part of 20, and 8 of 56. A sum or quantity is an aliquot part of a greater sum or quantity, when a certain number thereof will make the greater: thus a shilling is an aliquot part of a pound, because 20 shillings make one pound.

When the price is less than a penny, work by

RULE 1.

If the price be a farthing, or a halfpenny, set down the value of the given number at a penny, and take such part of that sum as the price is of a penny, for the answer in pence.

*

If the price be three farthings, find the value of the given number at a halfpenny, and afterwards at a farthing; then add the two results together, and their amount will be the answer.

*

** If the learner be un ble to tell the denomination of a quotient, or how to proceed with remainders, it would be useful to refer him to examples 14, 15, and 16, under Rule 1, and 7, 8, under Rule 3, Compound Division.

EXAMPLES.

1. What is the value of 4528 quills, at 4 each.

2. What is the value of 4528 quills, at

each?

4528 value at 1d.

2264 value at

1132 value at 1.

12)3396 Ans.

*The value of any number of articles at a penny, each, is that number of pence: thus, the value of two things at a penny, each, is two pence: of three things, three pence; of twenty things, twenty pence, &c.; and, as a farthing is the fourth part of a penny, the value at a farthing must be a fourth part of the value at a penny; and as two farthings are the half of a penny, the value at two farthings must be half of the value at a penny, &c.

This explanation of the rule, with a little variation, will apply to most of the other rules of Practice.

When the price is not less than a penny, but less than a shilling, and is an aliquot part of a shilling, work by

RULE 2.

Set down the value of the given number at a shilling and take such part of it as the price is of a shilling, for the answer.

EXAMPLES.

1. What is the value of 7612lb. of rosin, at 1d. per lb. and also at 11⁄2d. per lb.?

| 1d. | | 7612 value at 1s. | 14d. | | 7612 value at is

210)634 4

210)951 6

Ans. redu. 31L. 14s. 4d. Ans. reduced 47L. 11s 6d.

When the price is not less than a penny, but less than a shilling, and is no aliquot part of a shilling, work by

RULE 3.

Separate the price into parts, one of which shall be an aliquot part of a shilling, and the rest, either aliquot parts of a shilling or of one of the other parts. Find the value at each of the parts, agreeably to the tenor of the preceding rules, and add the several results toge ther, for the answer,

EXAMPLES.

1. What is the value of 6192 yards of tape, at 24d. per yard?

2. What is the value of 3711lb. of sugar, at 73 per lb.?

210)23916 84 Ans. in shillings, &c.

Answer reduced 119L. 16s. 84d.

Note. In werking the former of these examples, we find the value of the given number at 2d. by Rule 2, and divide the result by 8 to find the value at ; for as is an eighth part of 2d. the value at must be an eighth part of the value at 2d. The latter example is wrought in a similar manner.

d.

L. S. d.

Answer 33 14

When the price is not less than a shilling, but less than two shillings, work by

RULE 4.

Set down the value of the given number, at a shilling, and to this add the value at the rest of the price, found by the preceding rules.

EXAMPLES.

1. What is the value of 725 yards of muslin, 13 d.

20)8157 Ans. in shillings, &c.

Ans. reduced 40L. 15s. 74d.

When the price is any number of shillings under 20, work by

RULE 5.

Set down the value of the given number at a shilling, and multiply that sum by the number of shillings in the price: the product will be the answer.

*

Or,

If the price be an aliquot part of a pound, set down the value of the given number, at a pound, and take such part of that sum as the price is of a pound, for the answer.

EXAMPLES.

1. What is the value of 528 bu. of apples, at 3s. per bu.? 2. What is the value of 750 yards of linen, at 5s. per yd.?

S.

528 value at 1s.
3

L.

| 5s. | | 750 value at 11.

20)1584 Ans. in shillings.

Ans. 79L. 4s.

Ans. 187L. 10s.

As two shillings are twice one shilling, the value of any number of articles, at two shillings, each, must be twice their value at one shilling; and as three shillings are three times one shilling, the value at three shillings, must be three times the value at one shilling, &c.