13. In 1872 the following ships passed through the Suez Canal; find the total: English, 761; French, 80; Italian, 66; Austrian, 61; Turkish, 33; German, 16; Dutch, 13; Portuguese, 10; Russian, 10.

14. A gentleman died and left his eldest son £21,350; to each of his three younger sons £12,450; to his eldest daughter £10,000; to each of his five younger daughters £9450; and to his four servants £315, £250, £100, and £40. What is the amount of these legacies ?

15. The total imports into England of gold, chiefly from Australia, and silver for the month of April 1874, were £2,153,365, showing a decrease of £1,200,000 as compared with April 1873. Find the imports of gold and silver in April 1873.

16. According to the German Army Lists their field forces number 705,700, the field reserve forces 243,540, and the garrison troops 375,700 men. Find the grand total.

17. The following coals were shipped from Newcastle to Melbourne; find how many tons: 2407, 4185, 17,208, 209 475, 611. 18. The following bales of wool came down to Sydney in 8 days; find the total number: 784, 41, 908, 4205, 91, 604, 721, 411.

SIMPLE SUBTRACTION.

SUBTRACTION teaches us to take one number from another, or to find the difference between two numbers; it is divided into Simple and Compound.

If two different numbers are written down, the one will be greater than the other; the greater is named the minuend, the less the subtrahend; and if the less be taken from the greater, the result is said to be the remainder, difference, or

answer.

To work out the question, the smaller number is placed under the larger, units under units, tens under tens, hundreds

under hundreds, etc. Begin at the right hand and take the units from the units, tens from the tens, etc., setting the remainder under the respective figures. When the lower figure is greater than the upper, it is a usual plan to borrow ten and add it to the upper, then subtract, repaying the ten back again by carrying one to the next figure on the left.

EXAMPLE.-Subtract 4758 from 76145.

First place the figures one under the other, the units under units, tens under tens, etc., thus:

Commence the sum in the following manner: 8 units from 5 units we cannot, we therefore add 10 units to the 5 making 15, then we can take 8 from 15 and 7 are left, which digit is placed in the units' place. Because we have added 1 ten to the upper unit, we must add 1 to the 5 to maintain the balance, so that the difference between the two numbers may not be altered. Now we say 5 and 1 are 6; 6 from 4 we cannot, so borrow 10 (it is really 10 times 10), and say 10 and 4 are 14, 6 from this 14 leaves 8; place the 8 under the tens, and carry 1 to the 7, because a 10 was added to the 4. Next say 1 and 7 are 8, 8 from 1 we cannot, borrow 10 again, then 10 and 1 are 11, 8 from 11 leaves 3, which is placed under the hundreds, and 1 carried to the 4, because 10 was added to the 1. Now say 1 and 4 are 5, 5 from 6 leaves 1; put down the 1; lastly, O from 7 leaves 7; put down 7.

Second Method.-When the figures in the lower line are greater in value than the corresponding figures in the upper, there is great difficulty with beginners in working sums in simple subtraction correctly. Take the example below.

5865
2987

2878

Proceed thus: (1.) 7 from 5 we cannot; now add to the 7 a number that will make it 10, which in this case is 3; we add the 3 to the upper figure 5, which makes 8, the 8 is put down as the unit in the remainder.

(2.) Now carry 1 to the 8, which makes it 9; 9 from 6 we cannot, then add to 9 enough to make it 10, 1, this is added to the 6 to make 7 for the answer in the tens' place.

(3.) Carry 1, then 1 and 9 are 10; this number is already 10, so nothing is added to complete it, and we put down the 8 in the bottom line for the hundreds.

(4.) Carry 1; 1 and 2 are 3, which taken from the 5 leaves 2, completing the sum.

22. Subtract 356 from 634. Subtract 40009 from 67801, and 2,001,425 from three millions.

23. Add together forty-one thousand six hundred and sixty-two; eight million five thousand two hundred and thirty-four; nine hundred and nineteen thousand and nineteen; thirty thousand and six hundred; eight hundred and eight thousand and eighty-eight; and from the sum take away seven hundred and thirteen thousand six hundred and ninety-four; and write the answer in words.

