5. What must be paid for 105 hundred weight of bullets, at 5s. 72d. per hundred weight?

85. If the multiplier cannot be produced by the multiplication of two or more single figures, take the nearest number to it which can be so produced, and multiply by its factors as before. Then augment, or diminish the result by as many times the multiplicand as the said number is less or greater than the multiplier.

£ s. d.

6. At 4 1 10 per thousand, what is the cost of 58 thousand bricks?

I. When oats are at 1 17 9 per quarter, what is that per bushel?

2. If the interest of 100 for a year be 3, what is the interest of 70 for

87. When the divisor is the product of two or more simple aumbers, divide by them separately. (30)

£ s. d.

3. If a chaldron of coals cost 2 10 3, what is that' per bushel?

4. At 3 guineas the hundred weight, what is that per lh.?

88. If the divisor cannot be resolved into small factors, divide by the whole at once after the manner of long division.

£ s. d.

6. If the whole pay of 179 men for 61 days be 625 11 41, what is the daily pay of each?

89. III. When the multiplier, or the divisor, is a vulgar fraction, it is evident that the product in the former case, and the , quotient in the latter, will each be obtained by both multiplication and division, except the numerator of the fraction be 1.For the product of the numerator and multiplicand divided by the denominator will give the answer in multiplication. And the product of the denominator and dividend divided by the numerator is the quotient in division,

Ton. C. lb.

Examples.

1. If 86 17 100 of provisions will serve a garrison 12 months, what quantity will be necessary for 8 months?

8 months of 12 months.

T. C. lb.

86 17 100

2

3)173 15 88

57 18 66 Ans.

£ s. d.

2. If I agree to give a labourer 1 6 6 for working 10 days, what must

£ s. d.

4. If 7 hundred weight cost 6 13 4, what is that per ton?

70

90. When the multiplier is a mixt number, the multiplication may be made by the parts separately and the products added together for the answer. If the divisor is a mixt number reduce it to an improper fraction. And when decimals are in the multiplier or divisor, reduce the multiplicand or dividend to the lowest denomination, and find the answer by the rules of Reduction.

OF ALIQUOT PARTS.

91. AN aliquot part of a number is any other number which will divide it without leaving a remainder. Thus if the aliquot parts are confined to integers, 1, 2, and 3, will be all the aliquot parts of 6; 1 being the , 2 the 4, and 3 the of 6. Fractions 1/2/24 and mixt numbers however, are aliquot parts, as or the 5th of 1 is an aliquot part of 1; 3 or of 10, an aliquot part of 10; 4 or of 13, an aliquot part of 13, &c. Also 3s. 4d. and 2s. 6d. are aliquot parts of a pound, the former being %, and the latter. 4 inches is an aliquot part of a foot and also of a yard, being of the former, and of the latter, &c. ģ

The principal use of aliquot parts is to abridge the operations in compound multiplication, or when several numbers of differ ent denominations are to be multiplied together. The method by aliquot parts is also called Practice.

Here, instead of multiplying by 4, I take, the multiplicand, and again the of that, or 1; therefore both these parts together make of the multiplicand to be added to the product by 6.