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

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EXERCISES.
I.
1. Upon what principle is the ordinary methocl of multiplication
lased? Is there any advantage in beginning with the right-hand
figure (1) of the multiplicand, (2) of the multiplier?
2. Explain the method for the multiplication of two numbers, each
consisting of several figures, and multiply 30071 by 20590, explaining
the reason for each part of the process.
3. Shew that the product of any number by a composite number
nmay be found by multiplying by its factors successively. Ex. Multiply
3605 by 21.
4. Shew that the product of 2356 by 135 may be found by multiplying 2356 by 11 and that product by 12, and adding 3 times the
-lultiplicand to the product.
5. Exemplify the truth that two or more factors will give the same
product in whatever order they are multiplied.
6. Any number may be multiplied by 5, 25, 125, &c., by annexing 1, 2, 3, &c., ciphers respectively to the number, and then
dividing it by 2, 4, 8, &c. Explain the reason of this rule.
7. In the multiplication of numbers, how do you prove the correctness of the operation by casting out the nines? Explain and give
r-easons for the rule, and shew the errors to which it is liable.
II.
Find the products of the following numbers:
1. 2567 and 256: 57834 and 123456: 18007 and 70081.
2. 2187642 and 5874568: 9876423 and 99999.
3. 2500 and 27: 2589 and 1200: 786300 and 4000.
4. 8426000 and 8426000: 783410 and 70001.
5. 87, 97, 101, 113, and 6845.
6. 12, 123, 1234, 12345, 123456, and 1234567.
III.
Multiply the following sets of numbers, each by means of 3 lines
of multiplication:1. 578657 by 729819.
2. 1234567890 by 4321089.
3. 328560 by 121711.
4. 43002073252 by 133112111.
5. 12345678 by 28814412.
6. 30040769503 by 172814412.