81. A Creditor is the party to whom payment is due, or by whom it is expected. 82. When payment is made in full of a bill, it is receipted, and is then called a receipted bill. NOTE.-The following are simple forms of bills, serving as models, to which the teachers should add daily from dictation until pupils are familiar with the business forms. May 25. 27 yards of Cashmere, @ 2.75. 5. Springfield, Ill., July 1, 1876. Mr. Thomas Barnes, 1876. Bought of STONE, ANDERSON & Co. May 30. June 12. 6. Messrs. Paul, Everett & Co., May 28. 24 tons of Lackawanna Coal, @ $7.50. ./. @ 8.00. Madison, Wis., June 25, 1876. What What is the sum of several numbers? What is addition? sign is used to indicate addition? What are addends? Describe the sign of equality? What is the principle applicable to addition of numbers? How should numbers be written for addition? At which order begin the operation How may errors in addition be easily detected? What is meant by the difference of two numbers? Define subtraction. What terms are employed in subtraction? Define minuend. Define subtrahend. What sign is used to indicate subtraction? When is the difference called remainder? What is the principle applicable to subtraction of numbers? How should numbers be written for subtraction? At which order begin the operation? If a figure in any order of the minuend is less than the figure in the same order of the subtrahend, how is the deficiency supplied? What is a proof of subtraction? What is multiplication? By what other process may the same result be produced? What terms are used in multiplication? Define multiplicand. Define multiplier. Define product. What sign is used to indicate multiplication? What are the multiplicand and multiplier often called? What is the principle first named applicable to multiplication? Second principle? Third principle? Fourth principle? Of what denomination is the product? What is meant by partial product? What are the proofs of multiplication? How is the continued product of several numbers indicated? Mention two other methods of indicating the product of several numbers. How many forms of division are there? Define first form. Define second form. What difference of written operation in the two forms? What determines the particular form in oral and written analyses of examples? What are the terms used in division? Define dividend. Define divisor. Define quotient. Define remainder. How does the remainder compare with the divisor? What sign is ordinarily used to indicate division? In what other ways may division be indicated? How is division related to multiplication? With reference to the dividend, what are the divisor and quotient called? What is the proof of division? What is the first principle applicable to division? Second principle? Third principle? Fourth principle? In second form of division, how is the given part of the dividend found? At which order begin to divide? Of what denomination is the remainder? What is meant by short division? What is currency? Of what does it consist? Describe coin or specie. Define paper money. What is a decimal currency? Define United States money. By whom and when was it established as the U. S. currency? Of what does the coin of the U. S. consist? Name the gold coins. Name the silver coins. Name the nickel coins. Name the bronze coins. What is the composition of the gold coins? Silver coins? Nickel coins? Repeat the table of U. S. money. What is a bill of goods? An account? Define debit. A debtor. Define credit. A creditor. What is a receipted bill? SECTION VIII. PROPERTIES OF NUMBERS. FACTORS. The product of 3 times 4 is 12; 3 and 4 each is therefore called a factor of 12. Hence, Art. 83. A Factor of a number is one of the integers whose product is that number. It is also called a divisor or measure of the number. 84. The factors of a number may be unequal as the above, or they may be equal, if unity be excluded, whose use does not affect the product. As, 2=2; the product of 2 times 2 is 4; the product of 2 times 2 times 2 is 8. It will be seen that 2 is the only factor of 2, is one of the two equal factors of 4, and one of the three equal factors of 8. It is therefore called a root of 2, 4 or 8. Hence, 85. A Root of a number is the number itself, or one of the equal factors of the number. The root is designated as first, second, third, etc., root, according to the number of times it is used as a factor. 86. itself. 87. The First Root of a number is the number The Second Root of a number is each of the two equal factors of a number. The second root is usually called the Square Root. Thus, 3 is the square root of 9, since 9 is the product of 3X3. 88. The Third Root of a number is each of the three equal factors of a number. The third root is usually called the Cube Root. Thus, 2 is the cube root of 8, since 8 is the product of 2×2×2. 89. There are numbers that have no factors but themselves and unity. As, 3, whose factors are 3 and 1; 5, whose factors are 5 and 1; etc. Such numbers are called prime numbers. All other numbers are the product of factors each greater than unity; as, 15 is the product of 3 and 5, 24 is the product of 4 and 6. Such numbers are called composite numbers. Hence, 90. Numbers, considered with respect of their factors, are prime or composite. 91. A Prime Number is a number whose only factors are itself and unity. 92. A Composite Number is the product of two or more integers, each greater than unity. 93. A Prime Factor of a number is a factor which is a prime number. Thus, 2 and 3 are each prime factors of 6 or 12. 94. A Composite Factor of a number is a factor which is a composite number. Thus, 4 and 6 are each composite factors of 12 or 24. Since 2 and 3 are each factors of 6 and 12, they are called common factors of those numbers. Hence, 95. A Common Factor of two or more numbers is a factor of each of the numbers. 96. Numbers that have no common factor greater than unity are prime to each other. Thus, 4 and 5; 8 and 9 are prime to each other. 97. One number is divisible by another, when the latter is a factor of the former. Thus, 3 being a factor of 6, 6 is divisible by 3. 98. Even numbers are numbers which are divisible by 2. Thus, 2, 4, 6 and 8, are even numbers. 99. by 2. Odd numbers are numbers which are not divisible Thus, 3, 5, 7 and 9, are odd numbers. |