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ARITHMETIC.

SECTION I.

1. Explain each step in the process of subtracting 750 from 805.

2. Explain each step of the process in multiplying 1087 by 5050.

3. Explain each step in the division of £70 10s. 11d. by 820, and express clearly what is the value of the remainder.

SECTION II.

1. Find by practice the value of 5 cwt. 1 qr. 19 lbs. at £3 15s. per cwt.

2. If 11 articles cost 15s. what would 17 cost? Explain each step of the process of working the sum. 3. If 5 men receive £18 15s. wages for 12 months, what will be the wages of 16 men for 20 months?

1. Subtract of

16s. 8 d.

SECTION III.

from 1, and find the value of of

2. What part of 5 guineas is 13s. 4d.?

3. Show that dividing the numerator of a fraction by any number gives the same result as multiplying the denominator by the same number.

SECTION IV.

1. Multiply 0017 by 450, and give the reason for the correct placing of the decimal point in the product.

2. Reduce 4s. 7d. to the decimal of a pound.

B

3. Divide 570 by 005, and give the reason for the correct placing of the decimal point in the quotient. 4. Extract the cube root of '04 to 3 places of decimals. Give the reason for the operation by which you divide the number into periods at the commencement of the process.

SECTION I.

1. "Explain each step in the process of subtracting 750 from 850."

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The result is verified by the resolution of the respective numbers, as seen above; but to exhibit and prove the usual mode of operation, it must be premised that "the difference of two numbers is not affected by adding any equal number to each, and then performing the subtraction ;" thus, 6 4 16 14..

Now in order to make each figure in the subtrahend less than the corresponding one in the minuend, we will add a number of tens to the latter to accomplish the object; but the same must be added to the lower line; and as the numbers increase in a tenfold ratio, let us add ten tens, or one hundred to each. The figures will then stand thus,

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Hence the rule for "borrowing ten" and "carrying one."

2. "Explain each step in the process in multiplying 1087 by 5050."

This question requires us to find the resulting number after the continued addition of 1087 for 5050 times.

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As a cypher occupies the units' place in the multiplier, it is brought down to hold a similar position in the quotient. Then the operation of multiplying by 5 is commenced; and this is done in the same manner as though 5 held the units' place. Thus 5 times 7 units are 35 units 3 tens' + 5 units; the units may be placed under the 5, and the 3 tens carried to the result of the tens. The whole operation will be clearly seen as follows:

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1 thousand 5 thousands. Collecting these results, we obtain 5 thousand + 4 hundred + 3 tens + 5 units, or 5435. Now it was not 5, but 50, by which we were to multiply; consequently, the result is 10 times too small. To multiply by 10, the figures have only to be removed each one place to the left. Hence, by "bringing down the cypher," we obtain 50 times the multiplicand. The same process could be applied to the other significant figure of the multiplier; after the result is obtained, multiply by the third power of 10, or, which is the same

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