CHARACTERS USED IN THIS TREATÍSE. +{ or more. or $ The sign of equality, as 208.= £. 1. i. e. to twenty shillingsare equal to one pound, &c. The sign of Addition, and signifies that the numbers between which it is placed are to be added together, to discover their sum ; thus, 5+3=8. i. e. 5 more, 3 are Plus. equal to 8 ; or if 5 and 3 are added tu gether, their sum will be 8. When more than two numbers are placed in a line with this sign between them, it denotes that they are all to be added together; thus, 5+3+7+2=17 ; i. e. if 5, 3, 7, and 2, are added together, their sum will be equal to 17. The sign of Subtraction, and signifies that the number following is to be sub*Minus, | tracted from that which precedes it, to discover their difference or remainder, as Less. 7-2=5; i. e. 7 less 2 is equal to 5: Or 7, having 2 subtracted from it, the remainder or difference is equal to 5. The sign of Multiplication, and signi. fies that the number preceding is to be Into, With, multiplied by that which follows it, to dis. Or By cover their product; as 6X3=18; i. e. if 6 be multiplied by 3, their product will be 18. The signs of Division, as 9-3=3, or =3, also 39(3, either of these signifies that -Ву if 9 be divided by 3, the quotient will be or, equal to 3. Also 20-435; 4=5; or 3)9(3 4)20(5 The sign of Proportion used in stating questions in the Rule of Three ; also in **** Pro other cases in which proportion is portion. used : Thus, 5 10 :: 8 * 16; i. e, as 5 is to 10, so is 8 to 16. B { ✓ Root. The sign of the root of the number it precedes. Thus V or ✓ ? is the sign of the square root, and denotes that the square root is to be extracted from the number it precedes; 3 signifies the cubic root, and v4 the biquadrate root, &c : (thus, V 1296=36, or thus, ✓ ? 1296=36. EXPLANATION OF TERMS, WHICH THE PUPIL OUGHT TO LEARN AND REMEMBER. The number found by adding several together is called their sum. The number found by subtracting à less from a greater is called their difference, and sometimes the remainder. In Multiplication, The number to be multiplied is. called the multiplicand. The number by which it is to be multiplied is called the multiplier. The multiplicand and multiplier are in some cases called factors. The number found by the operation is called the product of the factors ; in some cases it is called the rectangle of the factors. In Division, The number given to be divided is called the dividend. The number by which it is to be divided is called the divisor. The number found by the operation is called the quotient. The number found by multiplying the divisor by a quotient figure, to set under the dividend and subtract from it, is called a subtrahend. The number set under, the subtrahend (found by subtraction) is called a remainder. Annex, is to place figures or ciphers at the right of others. Prefix, is to place figures or ciphers at the left of others. Integers are simple or whole numbers, as 26, 39, &c. Fractions are broken numbers or parts of an integer, as I is one fourth, jis three eighths, &c. Mixed numbers consists of integers and fractions, as 27 | is twenty-seven and three fourths. OF PRACTICAL ARITHMETIC. ARITHMETIC is the art of computing by numbers or figures, and has five principal Rules. viz. Noration, or NUMERATION, ADDITION, SUBTRAC: TION, MULTIPLICATION and Division. NOTATION OR NUMERATION Teaches how to express the value of the ten figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, by their relative places, as in the following NUMERATION TABLE. 9 9 8 9 8 7 9 8 7 6 9 8 7 6 5 9 8 7 6 5 4 9.8 7 6 5 4 3 9 8 7 6 5 4 3 2 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 1 5 3 9 8 7 6 5 4 3 2 1 0 1 2 9 8 7 6 5 4 3 2 1 0 1 2 3 6 5 9 8 7 6 5 4 3 2 1 0 1 2 3 4 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 9 8 7 6 5 4 3 2 1 0 1 3 4 5 6 7 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 0,1 2 3 4 5 6 7 8 9 Trillions NOTE. The cipher (0) when standing alone has no value ; but when annexed to a significant figure or figures, it increases their value ten fold, thus 0 is of no value ; 26 is twenty six, 260 is ten times twenty six, or two hundred and sixty. In the first line of the above Table, the figure 9 being in the unit's place, is called nine. In the second line there are two figures 98, the 8 in the unit's place is called eight, the 9 being in the ten's place is ten times nine or ninety ; therefore the two taken together are ninety eight, &c. The last or lowermost line in the Table is to be read thus, Nine trillions, eight hundred and seventy six thousand, five hundred and forty three billions, two hundred and ten thousand, one hundred and twenty three millions, four hundred and fifty six thousand, seven hundred and eighty nine. EXAMPLES FOR PRACTICE. Write down in figures, the following numbers, viz. Twenty seven ; three hundred and forty six; seven thousand, five hundred and eighty two; ninety five thousand, two hundred and forty six ; three hundred and forty six thousand, two hundred and twelve. SIMPLE ADDITION Teaches to collect numbers of the same denomination into one sum, which is called the sum of those numbers. Rule. Place units under units, tens under tens, &c. and draw a line under the whole. Begin with the lower figure of the units and add upwards ; if the result be contained in one figure, set it down under its column, but if in more than one figure, set the right hand figure only under its column, and add what the other figure or figures will make to the next or ten's place, with which proceed as with the units; and thus proceed through all the columns, setting down the whole under the left hand column. See the first ex- To prove Addition, add all but the upper line to- Or, EXAMPLES. 3 9364817 3721582 6485.136 4213751 8495279 2234 1998 2234 In the first example I begin with the lower figure in In the same manner are all examples. in Simple Ads To prove the work, I go over the addition again, B. |