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60 seconds make
1 minute, marked min. 60 minutes
hr. 24 hours
da. 7 days
wk. 52 weeks and 1 day,
yr. 365 days, make Every fourth year contains 366 days, and is called a leap year.
NAMES OF THE MONTHS, WITH DAYS IN EACH MONTH. January 31 days. July
31 days. February 28
DIVISIONS OF THE CIRCLE. 60 seconds make 1 minute, marked
min, or 60 minutes 1 degree
deg. or 30 degrees 1 sign
S. 12 signs
I circle of the zodiac, C.
gr. 20 articles
sc. 24 sheets of paper 1 quire,
qr. 20 quires
SIGNS USED IN ARITHMETIC. + The first, a straight cross, called plus, signifies more;
and when placed betwixt any two figures, denotes that they are to be added : thus 4 + 8 equal to 12. The second mark, a short horizontal line, means minus, less; and when placed between two figures, signifies that they are to be subtracted: thus 6 - 3
remains 3. x The third is a cross, but unlike the first; its lines
are sloping lines. It is sometimes called into, and signifies, when placed between two numbers, that
they are to be multiplied : thus 7 x 4, product 28. • The fourth is the sign of division, and is used instead
of the word by; and when written between two numbers, signifies that the greater is to be divided
by the less: thus 8 = 4, quotient 2. = The fifth, two parallel straight lines, is the sign of
equality, and signifies equal to. By understanding these signs, your work may be much abbreviated, as you will see by the following example :
5 + 7–8 x 9 6 = 6. The above line is thus read : 5 added to 7, from which subtract 8, multiply what remains by 9, and divide the product by 6 ; the result will be 6; or,
5 plus ï minus 8 into 9 by 6 is 6.
Being now able to read and write figures, and having acquired a knowledge of arithmetical tables, let us proceed to the working of figures, by which every object of business or calculation can be accomplished.
You will be surprised to learn that this art, so valuable in itself, and so necessary to know, requires but these two simple methods for working the most intricate questions, viz., first, to join numbers; secondly, to separate them.
For these two processes we have four rules, which are called the four fundamental rules, viz., Addition, Subtraction, Multiplication, and Division.
Addition and Multiplication are used for joining num. bers together ; Subtraction and Division are used for separating them.
ADDITION Is the art of adding numbers together, and collecting their amounts in one sum, or, as it is called, a total, and is thus performed.
Suppose you were required to add together the following figures, viz., 6, 4, 7, 9; you would write them in an upright row or column, thus : 6 drawing a line under the bottom figure, which 4 you begin to add, saying, 9 and 7 are sixteen, and ng 4 make twenty, and 6 make twenty-six; which 9 sum you write under the bottom line, and the work is complete. In like manner are all numbers 26 added, however large in their amount. The only care required is, when writing your figures in a column, to have each figure in its proper place; that is to say, the units under the units, the tens under the tens, and the hundreds under the hundreds, &c., as you will see in the following example.
Add together the following sums; 273, 97, 4769, 9, 6436, 17, 7983, 247.
Having written the first number, 273, you 273 write the remaining numbers, by beginning at 97 the right hand, placing the unit, or right 4769 figure of each number under the unit of the
9 number already written ; and by taking care
6436 that you copy each number correctly, from 17 right to left, you will by that means have 7983 each figure in its place. You then commence 247 at the bottom unit, saying, and 3 are ten, and 7 make seventeen, and 6 make twenty- 19831 three, and 9 make thirty-two, and 9 make forty-one, and 7 make forty-eight, and 3 make fifty-one; which is, as you know, five tens and one. I write the I down under the place of units, and carry or add the 5 to the next column, which you know from its place to be tens, and begin again by saying, 5 and 4 are nine, and 8 make seventeen, and 1 makes eighteen, and 3 make twenty-one, and 6 make twenty-seven, and 9 make thirty-six, and 7 make forty-three. I write the 3 under the place of tens, and carry the 4 to the next figure, which is in the third column, or place of hundreds, saying, 4 and 2 are 6, and 9 make fifteen, and 4 make nineteen, and 7 make twenty-six, and 2 make twentyeight. I write the 8 in the place of hundreds, and carry the 2 to the next figure, which is in the fourth column, or that of thousands, saying, 2 and 7 are nine, and 6 are fifteen, and 4 make 19, which I write in full, there being no more figures to add, the 9 in the fourth, or place of thousands, and the 1 in the fifth, or place of tens of thousands.
The total is nineteen thousand eight hundred and thirty-one.
Set the example down on your slate, and add each column as you read the instructions for doing so ; when you thoroughly understand it, add for practice the following sums.
(10.) How many days are in the first six months of the year ? how many in the last six ? and how many in the whole ?
(11.) Add 6247, 4976, 2795, 14, 4976, 8394 and 998.
(12.) A lease is granted in 1847 for 99 years; when will it expire?
(13.) A draper sold 47 yards of cloth on Thursday, 102 yards on Friday, and 76 on Saturday; how many yards did he sell in the three days?
(14.) If A. has £60, B. £4 more than A., and C. as much again as B. ; how much is the whole amount of their money?
(15.) I expended on Monday £20, on Tuesday £15, on Thursday £70, on Friday £3, and on Saturday £7; how much money have I expended in the five days?
(16.) A person deceased left his eldest son £410, to his widow £20 more than to his eldest son, to his two younger sons £10 each less than to his eldest son, and to his daughter £50 less than to her mother; what was the aggregate amount of his property?
ANSWERS TO ADDITION. (1.) 33. (2.) 35. (3.) 314. (4.) 299.
(5.) 346. (6.) 2849. (7.) 24648. (8.) 18560. (9.) 37431.
(10.) First six months 181 days, 2nd six months 184 days, in the year 365 days.
(11.) 27700. (12.) In the year 1946. (13.) 225 yds. (14.) £252. (15.) £115. (16.) 2020.
Having carefully worked the sums set down for prac. tice, and seen that their answers correspond with these set down in the book, we proceed to the next rule, which is
SUBTRACTION, Or the first rule given by which we can separate numbers, or withdraw one number from another.