into 60 seconds. The length of a degree, minute, or second, depends on the size of the circle. If the size of the circle is increased or decreased, the length of the degree, minute, or second is also increased or decreased. 3. For the explanation of the principles of Longitude and Time see Intermediate or Practical Arithmetic, page 225. TEST QUESTIONS FOR EXAMINATION. ADDITION.-What is addition? What is the result called in addition ? Give the formula for adding 20 and 50. 60 and 70. 30 and 40. 90 and 80. 1. Give the rule. What is the sum of 80 and 99. 30 and 70. 60 and 70. 20 and 30. 70 and 40. * For answers to these and similar questions the pupils are referred to the Practical or Intermediate Arithmetic. †These figures refer to the paragraphs in the text of the book. In examination the teacher should test the pupils upon the practical problems, and see that they can readily give the appropriate formulas. 2. Give the formula for adding 87 and 50. 36 and 80. 90 and 67. Give the rule. What is the sum of 39 and 20? Of 37 and 80? Of 90 and 47? Of 60 and 39? What is the sum of 3+2+5+8+9+3+8+6+7+2+4+3? Of 3+5 +6+7+8+9+3+4+7+6+4? 3. Give the formula for adding 63 and 25. 43 and 25. the rule. What is the sum of 43 and 62? Of 27 and 91 ? 93 and 74? 4. Give the formula for adding 36 and the rule. What is the sum of 37 and 867 98 and 71. Give Of 32 and 75% Of 78. 25 and 67. 97 and 39. Give Of 35 and 67 Of 83 and 95. Of What is the sum 24 and 39? Of 63 and 79? Of 39 and 78? Of 83 and 67? of 637 and 463? Of 325 and 4C7? Of 397 and 763 Of 273 and 34 ? 5. Add from the blackboard the following numbers 36+24+86 +37. Give the rule. SUBTRACTION.-What is subtraction? What is the result called? Which number is called the minuend? Which the subtrahend? Which the dif ference? Which the remainder? Which two terms are equal to the minuend? Which term subtracted from the minuend will give the remainder Which term subtracted from the minuend will give the subtrahend? 6. Give the formula for subtracting 60 from 130. 90 from 180. 70 from 260. 50 from 520. Give the rule. What is the difference between 60 and 180 50 and 170? 90 and 620? 40 and 520 30 and 640? 90 and 370? 60 and 560? What is the difference between 30 and 121? Give the formula. Give the difference between the following numbers :-36 and 128. 144. 976-35. 437-62. 73 and 7. Give the formula for subtracting 39 from 137. Give the rule. What is the difference between the following numbers? 176 and 86. 374 and 98. 673 and 87. 8. What is the difference between 88 and 100? 73 and 100? Give the rule. 300 less 37 are how many? 300-63=what? 9. Give the formula for taking 37 from 463. Give the rule. What is the difference of 467 and 93? Of 378 and 271 Of 386 and 977 Of 567 and 38? Of 476 and 39 ? MULTIPLICATION.-What is the result called in multiplication? Which number is the product? Which is the multiplicand? Which the multiplier ? Which two terms multiplied together equals the product? 10. Give the formula for finding the product of 3 and 90. 6 and 70. Give the rule. 6 times 20 are how many? 11. Give the formula for multiplying 98 by 4. Give the rule. 6 times 89 are how many? 5 times 37 equals what? 6 times 37 equals what? How much longer will a cheese last 1 man than 8 men? 8 men will eat a cheese how much quicker than one man? How much more work can 9 men do than 1 man? A certain piece of work will last 1 man how much longer than 9 men? 12. How many are 13 times 17 many are 16 times 13? 14 times 19 Give the formula. Give the rule. How 16 times 19? 13. How many are 13 times 871. Give the formula. Give the rule. How many are 13 times 27? 16 times 86 13 times 43? 12 times 83 } ! DIVISION.-What is the number to be divided called? The number by which it is divided is called what? What is the result called? The product of what two numbers equals the dividend? What is meant by one-half of a thing or number? What is one of an apple? How many in of 6 apples? What is meant by 3 fifths? What is 3 fifths of one apple? What is 3 fifths of 10 apples? Of 15 apples? Of 25 peaches? 14. Give Form I. What is the result called in this formula? 15. Give Form II. What is the result called in this formula? What number is called the minuend? Which the subtrahend? 16. Give Form III. Which number is the multiplicand? Which the multiplier? Which the product? Which the result? 17. Give Form IV. Which the quotient? Which number is the dividend? Which the divisor? Which the result? 18. Give Form V. Which is the divisor in this formula? Which the dividend? Which the quotient? Which the result? 19. Give Form. VI. Which is the dividend? What rule does the 6th formula illustrate? ANS.-Comparison. 20. What is U. S. Money? What is meant by currency? Repeat the table. How are dollars separated from cents and mills? How many dimes in $6? Give the formula. What are the denominations of U. S. Money? 21. Where is English money used? What are the denominations? What is the value of a sovereign? Repeat the table. Repeat the table in a reverse order. 22. What is the use of Troy Weight? What are the denominations? Repeat the table. Repeat the table in a reverse order. 23. What is the use of Avoirdupois Weight? What are the denominations? Repeat the table. Repeat the table in a reverse order. 24. What is the use of Apothecaries' Weight? What are the denominations? Repeat the table. Repeat the table in a reverse order. 25. What is the use of Long Measure? What are the denominations? Repeat the table. Repeat the table of Geographic Measure. 26. What is the use of Cloth Measure? Repeat the table. What are the denominations? 27. What is the use of Square Measure? What is a square? What is the difference between a square foot and a foot square? Between 2 square feet and 2 feet square? Between 5 square feet and 5 feet square? Give the formula for finding the number of square feet in a square yard. Repeat the table. 28. What is the use of Cubic Measure? What is a cube? Repeat the table. Give the formula for finding the number of cubic feet in a cubic yard. Give the rule. What are the dimensions of a cord of wood? 29. What is the use of Liquid Measure? Repeat the table. What are the denominations? 30. What is the use of Dry Measure? Repeat the table. Give the denominations. 31. What is time? How is time measured naturally? Artificially? Repeat the table. How is the year divided? Give the names of the months in their order. How many days has each? How many days has February in leap-year. Repeat the table of particulars. 32. What is the use of Circular or Angular Measure? Repeat the table. What is meant by circumference? By diameter? By arc? By right angle By quadrant? To the Teacher-The preceding subjects are to be studied in connection with the corresponding subjects of the Intermediate, Practical, or Commercial Arithmetics, and the time occupied is to vary according to the time spent in the same subjects in written arithmetic. It is very important that the pupil at each step should be subject to a searching examination. The test questions are only to be used as an aid for this purpose. Particular attention should be given to the following points: 1. Rapidity and accuracy in combining numbers at sight. 2. Promptness and accuracy in abstract mental operations. 3. Distinctness in stating the analytical steps of complex problems. 4. Familiarity with the application of the five arithmetical formulas. 33. Fractions are expressed by a numerator and a denominator. 34. The Denominator shows how many equal parts the unit is divided into, and gives the name to the fraction. (a.) It may be written at the right of the numerator in words; as, 4 tenths, 9 sevenths, 8 seventeenths, or under the numerator, thus : numerator. 35. The Numerator shows how many there are of those equal parts. (a.) It may be written either at the left of the denominator, as 3 tenths, 4 sevenths, or over the denominator, thus: denominator. numerator. 36. The Numerator and Denominator taken together are called the terms of a fraction. |