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B. 1. How many pictures at 3 cents each can be bought for 17 cents?

SOLUTION.-If one picture can be bought for 3 cents, as many pictures can be bought for 17 cents as there are times 3 in 17, which are 5 times and 2 over. Therefore 5 pictures at 3 cents each can be bought for 17 cents, and there will be 2 cents remaining.

2. How many toys at 4 cents each can be bought for 9 cents?

3. How many marbles at 2 cents each can be bought for 7 cents?

4. How many coats each containing 3 yards can be made from 14 yards of cloth?

5. How many bags each holding 3 bushels can be filled from 11 bushels of grain?

6. George has 15 cents. How many pencils at 4 cents each can he buy with his money?

7. How many cakes at 6 cents each can be bought for 4 three-cent pieces and a half-dime?

8. Arthur found 8 apples under one tree, 7 under another, and when he had found 5 under another he had enough to give 8 to each of his brothers, and still have a few left. How many brothers had he, and how many apples would he have left?

9. Jane had 20 cents. She bought as many pictures at 6 cents each as she could pay for, and then gave the rest of her money for apples at 2 cents each. How many pictures did she buy? How many apples?

ORAL EXERCISE ON FRACTIONS.

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EXHIBIT any convenient thing, as an apple, to the class, and cutting it into two equal parts, ask, "What have I done to this apple? Ans.-"You have cut it." Into how many parts have I cut it?" Ans.-"Into two parts." "How do the parts compare in size?" Ans."They are equal." "Then how have I divided the apple?" Ans.-"You have divided it into two equal parts." When anything is divided into two equal parts, the parts are called halves of the thing. What, then, will you call these parts of an apple?" Ans.- "Halves of an apple." "What will you call one part?" Ans. "One half of an apple." "What will you call both parts?" Ans.-"Two halves of an apple." "What do both together equal?" Ans."Then how many halves of an apple equal a whole one?" Ans.-"Two halves of an apple." Continue and extend these illustrations by exercises similar in character to those suggested below:

"A whole apple."

"How shall I divide this apple (showing another) into halves?" Dividing it, ask, "How many halves have I from it?" "How many halves did I have from the first apple?" "How many halves are there in all ?" "Then two halves and two halves are how many halves?" "If I should give away one half, how many halves should I have left ?" "Then one half from four halves leaves how many halves?"

Vary these exercises, dividing apples, strings, pieces of paper lines, &c., till the class understand fully the value of halves, thirds, &c., and see clearly that they can be added, subtracted, multiplied, and divided as whole numbers are. Such a course will save much hard labor afterwards, both to Teacher and Pupil.

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A. EXPLANATION.-Such parts as are obtained by dividing a thing into two equal parts are called halves of that thing.

1. What are the parts obtained by dividing an apple into 2 equal parts, called?

Ans.-Halves of the apple.

2. If I should divide an orange into 2 equal parts, what would one of the parts be called? What would 2 of them be called?

3. How many halves are there in the whole of anything?

4. Seth had a large apple, but he gave one half of it to his sister. What part of it did he have left?

5. Fanny's father gave her a half of a pound of raisins, and her mother gave her as many more. How many halves of a pound did both give her? How many pounds?

B. EXPLANATION.-Such parts as are obtained by dividing a thing into 3 equal parts, are called thirds of that thing.

1. Martha cut an orange into 3 equal parts. What ought she to call the parts? What should she call one of them? What should she call 2 of them? What should she call 3 of them?

2. David's mother gave him one third of a quart of chestnuts, and his father gave him two thirds of a quart. How many thirds of a quart did both give him? How many quarts?

3. Sarah had two thirds of a yard of ribbon, and she received a present of two thirds of a yard more. How many thirds of a yard did she then have? How many more thirds than there are in a yard ?

C. EXPLANATION. Such parts as are obtained by dividing a thing into 4 equal parts, are called fourths of that thing.

1. If you should divide a pear into 4 equal parts, what would you call the parts? What would you call 1 of the parts? What would you call 2 of them? 3 of them? 4 of them?

2. What part of an apple must the boy who has 3 fourths of an apple-get, in order to have as much as a whole apple?

LESSON XXIX.

A. 1. What are halves?

Ans. Halves are such parts as are obtained by dividing a unit into two equal parts.

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2. 2 fourths + 3 fourths =*fourths?
3. 2 tenths+ 3 tenths =* tenths?
4. 4 sevenths + 5 sevenths = sevenths?
5. 3 twelfths + 2 twelfths + 4 twelfths
6. 4 ninths from 7 ninths =* ninths?

7. 3 fifths from 9 fifths

8. 12 twentieths

=* fifths?

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9. 15 thirds - 7 thirds - 6 thirds

=twelfths?

twentieths? =*thirds?

10. 4 sixths + 9 sixths - 7 sixths =* sixths?

C. 1. If you should divide an apple into eighths, and give away 3 of the eighths, how many eighths would you have left?

2. William gave 2 sevenths of a watermelon to one boy, 3 sevenths of it to another, and 1 seventh of it to another. How many sevenths did he give away? How many did he have left?

3. Maria had a nice orange. She gave 3 ninths of it to her brother, 4 ninths of it to her sister, and kept the rest. How many ninths of it did she keep?

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