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- twelfths = — twelfths. Story-William had a piece of wire * of a foot long; he cut from it a piece $ of a foot long; what remained was twelfths of a foot long.

3. 4 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 & bu. of oats each day for a week; in all he fed and bushels.

4. 4 divided by 1, 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. Story-The teacher divided 4 oranges among some boys, giving to each f of an orange; there were boys.

5. of a bushel divided by 4, means, find 1 fourth of of a bushel. 1 fourth of $ of a bushel = - — of a bushel. Štory-A boy divided f of a bushel of oats equally among 4 ponies; each pony received - - of a bushel.

6. 63 plus 51, means, 63 and 51. 63 and 54 = — and Story-In one jar there were 6 lb. of butter; in another there were 51 lb.; in both there were and — — pounds.

7. 68 minus 55, means, 63 less 55. 68 less 5} = — and Story-A grocer had 63 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, & of a pound of meat costs cents.

9. divided by 1, 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 f of a pie among some boys, giving to each d of a pie; there were boys.

10. 61 yd. divided by 2, means, find 1 half of 68 yards. 1 half of 6 yards = — and — — yards. Story-A salesman cut 63 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.

14. 71 divided by 21, means, find how many times 24 is contained in 71. I can change 21 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 24 bushels in each bag; there were bags.

15. 54 tons divided by 2, means, find 1 half of 50 tons. 1 half of 54 tons = — and

tons. Story --54 tons of coal were divided equally between two families; each family received and — - - tons.

16. 124 multiplied by 21, means, take 2 times 12€ plus 3 fourths of 12€ (24 times 124). 2 times 124 plus 3 fourths of 12€ = — 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. 121 multiplied by 3, means, take 3 times 121 (3 times y, 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 24 feet, means, find how many times 21 feet are contained in 15 feet. I can change 15 ft. and 21 ft. to half-feet; 15 ft. = — half-feet; 21 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 21 ft. long; there were pieces.

21. 274 feet divided by 3, means, find i third of 271 feet. 1 third of 271 feet = — and — feet. Story-The perimeter of a triangle having equal sides is 273 feet; each side is and feet.

22. 12; multiplied by 21, means, take 2 times 124, plus 4 of 12]. 2 times 121, plus } of 12) = — and —

Story-At $121 per ton, 24 tons of hay cost and dollars.

23. 134 bu. divided by 24 bu., means, find how many times 27 bu are contained in 131 bu. I can change 24 and 13} to fourths. 24 = -- fourths. 131 = — fourths. — fourths are contained in - fourths — times. Story- A farmer had 131 bu. of oats which he put into bags, putting 24 bu. in each bag. There were --- bags.

.6+.2 = *
24 +.05 = (1)
.24 +.5 = (6)

176.4
148.75 -
(11)

.6 – .2 = * .6 X 2 = * 64 – .05 = (2) .12 x 9 = (3) .64 — .5 = (7) 20 X .2 = (8) 276.4

20 X 3.2 = (13) 148.23

.1 x.1 = (16) (12)

.3 x .2 = (19)

.6 = .2=* .08 = .02 = (4) 8 •.4 = (9) 4 = .05 = (14) 2.5 = .05 = (17) $.5)$24.5 (20)

.6 • 2 = *
$.08 • 2 = (5)
$6.36 = 3 = (10)
5.6 tons • 4 = (15)

5)$24.5 (18)
5)$8.2 (21)

1. .24 plus .05, means, 24 hundredths and 5 hundredths. .24 and .05 = — 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. .02 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 = 50 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.

-* See Elementary Arithmetic, pp. 153 and 155.

8. 20 multiplied by .2, means, find 2 tenths of 20. One tenth of 20 = — ; 2 tenths of 20 = — Story-At $20 an acre, .2 of an acre of land would cost dollars.

9. 8 divided by .4, means, find how many times 4 tenths are contained in 8. 8 = 80 tenths. 4 tenths are contained in 80 tenths

- times. Story-I paid $8 for potatoes at $.4 (4 dimes) a bushel; I bought bushels.

