LESSON XII.

Adding Fractional Units.

James and John have each an apple of the same size. James cuts his into 4 equal parts and gives away 2 parts. John cuts his into 5 equal parts and gives away 3 parts. They seek to find what part of an apple each has left, and what part both together have?

Now, says James, if I cut each of my fourths into 5 equal parts, I shall have 10 parts; that is, 10 twentieths of an apple: and says John, if I cut each of my fifths into 4 equal parts, I shall have 8 parts; that is, 8 twentieths of an apple; hence, James has 10 twentieths, and John 8 twentieths, and together they have 18 twentieths.

2. What is the unit of the fraction ? What is the fractional unit in 18 twentieths of an apple? How many fractional units are taken? If the numerator and denominator be each divided by 2, what does the fraction become? What, then, is each fractional unit? How many are taken?

3. What is necessary in order that two or more fractions may be added together.

That they have the same integral unit, and the same fractional unit.

4. When no integral unit is named, what unit is understood?

The abstract unit one.

5. Have the fractions and the same integral unit? What is it? Have they the same fractional unit? What is it?

6. How many fractional units in the first? How many in the second? How many in both? 7. What is the sum of the fractional units in } and ?

8. What is the sum of and ??

9. What is the sum of 1, 2, and ? 10. What is the sum of

11. What is the sum of 4. 12. What is the sum of

4, and?
5 and ?
34, and ?

8" 8" 8"

3 and ?

of 3, 5, and

of

of

7

13. What is the sum of 5,
14. What is the sum
15. What is the sum
16. What is the sum
17. What is the sum of
18. What is the sum of
19. What is the sum of
20. What is the sum of
21. What is the sum of
22. What is the sum of
23. What is the sum of
24. What is the sum of
25. What is the sum of
26. What is the sum of
27. What is the sum of
28. What is the sum of
29. What is the sum of
30. Add together and

21 21

2.2.

?

and

and

45 and

3' 6'

21

and

91 9

.

3

and ?

and?

10, and 12?

9 1

5 6 and ?

21 21 21

6 9 and ?

41

35 and ?
4. 1, and g?
6 and ?

69 6

10

First, is equal to 3, and is equal to ; then

and 34 and 511⁄2 ?*
and 43 and 61?

and 7.

and 2 and 7 16 and 28

5

42. What is the sum of 23
43. What is the sum of 2
44. What is the sum of 12 and 64
45. What is the sum of 43 and
46. What is the sum of 94 and
47. What is the sum of 53 and 45
48. What is the sum of 94 and 75 and ?
49. What is the sum of 5g
50. What is the sum of 63
51. What is the sum of 5
52. What is the sum of 5

7

18

2

9 ?

30

and 415
9 and
and 8 and 10,
8 and 2 9 ?

18

and 81
and 21⁄2 and 34 ?

QUESTIONS.

21

1 John buys a top for one sixth of a shilling, a stick of candy for one twelfth of a shilling, and a piece of india-rubber for one third of a shilling: what does the whole cost him?+

2. James pays of a dollar for a pair of gloves, and of a dollar for a handkerchief: how much do they cost him?

3. Nancy buys a work-box for of a dollar, a pair of gloves for of a dollar, and a comb for of a dollar: how much do they all cost?

4. Jane buys a yard of ribbon for of a dollar, a gold pin for of a dollar, and an inkstand for of a dollar: how much did she pay in all?

5. William buys a kite for of a dollar, and a string for of a dollar: how much did he pay? 6. Three ducks cost of a dollar, two fowls of a dollar, and two geese of a dollar: what is the entire cost?

* SUGGESTIONS. Add the integer numbers separately, and unite the sum to the sum of the fractional parts.

7. Three sheep cost

of a dollar, a calf

of a

dollar, and a lamb of a dollar: what is the entire cost?

8. Three yards of cloth cost of a dollar, a handkerchief of a dollar, and a pair of gloves of a dollar: what is the entire cost?

9. A father paid 3 quarters of a dollar for his own breakfast, one third of a dollar for his son's, and a quarter of a dollar for his daughter's: how much did he pay in all?

10. A merchant sold 3 yards of cloth from one piece, 23 yards from another, and 54 yards from another how much did he sell in all ?*

11. If a turkey costs of a dollar, a gooseof a dollar, and 2 chickens of a dollar: how much will the whole cost?

12. James spends 61 cents for candy, 12 cents for a top, and 5 cents for a slate how much does he spend in all?

13. A man travelled 2 miles the first hour, 34 miles the second, and 4 the third: how far did he travel in the three hours?

14. What amount was paid for 4 weeks board, the board for the first week being 5 dollars, for the second 34 dollars, for the third 4 dollars, and for the fourth 45 dollars?

15. A man paid a dollar for dinner,

of a dollar for a breakfast, 19 of of a dollar for supper, and of a dollar for lodging: what did he pay for the days' entertainment?

16. Jane paid 32 cents for tape, 63 cents for needles, and 4 cents for ribbon: how much did she pay in all?

17. If 5 yards of muslin cost of a dollar, 9 pairs of stockings 23 dollars, and 2 pairs of boots 9 dol lars, what will be the whole cost?

18. A laborer sawed wcod for 4 hours, and was to have 36 cents a cord. The first hour he sawed of a of a cord, the third of a cord,

cord, the second

and the 4th hour

10

of a cord: how much ought he

to receive?

LESSON XIII.

Subtracting Fractions.

1. What is necessary in order that one fraction may be subtracted from another?

That both fractions have the same integral and the same fractional unit.

Since the integer unit is the abstract unit one, and the fractional unit in both, is, the difference is found by subtracting 2 sevenths from 4 sevenths, which leaves 2 sevenths.

15
13

21

13

0

and 15

25

୯୯୯୯୯୯୯୯୯୯

3. What is the difference between 6 and 4. What is the difference between and 5 5. What is the difference between 14 and 6. What is the difference between 17 and 7. What is the difference between 8. What is the difference between 36 and 17? 9. What is the difference between 10. What is the difference between and 12? 11. What is the difference between 3 and 12. What is the difference between 16 and 13. What is the difference between 1 and 9 ?

2 29

37

19

and 40

18

?

37

37

14. What is the difference between and? Re

duce both to the fractional unit one sixth.

One half is equal to, and one third to ; hence,

their difference is equal to .

15. What is the difference between and ?
16. What is the difference between
17. What is the difference between

and ?

and ?