24. A corn merchant went to market with £1000, he purchased corn to the value of £844; how much had he left?

25. Suppose the distance between Sydney and Port Macquarie is 325 miles, between Sydney and Brisbane 420 miles; how much further is Brisbane from Sydney than Port Macquarie ?

26. If the equatorial diameter of the earth is 20,957,407 feet, and the polar 20,820,121 feet; find the difference between the two.

27. Suppose that the population of one of our towns is now 847,385, and that 10 years ago it was 804; how much has the number of the inhabitants increased?

SIMPLE MULTIPLICATION.

MULTIPLICATION is the method of finding the sum of a number after it has been repeated any given number of times; or it is the method of ascertaining the amount of several equal numbers when added together any given number of times.

Multiplicand is the number to be multiplied.

Multiplier is the number by which the multiplicand is multiplied.

Product is the result obtained by multiplying any two or more numbers together.

Factors. The multiplicand and multipliers are also named factors.

Continued Product.-When three or more numbers are multiplied together, the result or answer is often spoken of as the continued product.

FIRST ILLUSTRATION.-The following example will be taken to explain the method and theory of the multiplication of numbers. Multiply 71342 by 9.

(1.) To work out the sum, commence by placing the multiplier under the multiplicand, units under units, tens under tens, etc.

(2.) Begin at the right hand, and multiply each figure in the multiplicand separately, by the figure in the multiplier, setting down the figures in their order; if the product from multiplication consists of two figures, put down the right-hand figure and carry the left.

(3.) The working is begun by saying 9 times 2 units are 18 units, or 1 ten and 8 units; put down the 8 units under the units, and carry the 1 ten.

(4.) 9 times 4 tens are 36 tens, and one ten carried make 37 tens or 3 hundreds and 7 tens; put the 7 under the tens, and carry the 3 to the hundreds.

(5.) 9 times 3 hundreds are 27 hundreds, and 3 hundreds carried make 30 hundreds, or 3 thousands and no hundreds ; put O for hundreds under the hundreds, and carry the 3.

(6.) We have 9 times 1 thousand are 9 thousands, and 3 we carried are 12 thousands, or 1 ten thousand and 2 thousands ; putting down the 2 we carry the 1.

(7.) 9 times 7 tens of thousands gives 63 tens of thousands, to which, if the 1 ten thousand carried be added, gives 64 tens of thousands; these are put down as the completion of the product.

On the right hand at B will be seen the same sum with each figure put down according to its local value; when the operation is performed on the figures so standing, we see better the reasoning employed in the working.

SECOND ILLUSTRATION.-The same kind of reasoning must now be extended to two and more figures. Multiply 7564 by 234.

(1.) The multiplication by the 4 is performed as in the first illustration.

(2.) To multiply by the 3, which is 3 tens or 30, we proceed in the same manner, but mentally omit the tens. Thus we say 3 times 4 are 12; now it is not really 3 times 4, but 30 times 4, which are 120, so we put down the cypher in the units' place and the 2 in the tens' place, and carry the 1 hundred.

(3.) 3 times 6 are 18, but it is really 30 times 60, or 6 tens multiplied by 3 tens, which make 18 hundreds, and 1 hundred carried from the previous multiplication give 19 hundreds or 1 thousand 9 hundreds; placing the 9 under the hundreds, the 1 is carried forward for thousands.

(4.) 3 times 5 are 15, or actually 30 times 500, or 3 tens multiplied by 500 give 15,000, or 15 thousands, which, with the 1 thousand carried from the last operation, make 16 thousands; the 6 thousand is placed under the units of thousands, and the 1 tens of thousands carried forwards.

(5.) Three sevens are 21 (tens of thousands), and 1 carried makes 22 tens of thousands, which are placed down as the completion of the line.

The multiplication by the 2 or 200 may be thus explained: