ROMAN SYSTEM The seven letters used in Roman notation are: I 1 V. X L C D M The other numbers are represented by combinations thus: I. When a letter is followed by the same letter or by one of less value, the values of the letters are to be added: Thus, XX represents 20; XI represents 11. II. When a letter is followed by one of greater value, the value of the smaller is to be subtracted from that of the greater. Thus, IV represents 4; IX represents 9. III. When a letter is placed between two letters of greater value, the value of the smaller is to be subtracted from the sum of the other two. Thus, XIV represents 14; XIX represents 19. A bar placed over a letter multiplies its value by 1000. Thus, V represents 5000. The following table further illustrates the system. 2. XCIX MCMVIII MDLXXVI MDCCCLXI 3. Express in Roman notation: 41, 63, 84, 99, 107, 218, 572, 735, 996, 1907, 1564, 1616, 1000, 260,000, ADDITION Addition is the process of uniting two or more numbers to form one number. = The addends are the numbers to be added. The sum or amount is the result of addition. The sign, called plus, indicates addition; and the sign indicates equality. Like numbers are numbers that express the same units, as 3 pounds and 5 pounds, or 3 and 5. Unlike numbers are numbers that express different units, as 7 days and 3 yards. Only like numbers can be added. 1. Add the numbers that you wrote in examples 1-8, p. 8. Add the following. Drill until each example can be added in 1 minute or less. In adding, group numbers into SUBTRACTION Subtraction is the process of finding the difference between two numbers, or of taking one number from another. The minuend is the number from which we subtract. The difference or remainder is the result of subtraction. Only like numbers can be subtracted. The general method of subtraction has already been learned. The following methods are also convenient : 1. Take 378 from 653. I. By adding (the method used in making change). 653 What number added to 8 will make 13? 378 What number added to 8 will make 15? 275 What number added to 4 will make 6? II. By subtracting from 10. 653 Borrow 10, subtract 8, and add 3, thus: 378 275 108 in subtrahend 2; 2+3 in minuend = 5. 10-7 in subtrahend = 3; 3+ 4 (5 − 1) in minuẹnd = 7. 5-3=2. The steps in the general method of subtraction are borrow, add, subtract. In this, they are borrow, subtract, add. MULTIPLICATION AND DIVISION Multiplication is the process of taking one number as many times as there are units in another. The multiplicand is the number multiplied. The multiplier is the number by which we multiply. The sign indicates multiplication. A concrete number is a number that refers to some particular object; as, $8, 4 books. An abstract number is a number that does not refer to some particular object; as 8, 4. The multiplier must always be regarded as an abstract `Division is the process of finding how many times one number contains another or of separating a number into equal parts. The separation of a number into equal parts is also called partition. Thus, $2505, or of $250, is an example in partition. The dividend is the number divided. The divisor is the number by which we divide. The quotient is the result of division. The remainder is the part of the dividend remaining when the division is not exact. The sign indicates division. Division is also indicated as follows: 35 divided by 7 may be written 35 or 7)35. If both dividend and divisor are concrete, they must be like numbers, and the quotient is abstract. If the dividend is concrete and the divisor is abstract, the dividend and quotient are like numbers. Thus,$27 $39; but $27 ÷ 3 = $9. |