10. What part of 3 qt. is 1 qt? is 1 gal.? is 1 gal. 2 qt.?

is 2 gal.?

11. What part of 3 miles is 1 mile? of is? of ‡ is ? of 1 qt. 1 pt. is 1 pt.? of 1 is ?

12. What part of da.? of 12 is ? of 1 gal. 3 qt. is 1 qt.?

13. What part of 7 is ? of is 3? of is ?

is? of 14 is? of 1 week 1 da. is 1

14. What part of 24 is? 15. What part of 4 is 23? 16. What part of 23 is 73? 17. What part of the cost of 7 books is the cost of one book? of 3 books? of 5 books?

of 14 is?

of 24 is 14?

of 23 is 44?

of 74 is 2??

of 84 is 32?

of 32 is 44 ?

18. What part of the value of 2 bu. 1 pk. is the value of 1 pk? of 1 bu.? of 1 bu. 1 pk.? of 1 bu. 3 pk.? of 2 bu.?

19. A and B buy some goods for 8 dollars, of which A pays 5 dollars and B pays 3. What part of the goods ought each to have?

20. A and B trade in company; A puts in 4 dollars as often as B puts in 3. What part of the gain ought each to have?

21. A, B, and C traded together; A put in 2 dollars as often as B put in 3, and C 4. What part of the whole did each put in?

Solution. Since for every 2 dollars that A put in B put in 3, and C 4, it is evident that for every 9 dollars that all put in, A put in 2 dollars, B 3, and C 4. Therefore, A put in , B 3, and C of the whole.

22. A, B, and C hired a pasture together. For every cow that A put in, B put in 2 and C 5. What part of the expense of the pasture ought each one to pay?

E. 1. If 7 sheep cost 49 dollars, what will 3 sheep cost? Solution. If 7 sheep cost 49 dollars, 1 sheep will cost of 49 dollars, which is 7 dollars, and 3 sheep will cost 3 times 7 dollars, or 21 dollars. Therefore, 3 sheep will cost 21 dollars, if 7 sheep cost 49 dollars.

5

2. If 8 papers of candy cost 56 cents, how many cents will papers cost?

3. If a girl receives 45 merit marks for 9 good lessons, how many will she receive for 4 good lessons?

4. If 3 milk-cans will hold 24 qts. of milk, how many quarts will 7 milk-cans hold?

5. If 9 boys can pick 54 quarts of blueberries in an afternoon, how many quarts can 7 boys pick in the same time?

6. How much will 3 quarts of molasses cost at 32 cents per gallon?

Solution. If 1 gallon, or 4 quarts, cost 32 cents, 1 qt. will cost of 32 cents, or 8 cents, and 3 quarts will cost 3 times 8 cents, or 24 cts. Therefore, 3 quarts of molasses at 32 cents per gallon will cost 24 cts.

7. How much will 7 quarts of meal cost at 24 cents per peck?

8. How much will 3 gills of lamp oil cost at 48 cents per quart?

9. If a yard of cloth is worth 24 cents, how much is a piece 2 ft. in length worth?

10. If 1 acre, 3 roods (or 7 roods) of woodland cost 63 dollars, how many dollars will 1 acre cost?

11. If 1 gallon and 1 pint of burning fluid cost 81 cents, how much will 1 quart cost? will 1 gallon cost?

12. If it cost 45 cents to dig a trench 1 yd. 2 ft. in length, how much will it cost to dig one 2 feet in length? How much to dig one 1 yd. 1 ft. in length?

13. If for 2 three-cent pieces and 2 cents, 64 marbles can be bought, how many can be bought for 1 three-cent piece and 2 cents? for 3 three-cent pieces?

14. Julia's basket holds 2 pt. 1 gi. If she can fill it with berries in 45 minutes, how many minutes will it take her to fill Susan's basket, which holds but 1 pint? How long to fill Josephine's, which holds but 3 gills?

15. What will of a pound of tea cost at 42 cents per pound? Solution. If 1 pound of tea costs 42 cents, of a pound will cost of 42 cents, or 6 cents, and of a pound will cost 6 times 6 cents, or 36 cents. Therefore, of a pound of tea at 42 cents per pound will cost 36 cents.

16. If a man can perform a piece of work in 72 minutes, how many minutes will it take him to perform of it?

17. What will of a yard of linen cost at 54 cents per yard? 18. Deborah had 48 cents, and she gave of them for a doll. How many cents did the doll cost her?

19. Brass is composed of copper and zinc. If of it is composed of zinc and the rest of copper, how many pounds of copper will there be in a bar of brass weighing 25 lb.?

20. How much will 5 lb. of sugar cost at 8 cents per pound?

21. How much will 83 barrels of flour cost at 6 dollars per barrel?

22. If a man can walk 32 miles in 8 hours, how far can he walk in 1 hour? in 93 hours?

23. If 8 tons meadow hay cost 72 dollars, how many dollars will 5 tons cost?

24. If 7 yards of cloth are worth as much as 49 lb. of butter, how many pounds of butter ought 4 worth?

yards of cloth to be

25. Olive has 40 picture books, Ella has as many as Olive, and Ada has as many as Ella. How many has Ella? has Ada ?

26. John is as old as his father, who is 36 years old, and William is as old as John. How old is John? is William?

27. It is 45 miles by rail-road from Worcester, Mass., to Nashua, N. H. W. Boylston is of this distance from Worcester, New Boston is of it, Harvard is § of it, and Pepperell is of it. How far is each of the above places from Worcester ? from Nashua ?

