Use and Explanation of Characters. Certain characters or signs are frequently used for the sake of brevity, in solving questions; each character indicates some particular operation. As a sometimes called St. George's cross, represents Addition. An X sometines called St. Andrew's cross, represents Multiplication. A horizon, vision. represents Subtraction. between 2: s, represents Di Two parallels, dozen. 100 cents things are equal or cents are equal, or will make 1 dollar. represent equality, as 12 =1 1 dollar; that is, 12 particular will make 1 dozen, and 100 EXAMPLES. 2+24 means that 2 and 2 when added together will make 4. 422 means 4 made less by 2, is equal, or will leave 2. 2×6= 12 means 2 multiplied by 6 is equal to 12. 824 means 8 divided by 2 will be equal to a quotient of 4. 1. 2. Of multiplying 7 by 3. Of multiplying 9 by 3, and adding 4 to the product. 3. Of adding 9 and 8 and 7, and dividing the amount by 2. 4. Of subtracting 9 from 36, and adding 3 to the remainder. 5. Of multiplying 16 by 2, and adding 20 to the product. [amount. 6. Of adding 59 and 76 and 42 together, and subtracting 16 from the 9. Of dividing 132 by 6, and multiplying the quotient by 2. 10. Of multiplying 144 by 12, and dividing the product by 4. [gether. 11. Of subtracting 144 from the product of 36 and 40 multiplied to12. Of adding 144 and 12 and 8 and 9 and 6 and 4 together. 13. Of multiplying 196 and 15 and 6 and 4 and 3 together. [millions. Of subtracting two hundred millions from two hundred and four Of multiplying 97 and 43 together. Of dividing 236 by 4, and adding 2 to the quotient. Of multiplying 14 by 42, and adding 100 to the product. NOTE. Much time is saved by this method of mutual instruction. ject, each scholar being provided with a slate, and answering in rotation. put to a whole class by the master, or some pupil who understands the sub Questions on this and many other pages of this work can be PARTICULAR RULES. THE operation of Multiplicátion may be contracted or shortened in several instances. When the mul. tiplier is 10, 100, or 1000, &c. what is to be done? 1st. When the multiplier is 10, 100, or 1000, annex the ciphers in the multiplier to the multiplicand, and the work is finished. EXAMPLES. 1. Multiply 379 by 10. What is to be done when there are ciphers at the right hand of the multiplier ? Ans. 3790. Ans. 674600. 2d. When there are ciphers at the right hand of the multiplier, multiply by the significant figures only, and bring down the ciphers at the right hand of the product. EXAMPLES. I. 48 5 240 19400 970 Prod. 1 1 6 4 0 0 2. What will 398 acres of land cost, at 20 dollars per acre ? 3. What will 762 hogsheads of molasses cost, at 30 dollars per hogshead for half of it, and 40 dollars per hogshead for one third of it, and 50 dollars per hogshead for the remainder? What do you do when there are 3d. When there are ciphers beciphers between tween the significant figures of the the significant fig-multiplier, omit them. ures of the multi plier ? EXAMPLES. I. 85743 7006 5 1 4 458 600 201 600715458 2. How much will 520 acres of land cost, at 109 dollars per acre? 3. What is the product of seven million, two hundred and two thousand, five hundred and thirty-three multiplied by half of forty-two millions and two? When there are ciphers at the right hand of both the multiplier and the multiplicand, what is to be done? Prod. 4th. When there are ciphers at the right hand of both the multiplicand and multiplier, place the first significant figure of the multiplier directly under that of the multiplicand; usual manner, and place as many cimultiply the significant figures in the phers to the right hand of the product, as there are in the multiplicand and multiplier both. EXAMPLES. 1. 378500 34000 15140 11355 1286900 00 2. Multiply twenty-four thousand by two thousand four hundred. 3. What is the value of twenty-three thousand acres of land, at twenty dollars per acre ? 4. How much is the product of 69, multiplied by 100? 5. How much is the value of 196 acres of land at 102 dollars per acre? 6. How much is the value of one million acres of land, at 10 dollars per acre for of it, 20 dollars per acre for of it, 30 dollars per acre for of it, and forty dollars per acre for the remainder ? 7. If London contain 1,225,000 inhabitants, and each person consume 300 pounds of provision in one year, how many pounds of provision do they all consume annually? How many in 10 years? How many teams, each carrying 2000 pounds, would it require to transport it? And allowing 320 rods to make a mile, and each team to occupy the space of 1 rod, how many miles would they reach? When the multiplier or divisor is a composite number, the same rule will apply as in Compound Multiplication or Compound Division. For an explanation of the terms and method of operation, the pupil is referred to pages 113, 114, and 122. In performing Division, when the divisor is under 12, the method of operation may be performed mentally. This is sometimes called |