1.

V. COMPOUND MULTIPLICATION AND DIVISION.

TO MULTIPLY BY ANY NUMBER A GIVEN COMPOUND QUANTITY.

Rule 1. If the multiplier be not greater than 12, write the multiplier under the number of the lowest denomination in the multiplicand, and multiply this by the multiplier. Convert the product into units of the next higher denomination; set down the remainder, if any, and carry the higher units to the next denomination.

Multiply the number of the next denomination by the multiplier, and to the product add the units carried from the former product.

Proceed in this way, till all the numbers in the multiplicand have been multiplied; write the last product in full.

Rule 2. If the multiplier be greater than 12, and capable of being resolved into factors not greater than 12, multiply by any one of the factors, this product by another, this by a third, and so on. till all the factors have been used.

Rule 3. If the multiplier be greater than 12, and not capable of being resolved into factors less than 12, take the next smaller or greater number than the multiplier, which is capable of being resolved into factors not greater than 12. Multiply by this, by last Rule; and multiply the multiplicand by the difference between the multiplier used and the given one. Add, or subtract, this product to or from the former one, according as the multiplier used was too small or too large.

Or-Multiply by 10's in succession, a number of times less by one than the number of figures in the multiplier. Multiply the multiplicand by the units' figure in the multiplier; the 1st product by the tens' figure; the 2nd by the hundreds' figure, and so on. Add these last products together: the sum is the product required.

6. Bought pieces of silver plate weighing 6 oz. 10oz. 25 oz. find their cost at £2: 12 : 3 per oz.

7. Given to an equal number of men, women, and children, in all 99 persons, sums of 2s. 6d., Is. 6d., 6d. respectively, how much was given altogether?

II. TO DIVIDE A COMPOUND QUANTITY BY ANY NUMBER.

Rule. Write the dividend and divisor in a line, with a curved line between them.

Divide the number of the highest denomination by the divisor; the quotient is the first term of the quotient required.

Change the remainder into a number of the next lower denomination,

add it to the number of that denomination in the dividend, and divide the sum by the divisor.

Proceed in the same manner, till the whole dividend has been divided.

Note. If the divisor be not greater than 12, or composed of factors not greater than 12, the division may be carried on in the method of short division. If the divisor be greater than 12, and not composed of such factors, the division will be in the manner of long division.

4. Divide 1087 tons 10 cwt. 1 qr. 15 lbs. by 196.

5. If 53 purses contain £4307: 11: 6, how much is in each, supposing all to contain the same?

III.

TO MULTIPLY A COMPOUND QUANTITY BY A VULGAR FRACTION.

Rule 1. Express the compound quantity as a fraction of some one denomination involved; multiply by the multiplier, and express the result in positive terms.

Rule 2. Multiply by the numerator of the fraction, and divide by the denominator. If the multiplier be a mixed number, multiply by the integer and fraction separately, and add the products.

Note. The 1st method is preferable, when denominator is large; the 2nd, when small.