12 is contained times in 4 times of 56. of 56 is 8, and of 56 is 4 times 8; 4 times 8 is 32; 3 times 12 is 36, of 36 is 4, and 4 is contained in 32, 8 times. Therefore of 56 is 8 of 3 times 12.

4. of 56 is 8 times what part of 3 times 12 ?

Such a part of 3 times 12 as 3 times 12 is contained times in of 4 times of 56. of 56 is 8, and 4 times 8 is 32; of 32 is 4; 3 times 12 is 36, and 36 is contained in 4, or Therefore of 56 is 8 times , or, of 3 times 12.

4

times.

5. of 3 times 12 is of what number?

of 3 times 12 is of 7 times of 8 times of 3 times 12; of 36 is 4, and 8 times 4 is 32; of 32 is 8, and 7 times 8 is 56. Therefore of 3 times 12 is 4 of 56. 6. of 3 times 12 is how many sevenths of 56? As many sevenths of 56 as of 56 is contained times in 8 times of 3 times 12. 1909 3 times 12 is 36, of 36 is 4, and times 4 is 32; of 56 is 8, and 8 is contained in 32, 4 times. Therefore of 3 times 12 is of 56. 7. of 3 times 12 is 4 times what part of 56 ? Such a part of 56 as 56 is contained times in of 8 times of 3 times 12; 3 times 12 is 36; of 36 is 4, and 8 times 4 is 32; of 32 is 8, and 56 is contained in 8, or times. Therefore of 3 times 12 is 4 times 4, or 4, of 56.

8

71. 1. 4 of 35 is of how many thirds of 18? Expressed by signs on the blackboard thus:

Of as many thirds of 18 as of 18 is contained times in 9 times of 4 times of 35; 4 of 35 is 5, and 4 times 5 is 20; of 20 is 4, and 9 times 4 is 36; and 6 is contained in 36, 6 times. Therefore

of 6 thirds of 18.

2.

of 18 is 6,

of 35 is

of 35 is of of 3 times of 9 times of 4 times

of 35; of 35 is 5, and 9 times 4 is 36; Therefore of 35 is 4

and 4 times 5 is 20; of 20 is 4, of 36 is 6, and 3 times 6 is 18. of of 18.

3. of 35 is of 6 times what part of 18 ?

4x35xx 18 ?

4 of 35 is of 6 times such a part of 18 as 18 is contained times in of 9 times of 4 times of 35.

of

35 is 5, and 4 times 5 is 20; of 20 is 4, and 9 times 4 is 36; of 36 is 6, and 18 is contained in 6, or times. Therefore of 35 is of 6 times, or §, of 18.

18

4. of 35 is how many ninths of § of 18? x35xx 18?

of 35 is as many ninths of of 18 as of 6 times of 18 is contained times in 4 times of 35. of 35 is 5, and 4 times 5 is 20; of 18 is 6, and 6 times 6 is 36; of 36 is 4, and 4 is contained in 20, 5 times. fore of 35 is of of 18.

5.

4 of 35 is 5 times what part of of 18?
4x35 5xx 18 ?

There

of 35 is 5 times such a part of of 18 as 6 times of 18 is contained times in of 4 times of 35. of 35 is 5, and 4 times 5 is 20; of 20 is 4; of 18 is 6, and 6 times 6, is 36; 36 is contained in 4, 6 4 or Therefore of 35 is 5 times, or §, of § of 18. 6. of of 18 is of what number?

៖

of of 18 is of 7 times of 5 times of 18; of 18 is 6, and 6 times 6 is 36;

times.

of 6 times

of 36 is 4,

and 5 times 4 is 20; of 20 is 5, and 7 times 5 is 35. Therefore of § of 18 is of 35.

7. of of 18 is how many sevenths of 35?

of of 18 is as many sevenths of 35 as of 35 is contained times in 5 times of 6 times of 18; of 18 is 6, and 6 times 6 is 36; of 36 is 4, and 5 times 4

is 20; of 35 is 5, and 5 is contained in 20, 4 times. Therefore of of 18 is of 35.

8. of of 18 is 4 times what part of 35 ?

