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

31
4. If the number 12 be increased by its double and be multiplied
by its treble, what multiple of the original number is the product?
5. Explain how any number may be multiplied by 11 by addition,
and divided by 9 by subtraction. Ex. 45789 x 11 and 45789 9.
6. Find the sum of all the numbers between 5000 and 5025 which
are not divisible by any one of the numbers 2, 3, 5, 7, or 11.
7. What equimultiples of 12, 18, 24, added together, make up
7776?
8. Divide the number 960 into four parts so that the parts may bo
equimultiples of 1, 3, 5, and 7.
9. Divide the number 1014 into three such parts such that 88 the
excess of the first part above the second may be equal to the excess of
the second above the third.
X.
1. If 19 be subtracted as often as possible from 1499, what will be
the final remainder?
2. How many times must 236 be subtracted from 114309 that the
final remainder may be 73245?
3. Divide 10149 by 7 and the quotient by 5; thence deduce the
true remainder, and shew that it is the same as after the division of
10149 by 35.
4. If division by a composite number be performed by successively
dividing by its prime or composite factors, shew how the complete
remainder may be found. Ex. 1437281 divided by 105.
5. The product of two numbers is 373625, the greater of them
is 875; find the sum and the difference of the two numbers.
6. Shew that the product of 3846 and 705 is equal to the quotient
arising from 51517170 divided by 19.
7. What number multiplied by 345 will give the same product as
2415 multiplied by 197.
XI.
1. Any number composed of three consecutive significant figures
is divisible by 3.
2. A number of six digits consisting of the repetition of any one of
the nine digits is divisible by 7, 11, and 13.
3. All numbers expressed by any number of the same digits are
respectively divisible by the sum of the digits. Exemplify this property by examples consisting of 5, 7, and 12 digits respectively.
4. If any numbers consisting of one, two, three, four, &c., figures
be multiplied by 9, the sums of the digits of the successive products
are either 9 or a multiple of 9.
5. In a number consisting of two digits, if the figure in the place
of tens be double that in the place of units, the number is divisible
by 7, and the quotient is the sum of the two figures. Explain why
this is so.
6. If any given number be separated into periods of three figures