Elementary arithmetic, with brief notices of its history... by Robert Potts.

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IV.
1. Shew that the product of two odd numbers is an odd number;
the product of two even numbers an even number; and the product,of an odd and an even number an even number.
2. How many times must 1874 be added to itself to make a total,of 163038?
3. Find the sum of twenty consecutive numbers beginning with
18547 by the shortest process.
4. Shew how to multiply 32165 by 648 in two lines.
5. Multiply 967548 by 492 in two lines.
6. Determine a number by which 4389 can be multiplied, so that
the product may lie between the limits of 500000 and 1000000.
7. Express MMIDCXCIX. and CCCXXIX. in the ordinary nu-merical characters; find their product, and express the result in the
-Ioman characters.
8. The product of 75 by 43 is 3225; how much must be added to it
to obtain the product of 77 by 43?
V.
1. WVhat is the object of division? In what cases may it be considered as a shortened subtraction?
2. What arithmetical operation bears the same relation to division
-that addition bears to multiplication?
3. The quotient of two numbers is the same as the quotient of any:equimultiples or equisubmultiples of the given numbers. Are the
remainders the same in the three cases? Give an example.
4. Explain clearly the process of dividing one large number by
another. Ex. Divide 143255 by 4093.
5. A number can be divided by 5, 25, 125, &c., by multiplying the
dividend by 2, 4, 8, &c., and marking off towards the left from the
unit's place, one, two, three, &c., figures. The figures on the left will
be the quotient, and those on the right will be 2, 4, 8, &c., times the
respective remainders. Explain the reason of this.
6. Express by means of figures and symbols of operation1. That the number eight increased by seven is equal to tho
product of five multiplied by three.
2. That the number ten diminished by four is equal to the
same number as thirty divided by five.
VI.
Find the quotient of the following numbers, and verify the truth,of each process:1. 3745687 divided by each of the nine digits respectively.
2. 28796478 by the factors of each of the numbers 49, 64, 120,
zand 132 respectively.:.. 1628756 by 3840, by 38400, and by 384000 respectively.