MULTIPLICATION. Multiplication is a short method of adding a number to itself, any number of times. Two numbers, called factors, are always given to find a third. 1. The Multiplicand, or number to be multiplied. 2. The Multiplier. The Third is called the Product. The Table must be learned by heart. RULE 1.—In multiplying, carry one for every ten, as in Addition. Multiply the same Multiplicand separately by 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. RULE 2.-When the Multiplier consists of several figures, multiply every figure of the Multiplicand, by each figure of the Multiplier, taking care to place the first figure of each line under its Multiplier. Add all the lines of products together, and their sum will be the total. Proof. Multiply the Multiplier by the Multiplicand. Observe, for Multiply 729 read equal to. 6561= 9 times 729 * 21870= 30 729 1678 *The ciphers in such products may be omitted; here, they are put only for explanation. RULE 2.-When the Multiplier is the product of two numbers in the table, multiply by one of them and the product by the other. Examples. Multiply 195084 by 14, and the same Multiplicand separately by 16, 18, 21, 49, 72, 108, and 144. SUBTRACTION. Subtraction teacheth to take a less number from a greater, to find the remainder or difference. RULE.-Place the less number under the greater, units under units, tens under tens, &c. Begin at the right hand figure and subtract it from the figure above it, and continue from right to left. Add the remainder to the number subtracted, and, the sum, if the work be right, will be the same as the upper line. OBSERVE.When the under figure is less than the upper one, add ten to the latter, and from their sum subtract the under figure, carrying one to the next figure to From 71867000 subtract 87614. Take 876 out of 3786, and then out of the remainder as often as you can. How often may 796 be taken out of 7864 ? Subtract 17816 from 127658 as often as you can. DIVISION. Division is a short method of performing several subtractions, and finds how often one number may be taken out of another, or is contained in it. Two numbers are always given to find a third. 1. The Dividend, or number to be divided. 2. The Divisor. The third, or number to be found, is called the Quotient, and shews how often the Divisor may be subtracted from the Dividend, or how many times it is contained in it. RULE 1.-Place the Divisor and Dividend as in the following examples, and observe the manner of working them. Proof.-Multiply the Quotient by the Divisor, or the Divisor by the Quotient; and to the Product, add the remainder, the sum will be the same as the Dividend if the work be right. The figures in the Quotient of the first example are found thus; say, how often 7 in 16, the answer is twice, put 2 in the Quotient, and 14 for twice 7, under 16 and subtract; to the remainder bring 7 from the Dividend. Then say how often 7 in 27, the answer is 3 times, write 3 in the Quotient, and 21 for 3 times 7, under 27 and subtract; to the remainder annex the 8, the next figure of the Dividend, and for 68 proceed as has been explained. The Quotient shows that 7 may be taken 239 times from 1678. Whenever there is a remainder, place it after the Quotient above a line, and the Divisor under it thus, 4. RULE 2.-When the Divisor is less than 13, ask how often it may be had in the first figure or figures on the left; set the Quotient under the figure or figures taken; and when there is a remainder, suppose it to be placed before the next right hand figure, then ask again and thus proceed through the Dividend. 3)56103961 Examples. 5) 1370192 Quotient 18701320 In the same manner divide the last number by 10, 11, 12, 6, 7, 8, and 9. RULE 3.-When the Divisor has ciphers on the right hand, cut them off; also cut off as many figures from the right hand of the Dividend, and divide by the left hand figure or figures of the Divisor. 2,0)17864,8 Examples. 12,00)1068764,76 Divide 147683796 by 8700. What is the Quotient of 37167896 by 950000 ? ADDITION OF MONEY. These Tables must be learned by heart. for three Farthings. Observe.--stands for Farthing. for Halfpenny. RULE.-Place Farthings under Farthings, Pence under Pence, Shillings under Shillings, Pounds under Pounds; and be careful to put Units under Units, Tens under Tens, &c. Add the Farthings together, and always finding from the Table, or from memory, how many Pence are in the Farthings, how many Shillings in the Pence, how many Pounds in the Shillings, proceed as is shown in doing the first of the following example: £. s. d. f. 4 16 71 21 4 17 6 Here the sum of the Farthings is 7, or 11d; set down and carry 1 to the Pence, and the sum will be 34d., or 2s. 10d., the 10d. is set down, and 2s. are carried to the |