10. $6.36 divided by 3, means, find 1 third of $6.36. One third of $6.36 = - Story-I paid $6.36 for 3 barrels of apples; 1 barrel cost

11. The sum of 176.4 and 148.75 is —
12. The difference of 276.4 and 148.23 is -

13. 20 multiplied 3.2, means, take 3 times 20, plus 2 tenths of 20. 3 times 20 = — 2 tenths of 20 = - 3 times 20, plus 2 tenths of 20 = - Story-At $20 an acre, 3.2 acres of land are worth -- dollars.

14. 4 divided by .05, means, find how many times 5 hundredths are contained in 4. 4 = 400 hundredths. 5 hundredths are contained in 400 hundredths — times. Story-I paid $4 for tablets at $.05 (5%) each; I bought - tablets.

15. 5.6 tons divided by 4, means, find 1 fourth of 5.6 tons. One fourth of 5.6 = - and - - tons. Story-A farmer sold 4 loads of hay, the entire weight of the hay was 5.6 tons; the loads averaged - and - - tons.

16. .1 multiplied by .1, means, find 1 tenth of 1 tenth. One tenth of 1 tenth = -

17. 2.5 divided by .05, means, find how many times 5 hundredths are contained in 2.5. 2.5 = 250 hundredths. 5 hundredths are contained in 2.5 (250 hundredths) — times. Story-I paid $2.5 for pencils at $.05 (54) each; I bought pencils.

18. $24.5 divided by 5, means, find 1 fifth of $24.5. One fifth of $24.5 = — Story-I paid $24.5 for 5 tons of coal; 1 ton cost

19. .3 multiplied by 2, means, find 2 tenths of 3 tenths. One tenth of 1 tenth = ---. One tenth of 3 tenths = - Two tenths of 3 tenths =

20. $24.5 divided by $.5, means, find how many times 5 tenths of a dollar are contained in $24.5 (245 tenths dollars). 5 tenths are contained in 24.5 (245 tenths) --- times. Story-I paid $24.5 for apples at $.5 (5 dimes) a bushel; I bought a bushels.

21. $8.2 divided by 5, means, find 1 fifth of $8.2. One fifth of $8.2 ($8.20) = - Story-I paid $8.2 for 5 yards of cloth; 1 yard cost

SUGGESTIONS TO TEACHERS.

1... ORDER OF PROCEDURE IN PART I. STEP 1.—Prepare the pupil by means of oral instruction for the work of a given page. This preparation may be, in part, the slow reading to the pupil of the figure problems* upon the page, the teacher hesitating at each blank for the pupil to supply the word. In this preparatory work, no book should be in the hands of the pupil. New words should be first presented through the voice of the teacher in the expression of thought. They may then be written upon the blackboard by the teacher, erased, and the pupil exercised in both oral and written reproduction.

STEP 2.—The book should be put into the hands of the pupil, and he should read, first silently, then orally, the figure problems upon any page for which proper preparation has been made.

STEP 3.—The pupil may attempt the letter problems* at his desk without further assistance. If he is unable to solve these, review the figure problems and give others similar to them. In some instances it may be well to have the figure problems solved upon the blackboard as preparation for the letter problems.

. 2. Wherever the word “storyfollows a problem, as on pp. 12 and 13, require the pupil to make a statement showing how the problem might originate in business or other experience; thus, the story for problem (f), page 12, might be, A man divided 43 acres of land into lots each containing ab of an acre. There were 95 lots.

3. The separatrix, as an aid in “pointing off” in multiplication and division of decimals, is mentioned in a note on page 133. Its use is illustrated on page 143. Its occasional use in blackboard work earlier in the course may be helpful; but a too early reliance upon formal rules is to be avoided if the purpose of the work is the development of the thought-power of the pupil.

* The figure problems are those designated by figures; the letter problems, those designated by letters.

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