remain? How many hundreds and how many units reAns. 3 hundreds and 25 units. main? 36. 85. In 1500 how many tens? How many hundreds? How many thousands and how many units remain? How many thousands and how many hundreds remain ? 86. In 25 hundreds how many thousands and how many hundreds remain? How many thousands and how many hundreds remain 87. In 99 hundreds? 88. In 106 hundreds? 89. In 110 hundreds? 37. In which place shall I write 9 so that it shall express 91. 9 units? | 93. 9 thousands? 95. 9 tens of thousands? 92. 9 tens? 94. 9 hundreds? 96. 9 millions? 38. 97. In 1 ten how many units? 98. In 1 hundred how many tens? how many units? 99. In 1 thousand how many hundreds? tens? units? 100. In 9 tens how many units? 101. In 2 hundreds how many tens? units? 102. In 2 tens of thousands how many thousands? hundreds? tens? units? 103. In 12 thousands how many hundreds? tens? units? 104. In 25 hundreds of thousands how many tens of thousands? thousands? hundreds? tens? units? COUNTING. 39. One marble with one marble is two marbles; one marble with two marbles is three marbles. One of three marbles taken leaves two marbles. Taking a unit or a number of units with another to find how many are made, or out of another to find how many are left, is called counting. What is counting? EXERCISES. 40. Count by ones 1. From one to twenty; from twenty to one. Count by twos 2. From two to twenty; from twenty to two. 3. From one to twenty-one; from twenty-one to one. Count by threes 4. From three to thirty; from thirty to three. 5. From one to thirty-one; from thirty-one to one. 6. From two to thirty-two; from thirty-two to two. Count by fours 7. From four to forty; from forty to four. 8. From one to forty-one; from forty-one to one. 9. From two to forty-two; from forty-two to two. 10. From three to forty-three; from forty-three to three. 11. Count by fives, sixes, sevens, eights, and nines in a manner similar to the above. 41. In counting as above, from two to twenty, all the twos of twenty are counted together. In counting from twenty to two, first one two, then two twos, then three twos, are counted apart from the rest of twenty. At each step in counting we have a new combination. Counting numbers of units together, or apart, is called combining numbers. What is combining numbers? Numbers are combined by processes illustrated in the following lessons. 43. If I put one apple with one pebble, have I two pebbles? Have I two apples? Objects counted together must be of the same kind.* 44. The process of counting together numbers of the same kind is Addition. What is addition? 45. The number found by counting numbers together is the sum or amount. What is the sum or amount? * I may count one apple as one thing with one pebble as another thing, and then have two things, though they will be neither two apples nor two pebbles; but in this case, I only consider them as things, in which particular they are alike. If 2 pebbles are added to 5 pebbles, what is the sum or amount? 46. EXAMPLES. Commencing at the bottom of each of the following columns, add the numbers as expressed from the bottom upward. (1.) (2.) (3.) (4.) (5.) (6.) (7.) (8.) (9.) (10.) NOTE TO THE PUPIL. In adding orally the numbers in any example, name the results simply; thus, in Example 1, say "1, 2, 4, 7," and not "1 and 1 are 2, and 2 are 4, and 3 are 7." PROOF. To prove the work, add the numbers in the reverse order; that is, if you commenced at the bottom, commence at the top; if the work is right, the same sum will be obtained as before. NOTE. The pupil should prove every example till he can add accurately, and continue to practice adding until he can add rapidly as well as accurately. (11.) (12.) (13.) (14.) (15.) (16.) (17.) (18.) (19.) (20.) |