Ex. 9. How many days difference is there between what are usually called the Summer and Winter portions of the year, or between the days from the Vernal to the Autumnal equinox, and the days from the Autumnal to the Vernal equinox? (See Ex. 6. Compound Addition.)

Ex. 10. If I have to pay for certain goods purchased at twelve months' credit, £ 171 3 6-What shall I have to pay for them at present, if a discount of £ 17 3 6 be allowed me for ready money?

Ex. 11. What must be paid for goods which amount to £ 3 7 7, upon which a discount is allowed of 3 s. 6 d.?

Ex. 12. If the produce of certain goods sold by my agent on my account be £ 571 14 4, and the amount of his charges be £ 47 3 11-What would be the net proceeds, or the amount that would remain after the charges were deducted?

Ex. 13. I borrowed of my friend £ 200, and I have repaid him £18 10, £ 25, £ 17 6 4, £ 100, and £ 13 18 6-How much am I still indebted to him?

Ex. 14. An agent in London had consigned to him by a planter in Jamaica 60 barrels of Coffee, which produced £ 1074 13 0, upon which the charges were £ 477 16 4; 10 tons of Logwood, which produced £ 142 9 2, upon which the charges were £ 46 2 2; 16 bags of Pimento, which produced £ 41 13 11, upon which the charges were £ 15 9 6; and 20 hhds. of Sugar, which produced £ 1155 13 6, upon which the charges were £ 621 14 0-What were the net proceeds of each of these sales, and if the planter had drawn £ 1000 on the credit of these consignments, what balance would be due to him?

ANSWERS.

Ex. 1. £

2.

1118 11 6

122 17 1 Ex. 8. Dr. Side £ 256802 9 7 Cr. Side 169077 14 3

COMPOUND MULTIPLICATION.

Rule. Multiply each part of the given quantity, beginning with the lowest, by the given number, and put down the product as in Compound Addition.

Observe. When the multiplier is above 12, if it is a double multiplier, multiply successively by each factor; if it is not a double multiplier, either multiply by the nearest double multiplier, and add or subtract the product of the top line by the difference, or multiply by the units, tens, &c. and add the products together.

If the multiplier is very large, take 10 times, 100 times, 1000 times, &c. as far as the highest denomination of the multiplier; then multiply each product and the top line by the proper figures in the multiplier, and add the products together. Or, reduce the given quantity into its lowest denomination, multiply it as in Simple Long Multiplication, and reduce the product into as high a denomination as is required.

To multiply by 17, we take 7 times and 10 times, and add the products together; but we may take 4 times 4 for 16 times, and add in once the top line.

Observe. In multiplication of money, farthings multiplied by 4 produce the same number of pence; pence multiplied by 12 produce the same number of shillings; and shillings by 20, the same number of pounds. So, generally, a quantity in a lower denomination multiplied by the number making 1 of a higher denomination, produces the same number of that higher denomination; as 7 inches multiplied by 12 produce 7 feet.

See the Examples and Exercises in page 40.

£ S. d.

81 9

When the nearest double multiplier is used, the number of times to be added or subtracted may be put against the 1st multiplier, with the sign + (plus) or (minus).

Example 2. To multiply by 29, 58, and 59.

£ S. d.

42 14 73
4+1

170 18 5

£ 1239 3 931

£ 1346 13 6

£ 4726 3 1

When we have to add in only once, we take it in while we work the second product; or when we have to subtract only once, we subtract the top line after we have taken the second product; but if we have to add or subtract more than once, it is necessary to express the additional product.

In the multiplication of money by 10, it is to be observed, that we may at once put down the shillings and pence that make the product of the given pence; and that half the number of the shillings is the unit figure of the number of the pounds, putting down 1 ten shillings if there is 1 over; then the figures of the given pounds may be put down as so many tens, without the trouble of multiplying them.

N. B. As these Exercises, as well as those to the following Examples, and those on the Weights and Measures in the following page, are rather difficult for a young beginner, they may be omitted the first time of the pupil's going through Compound Multiplication; therefore from Ex. 18. he may go forward to Compound Division.