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THE FOUNDATION.

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TO THE PUPIL.-Read each problem and (a) tell its meaning, (b) solve it, and (c) tell the suggested number story. Do this until you can easily give the meaning of all problems similar to these, solve them, and tell the suggested number stories without reference to the notes that follow. 6¢ + 24 = * 60 - 20 = *

64 x 2
+1= (1) - } = (2) ibu. X 7= (3)
61 +5} = (6) 64 – 5 = (7) 124 x * = (8)
2 bu. 3 pk.
5 bu. 1 pk.

$* X 1 = (13)
2 bu. 2 pk.
1 bu. 3 pk.

120 x 2 = (16)
(11)

(12)

124 x 3 = (19)

12} x 21 = (22) 66 = 20 = *

60 = 2 = * 4• j = (4)

1 bu. 4 = (6) #: 5 = (9)

6 yd. + 2 = (10) 7: 24 = (14)

53 tons - 2 = (15) 2 ft.)46 ft. (17)

2)46 ft. 21 ft.)15 ft. (20)

(18) 21 bu.)131 bu.

3)27 ft. (23)

(21)

1. , plus , means, j and 1. I can change thirds and fourths to twelfths;

twelfths; } = twelfths; twelfths and twelfths

twelfths. Story--Harry played ball į of an hour, and hide and seek4 of an hour; in all he played twelfths of an hour. (See First Book, pages 125, 135, 145, 147, 149.)

2. i minus , means, less . I can change fourths and thirds to twelfths. twelfths; $

twelfths; twelfths less * See Elementary Arithmetic, pp. 89 and 153.

=

- twelfths twelfths. Story-William had a piece of wire 1 of a foot long; he cut from it a piece f of a foot long; what remained was twelfths of a fout long.

3. f of a bushel multiplied by 7, means, take 7 times three fourthbushels; 7 times 3 fourth-bushels = fourth-bushels, or and

bushels. Story-A farmer fed to his horses 4 bu. of oats each day for a week; in all he fed and

bushels. 4. 4 divided by $, means, find how many times 1 third is contained in 4. I can change 4 to thirds. 4 is 12 thirds. 1 third is contained in 12 thirds times. StoryThe teacher divided 4 oranges among some boys, giving to each j of an orange; there were boys.

5. ß of a bushel divided by 4, means, find 1 fourth of J of a bushel. 1 fourth of j of a bushel =

of a bushel. StoryA boy divided } of a bushel of oats equally among 4 ponies; each pony received

of a bushel. 6. 6/_plus 53, means, 64 and 54. 64 and 5% and Story-In one jar there were 6 lb. of butter; in another there were 5} lb.; in both there were and

pounds. 7. 64 minus 53, means, 63 less 5. 64 less 5% and Story-A grocer had 6 lb. cheese, from which he sold 58 lb.; there remained and

pounds. 8. 12% multiplied by }, means, take of 124. 3 fourths of 124 =

cents. Story-At 124 a pound, f of a pound of meat costs cents.

9. divided by ), means, find how many times 1 sixth is contained in 2 thirds. I can change thirds to sixths; 2 thirds sixths; 1 sixth is contained in 4 sixths times. Story Mrs. Smith divided s of a pie among some boys, giving ach of a pie; there

boys. 10. 63 yd. divided by 2, means, find 1 half of 68 yards. 1 half of 63 yards

and

yards. Story-A salesman cut 64 yd. of ribbon into 2 equal pieces; there were and yards in each piece.