28. It is 50 miles by the Fitchburg rail-road from Boston to Fitchburg. It is as far by the same road to Waltham, as far to Concord, as far to S. Acton, 7 as far to Groton Junction, and as far to Shirley. How far is each of the above places from Boston? from Fitchburg ?

29. I bought 3 pecks of corn at 40 cents per bushel, 3 pecks of oats at 36 cents per bushel, 5 quarts of walnuts at 48 cents per peck, 6 quarts of salt at 24 cents per peck, and 3 quarts of molasses at 28 cents per gallon. What was the amount of my purchase?

30. Edward had 3 cents and Robert had 5. They put their money together and bought 72 filberts. How many filberts ought each to have?

31. Harriet, Maria, and Caroline, send some berries to market, for which they receive 63 cents. Now if Harriet sent 3 qt., Maria 2, and Caroline 4, how many cents ought each in justice to receive?

32. Joseph Fisher and Reuben Guild buy a horse together, towards which Fisher pays 5 dollars as often as Guild pays 2. They sell him so as to gain 56 dollars. What will be each man's share of the gain?

33. Hiram picked 1 qt. 1 pt. of strawberries, Arthur picked 2 qts., and Rowland picked 1 qt. They put them all together and sold them for 81 cents. How many cents should each receive?

8*

SECTION XII.

A. 1. Any number which is an exact number of times a given number, is a multiple of that given number. Thus 21 is a multiple of 3, because it equals 7 times 3.

2. The multiples of a number are those numbers which would be produced by successive additions of the given number to itself. Thus, 2, 4, 6, 8, 10, 12, &c., are multiples of 2; 7, 14, 21, 28, &c. are multiples of 7.

3. What are the first 10 multiples of 2? of 3? of 4? of 5 of 6 of 7? of 8? of 9? of 10?

4. Of what numbers is 24 a multiple? is 20? 21? 36? 30? 28? 25? 32? 35? 40? 42? 45? 48? 50? 54? 56? 60? 64? 70? 72? 80? 81? 90?

5. What is the largest multiple of 4 less than the number 23? Ans. 20, which is 5 times 4.

6. What is the largest multiple of 5 less than the number 26? of 3? of 7? of 4? of 8? of 9? of 6? of 10?

7. What is the largest multiple of 6 less than the number 35 of 8? of 4? of 10? of 9?

8. What is the largest multiple of 8 less than the number 43 of 7 of 4? of 9? of 8? of 5? of 6?

9. What is the largest multiple of 7 less than the number 73? of 10 of 9? of 8?

10. What is the largest multiple of 6 less than the number 51 of 9 of 7? of 10? of 5? of 8?

11. What is the largest multiple of 4 less than the number 29 of 7? of 6? of 9? of 8? of 3? of 5? of 10 ?

12. What is the largest multiple of 6 less than the number 62 of 8? of 10? of 9? of 7?

13. What is the largest multiple of 7 less than the number 39 of 4 of 6? of 7? of 5? of 9? of 10? of 8?

B. 1. 25 how many times 7?

In these questions it should be borne in mind that the pupil has not yet been led to multiply or divide by any number larger than 10. Не should not therefore be required to mention any factor greater than 10, or any factor which is contained in the number considered more than 10 times.

Solution 1st. 25

7

= 21, and 4 added Solution 2nd. 25

3 times 7, and 4 over, because 3 times = 25.

= 3 times 7, because 3 times 7 = 21,

and of 7, which are 4, added to 21 — 25.

NOTE. It is essential that the pupil become perfectly familiar with both the above forms of solution. The best method will doubtless be to have him use one form till he masters it, and then use the other. In the first form the 4 should be regarded as an undivided number or remainder, but in the second, the should be regarded as a part of the quotient, and not as a remainder.

2. 26

3. 33

4. 37

5. 41= 6. 83

how many times 5? 9? 3? 8? 10? 6? 4? how many times 6? 9? 4? 7? 5? 8? 10? how many times 4? 8? 6? 10? 5? 7? 9? how many times 9? 10? 7? 5? 4? 8? 6? how many times 10? 8? 9?

10. 29

11. 48

how many times 7?

how many times 10? 9? 3? 5? 7? 4? 8? 6? how many times 8?7? 10? 5? 6? 9?

10? 8? 6? 9?

16. 21 = how many times 7? 3? 9? 2? 8? 5? 4? 6? 10? 17. 39 = how many times 10? 9? 8? 7? 6? 5? 4?

18. 51= how many times 8? 9? 10? 6? 7? 5?

19. 42

20. 28

21. 62= 22. 76

how many times 6? 9? 4? 7? 5? 8? 10?

how many times 9? 10? 4? 6? 7? 3? 5? 8? how many times 10? 81 6? 7? 9?

how many times 7? 9? 10? 8?

23. 59 how many times 6? 10? 9? 7? 8?
how many times 10? 5? 6? 9? 8? 7?

24. 45

C. 1. Reduce 29 to ones.

Solution. Since 6 sixths =

1, 22 must equal as many ones

as there are times 6 sixths in 29 sixths, which are 4 times. Therefore, 248.