ADVANCED ARITHMETIC PART ONE: SEVENTH YEAR I. GENERAL REVIEW 1. WHOLE NUMBERS; FRACTIONS; DECIMALS 1. What does thirteen mean? Fourteen? 2. Explain the meanings of all the numbers from 13 to 19. 3. What does the syllable teen mean? 4. What does twenty mean? Thirty? Forty? 5. What does ty mean? 6. What do we call 10 tens? 10 hundreds? 10 thousands? 7. How many different figures do we use in writing numbers? 8. How is it that we can express all numbers, however large, by the use of nine figures and a zero? 9. How does the value represented by 5 change in the following: 5; 50; 500; 5000; 50,000? 10. What value has the zero? Why is it used? 11. Then the value represented by a figure depends upon what two things? Each figure has a value denoted by its form, and also a value denoted by its position. 12. In 347, what does 7 represent? What does 4 repre sent? What does 3 represent? The names of the orders, reading from right to left, are: ones, tens, hundreds, thousands, ten thousands, etc. 13. What is the largest number you can express with the figures 1, 4, 9, and 0, using each figure but once? 14. Explain why you placed them in the orders that you did. 15. How many units of any unit of the next higher order? order does it take to make one Since ten units of any order make one unit of the next higher order, we call our system of writing numbers a decimal system. Decimal comes from the Latin decem, meaning ten. 16. Read the following: 3,436,585; 17,309,607; 906,350,780; 100,040,065. Each period of three figures is set off by commas so that it may be more easily read. The names of the first six periods, reading from right to left, are ones, thousands, millions, billions, trillions, and quadrillions. 17. Read the following: 3,709,068,345; 17,836,405,736,400; 15,040,048,304. Do not use "and" in reading whole numbers. 18. Read without using the word "and": 19. Write the above numbers as your teacher reads them. Our method of writing numbers is called the Hindu method, for it was invented by the Hindus. The ten symbols, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, used in the Hindu notation, are called the ten digits. The Roman Notation 1. Read: I, II, IV, V, VI, X, IX, XI, XII, XX. 2. Give the values of V, X, L, C, D, and M. 3. Read: XX, XXX, XII, XV, XVII, LX, CL, CLX. 4. When a letter is followed by the same letter or by one of less value, how is the value of the whole expression found? 5. Read IV, IX, XL, CD. 6. When a letter is followed by one of greater value, how is the value of the whole expression found? 7. To write 1492, we write the symbols for 1000+ 400+ 90 +2, which are M + CD + XC + II, or MCDXCII. In the Roman notation : I. Add the values of the letters when a letter is followed by the same letter or one of less value; and II. Subtract the values of the letters when a letter is followed by one of greater value. A dash over a letter multiplies its value by 1000. Thus, X=10,000; C100,000; L = 50,000. Addition 1. Add 7 and 9. Add 3 ft. and 8 in. What change did you make before adding 3 ft. and 8 in.? Why? Addition is the process of uniting two or more numbers (addends) into one number (sum). Numbers expressed in unlike units cannot be added until the units are made alike. See how quickly you can give the sums of the following: 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. |