OF CALIFORNIA SENIOR ARITHMETIC. DEFINITIONS. 1. A Unit is one, or one thing. 2. A Number is that which tells how many. 3. The Unit of a Number is one of its units. 4. Numbers having the same unit are Like Numbers. 5. A number not applied to any particular object is an Abstract Number; as 6, 11, 15. 6. A number that is applied to a particular object is a Concrete Number; as 6 men, 11 lb., 15 days. 7. An Integer is a whole number. 8. Expressing numbers by figures or letters is called Notation. 9. Arabic Notation is expressing numbers by figures. 10. Roman Notation is expressing numbers by letters. 11. Naming the places of figures and reading numbers is Numeration. 12. A figure standing alone expresses units. 13. When figures stand side by side, the right-hand figure expresses units, the next tens, the next hundreds, etc. 1 14. The value of a figure, without regard to its place, is its Simple Value. The value of a figure with reference to its place in a number is its Local Value. NOTE. In the number 5555, the simple value of each figure is 5. The local value of the right-hand figure is 5. Of the second, 50. Of the third, 500. Of the fourth, 5000. 15. Each group of three figures, beginning with units and counting to the left, is a Period. Rule. TO READ NUMBERS. Begin at the right, and separate the numbers into groups of three figures each, using the comma. Begin at the left, and read the number in each group, giving to it the name of that group. No name is given to the number in the last group. 16. Addition is the process of uniting two or more like numbers into one sum. 17. The result of addition is called the Sum or Amount. 18. Subtraction is the process of finding the difference between two like numbers. 19. The number from which we subtract is called the Minuend, and the number subtracted, the Subtrahend. The result in subtraction is the Difference or Remainder. 20. Multiplication is the process of finding a number that is a given number of times another number. 21. The Multiplicand is the number multiplied. 22. The Multiplier is the number multiplied by. 23. The result of multiplication is called the Product. PRINCIPLES. The multiplier must be an abstract number. The multiplicand and product are like numbers. The product is the same in whatever order the numbers are taken. 24. Division is the process of finding how many times one number is contained in another. 25. The number divided is the Dividend. 26. The number by which the dividend is divided is the Divisor. 27. The result of division is the Quotient. 28. When the divisor is not exactly contained in the dividend, the part of the dividend that is left is the Remainder. 29. PRINCIPLES. The remainder and dividend are like numbers. When the divisor is abstract, the dividend and quotient are like numbers. When the dividend and divisor are concrete, the quotient is abstract. 30. The Sign of Division is÷, and when placed between two numbers signifies that the first is to be divided by the second. FACTORS AND MULTIPLES. 31. A Factor of a number is any integer that will exactly divide it. 32. A number that has no factors except itself and 1 is a Prime Number. 33. A number that has other factors besides itself and 1 is a Composite Number. 34. A prime number used as a factor is a Prime Factor. 35. What are the prime factors of 1155? Rule. Divide the number by any prime fac- 5/1155 3/231 7/77 11 5, 3, 7, and 11. Ans. The divisors and the last quotient are the prime factors. 36. Numbers that have no common factor or divisor are Prime to Each Other. 37. A Multiple of a number is a number that exactly contains that number. 15 is a multiple of 5. 38. A number that is a multiple of two or more numbers is a Common Multiple of them. 24 is a common multiple of 4 and 3. 39. The least multiple of two or more numbers is their Least Common Multiple. 12 is the least common multiple of 3 and 4. 40. What is the least common multiple of 18, 27, and 30? before, continuing the division until the quotients and undivided numbers are prime to each other. The product of the divisors, quotients, and undivided numbers is the least common multiple. 41. A number that is a factor of two or more numbers is a Common Divisor of them. 5 is a common divisor of 30 and 40. 42. The greatest factor of two or more numbers is the Greatest Common Divisor of them. 10 is the greatest common divisor of 30 and 40. 43. What is the greatest common divisor of 324 and Rule. Divide the greater 324/372 (1 number by the less, then 324 der, until there is no re mainder. The last divisor is the greatest common 48/324 (6 36/48 (1 36 12/36 (3 When there are more than two numbers, first find the greatest common divisor of two of them, then of this divisor, and a third number, until all the numbers are used. CANCELLATION. 44. Cancellation is a process of shortening indicated division by rejecting the same factors from both dividend and divisor. 45. PRINCIPLES. Rejecting the same factor from dividend and divisor divides both by that factor. Dividing both dividend and divisor by the same number does not affect the quotient. COMMON FRACTIONS. 46. A Fraction is one or more of the equal parts of a unit. The unit of which the fraction is a part is called the Unit of the Fraction, and one of the equal parts is called the Fractional Unit. Two or more fractions having the same fractional unit are Like Fractions. 47. A fraction is written with two numbers, one above the other, with a line between; as, . 48. The number below the line in a fraction is the Denominator, and shows into how many equal parts the unit is divided. 49. The number above the line in a fraction is the Numerator, and shows how many of the parts are taken. |