3. Subtract 267 from 345 and add 150 to the remainder. Facit 228. 4. A person had in his desk 1000 dollars. He took out 120 dollars to pay a debt. He afterwards put in 75 dollars. How much was there then in the desk? Ans. 955 dollars. SIMPLE MULTIPLICATION. Multiplication teaches to find what a number amounts to when repeated a given number of times. The number to be multiplied is called the multiplicand. The number to multiply by is called the multiplier. The number produced by multiplying is called the product. Note.—The multiplier and multiplicand are also called factors. 7 The scholar should commit the following table to memory before he proceeds further. MULTIPLICATION TABLE. 11 21 31 41 51 61 781 91 101 111 12 9 18 27 36/45 54/6372 811 901 99 108 When the multiplier does not exceed 12, work by RULE I. Set the multiplier under the units place of the multiplicand. Then, beginning with the units, multiply each figure of the multiplicand, in succession, disposing of their several products as the amounts of the columns are disposed of in addition. Thus: if the product of the units figure do not exceed 9, set down that product : but if it exceed 9, set down its right hand figure, and add its left hand figure or figures to the product of the tens, &c. PROOT. Multiply by double the multiplier, and the product will be double the former product. EXAMPLES. Multiplicand 2 4 3 274 2005 2 40092 Multiplier 2 3 1 2 Multiply by each figure of the multiplier separately, first by the one at the right hand, then by the next, and $o onplacing their respective products one under ano ther, with the right hand figure of each product directly under that figure of the multiplier by which it is produced. Add these products together and their amount will be the product required. Note.-When cyphers occur at the right hand of ei. ther or both of the factors, omit them in the operation, and annex them to the product. 3. Multiply 25 by 325 4. 125 by 4500 5. 5231 by 758495 6. 129186 by 98 12660228 7. 23430 by 5388900 8. 756 by 1512000 9. 5400420 by 23000 124209660000 10. 674200 by 2104 1418516800 il. 5401 by 300400 1622460400 Note.-When the multiplier is the exact product of any two factors in the multiplication table, the operation may be performed thus: multiply by one of the factors, and then multiply the number produced by the other faotor. Facit 3. Multiply 43102 by 66 4. 12071 by 99 5. 871075 by 42 6. 526473 by 144 2844732 1195029 36585150 75812112 APPLICATION. 1. Richard has 125 nuts, and George has 6 times that number. How many has George? Ans. 750. 2. There are 20 boxes of raisins with 14 pounds in each box. How many pounds are there in all ? Ans. 280. 3. The price of one orange is 9 cents : how many cents will 5 oranges come to, at the same price? Ans. 45. 4. There are 12 pence in one shilling. How many pence are there in 40 shillings? Ans. 480. 1. Multiply 25 by 10, and 36 by 14, and 124 by 45. Add the several products and tell their amount. Ans. 6334. 2. There are 10 bags of coffee weighing each 120 pounds; and 12 bags weighing each 135 pounds. What is the weight of the whole? Ans. 2820 pounds. 3. A merchant bought five pieces of linen containing 25 yards each, and 2 pieces containing 24 yards each, and 1 piece containing 26 yards. How many yards were there in the whole ? Ans. 199. SUBTRACTION AND MULTIPLICATION. 1. Multiply 342 by 22 and from the product subtract 400. Facit 7124. 2. There are 15 bags of coffee, each of which weighs 112 pounds. The bags which contain the coffee weigh 22 pounds. How much would the coffee weigh without the bags? Ans. 1658 pounds. 3. There are 12 chests of tea, each of which weighs 96 pounds. The chests which contain the tea weigh. each 20 pounds. What would the tea weigh without the chests? Ans. 912 pounds. DIVISION. By division we ascertain how often one number is contained in another. The number to be divided is called the dividend. The number of times the dividend contains the divisor is called the quotient. If, on dividing a number, there be any overplus, it is called the remainder. The dividual is a partial dividend, or so many of the dividend figures as are taken to be divided at one time, and which produce one quotient figure. When the divisor does not exceed 12 work by RULE 1. Place the divisor on the left of the dividend, and see how often it is contained in the first left hand figure or figures thereof.* If it be contained an exact number of times, set down that number; and then see how often it is contained in the next figure or figures. But if it be contained any number of times with a remainder, set down the number of times, and conceive the remainder to be prefixed to the next figure of the dividend ; then see how often the divisor is contained in these, and proceed as before: or if these will not contain the divisor, set down a cypher, and take the next figure with them; and if they will not still contain the divisor, set down a cypher again, and take the next figure with them; set down the number of times they contain the divisor, and proceed as before. PROOF. Multiply the quotient by the divisor, and to their product add the remainder (if any) and the result will be equal to the dividend. The multiplication table shews how often any number, not ex. ceeding 12, is contained in any other number not exceeding 144: as that 4 is contained in 12 three times, because 3 times 4 are 12; 10 is contained in 115 eleven times with 5 over, because 11 times 10 are 110, which, with 5, makes 115. EXAMPLES. 5 2960 12112813 12)970811280 Quotient 321 592 9401 +1 80900940 |