11. 2 bu, 3 pk. plus 2 bu. 2 pk., means, 2 bu. 3 pk. and 2 bu. 2 pk. 2 bu. 3 pk. and 2 bu. 2 pk. = bu. pk. Story - A dealer put 2 bu. 3 pk. of oats into one bag and 2 bu. 2 pk. into another bag; in both there were bushels

peck. 12. 5 bu. 1 pk. minus 1 bu. 3 pk., means, 5 bu. 1 pk. less 1 bu. 3 pk. 5 bu. 1 pk. less 1 bu. 3 pk.

bu. pk. Story-Mr. Bean had 5 bu. 1 pk. of oats, from which he fed 1 bu. 3 pk.; there remained

bushels pecks. 13. $; multiplied by ), means, take 1 half of 3 fifths of a dollar. 1 half of 3 fifths of a dollar =

of a dollar. Story-At of a dollar ( yard, 1 half of a yard of ribbon is worth

of a dollar.

were

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14. 73 divided by 21, means, find how many times 24 is contained in 73. I can change 24 and 71 to halves; 2) halves; 7) =

halves. halves are contained in halves times. Story-A farmer put 7} bushels of oats into bags, putting 21 bushels in each bag; there were bags.

15. 5f tons divided by 2, means, find 1 half of 54 tons. 1 half of 54 tons = and

tons. Story -51 tons of coal were divided equally between two families; each family received and

tons. 16. 124 multiplied by 27, means, take 2 times 124 plus 3 fourths of 12¢ (24 times 124). 2 times 124 plus 3 fourths of 124 = cents. Story-At 124 a pound 23 lb. of cheese cost cents.

17. 46 ft. divided by 2 ft., means, find how many times 2 ft. are contained in 46 ft. 2 ft. are contained in 46 ft. times. StoryA mechanic cut 46 ft. of moulding into pieces, each piece being 2 ft. long; there were pieces. 18. 46 ft. divided by 2, means, find 1 half of 46 ft. 1 half of 46 ft.

ft. Story-Henry divided 46 ft. of wire into 2 equal parts; each part was feet long.

19. 12} multiplied by 3, means, take 3 times 121 (3 times ], plus 3 times 12). 3 times 12) = Story-One side of a triangle having equal sides is 121 ft., the perimeter of the triangle is and

feet. 20. 15 feet divided by 21 feet, means, find how many times 2! feet are contained in 15 feet. I can change 15 ft. and 21 ft. to half-feet; 15 ft. = half-feet; 2į feet = half-feet;

half-feet are contained in half-feet times. Story--A mechanic had 15 feet of moulding which he cut into pieces, each piece being 23 ft. long; there were pieces.

21. 271 feet divided by 3, means, find i third of 271 feet. 1 third of 273 feet

and

feet. Story-The perimeter of a triangle having equal sides is 271 feet; each side is and

feet.

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22. 121 multiplied by 21, means, take 2 times 12), plus } of 121. 2 times 12), plus 1 of 12)

and

Story-At $12) per ton, 2} tons of hay cost and

dollars. 23. 13} bu. divided by 21 bu., means, find how many times 21 bu. are contained in 13} by. I can change 21 and 13] to fourths. 21 fourths. 13

fourths. fourths are contained in fourths times.. Story-A farmer had 13} bu. of oats which he put into bags, putting 24 bu. in each bag. There were bags.

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.05 =

1. .24 plus .05, means, 24 hundredths and 5 hundredths. 24 and

hundredths. Story-William had $.24; he earned $.05; he then had

2. .64 minus .05, means, 64 hundredths less 5 hundredths. .64 less .05 hundredths. Story-Martha had $.64; she spent $.05; she then had

3. .12 multiplied by 9, means, take 9 times 12 hundredths. 9 times .12

hundredths, or and hundredths. 4. .08 divided by .02, means, find how many times 2 hundredths are contained in 8 hundredths. .O2 are contained in .08 times. Story-I paid $.08 for oranges at $.02 each; I bought oranges.

5. $.08 divided by 2, means, find 1 half of 8 hundredths of a dollar. One half of $.08 = Story-I paid $.08 for 2 lemons; one lemon cost

6. .24 plus .5, means, 24 hundredths and 5 tenths. 5 tenths hundredths. .24 and 50

hundredths. Story-John had $.24; Alfred had $.5; together they had

7. .64 minus .5, means, 64 hundredths less 5 tenths. 5 tenths 50 hundredths. .64 less .50 = hundredths. Story-Sarah had $.64; Mary had $.5; Sarah had $ more than Mary.

= 50

* See Elementary Arithmetic, pp. 153 and 155.

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