៖

of of 18 is 4 times such a part of 35 as 35 is contained times in of 5 times of 6 times of 18. of 18 is 6, and 6 times 6 is 36; of 36 is 4, and 5 times 4 is 20; of 20 is 5, and 35 is contained in 5,355 or 4 times. Therefore of g of 18 is 4 times, or 4, of 35.

72. 1.4 of 36 is Of as many times tained times in 9 times and 4 times 12 is 48; 108; of 42 is 6, and tained in 108, 9 times. of 42.

2.

of 36 is

of 9 times of what number? of 36 is of 9 times of 7 times of of 9 times of 4 times of 36; of 36 is 12, and 4 times 12 48 is 12, and 9 times 12 is 108; of 108 is 12, and 7 times 6 is 42. Therefore of 36 is of 9 times of 42.

is 49; of of 12 is 6,

3. of 36 is of 9 times how many sevenths of 42 ? of 36 is of 9 times as many sevenths of 42 as of 42 is contained times in of 9 times of 4 times of 36; of 36 is 12, and 4 times 12 is 48; of 48 is 12, 9 times 12 is 108; of 108 is 12; tained in 12, 2 times. Therefore of 36 is 4 of 9 times of 42.

of 42 is 6, and 6 is con

4. of 36 is 4 of 9 times 2 times what part of 42 ? of 36 is of 9 times 2 times such contained times in of of 9 times of 36 is 12, and 4 times 12 is 48; times 12 is 108; of 108 is 12, and

a part of 42 as 42 is of 4 times of 36; of 48 is 12, and 9 of 12 is 6; 42 is

contained in 6,

9 times 2 times

or times. Therefore of 36 is of or, of 42.

5. of 36 is how many ninths of 9 times

of 42 ?

of

of 36 is as many ninths of 9 times of 42, as 9 times 2 times of 42 is contained times in 4 times of 36; of 36 is 12, and 4 times 12 is 48; 6, and 2 times 6 is 12; 9 times 12 is 108, and 12; 12 is contained in 48, 4 times. Therefore of 9 times of 42.

14

of 42 is of 108 is

of 36 is

of 42 ?

of 42, as

6. of 36 is 4 times what part of 9 times of 36 is 4 times such a part of 9 times 9 times 2 times of 42 is contained times in 1 of 4 times of 36; of 36 is 12, and 4 times 12 is 48; of 48 is 12; of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108; 108 is contained in 12, 12 108 or times. Therefore of 36 is 4 times, or, of 9 times

of 42.

of what number?

7. of 9 times of 42 is of 9 times of 42 is of 3 times times 2 times of 42. of 42 is 6, 2 9 times 12 is 108; of 108 is 12, and of 48 is 12, and 3 times 12 is 36. times of 42 is of 36.

of 4 times of 9 times 6 is 12, and 4 times 12 is 48; Therefore of 9

8. 4 of 9 times of 42 is how many thirds of 36 ? of 9 times of 42 is as many thirds of 36, as of 36 is contained times in 4 times

of 9 times 2 times of 42; of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108; of 108 is 12, and 4 times 12 is 48; of 36 is 12, and 12 is contained in 48, 4 times. Therefore of 9 of 42 is of 36.

times

9.

of 9 times of 42 is 4 times what part of 36 ? of 9 times of 42 is 4 times such part of 36 as 36 is contained times in of 4 times of 9 times 2 times of 42; of 42 is 6, 2 times 6 is 12, and 9 times 12 is 108; of 108 is 12, and 4 times 12 is 48; of 48 is 12, and Therefore

36 is contained in 12,

or

times of 42 is 4 times,

times. or, of 36.

times.

of 9

48 are 54 are

66 are

72

84

88 are 96

6 times are 42 are 60 are 7 times are 49 are 56 are 63 are 70 are 77 are 8 times are 56 are 64 are 72 are 80 are 9 times are 63 are 72 are 81 are 90 are 99 are 108 10 times are 70 are 80 are 90 are 100 are 110 are 120 11 times are 77 are 88 are 99 are 1:0 are 121 are 132 12 times are 84 are 96 are 108 are 120 are 132 are 144

48 are

52 are 65 are 78
56 are 70 are
60 are
75 are
64 are

84

90

80 are 96

68 are

85 are 102

80

72 are
76 are
are 100 are 12)

90 are 108

95 are 114

13 times are 13 are 26 are 39 are 14 times are 14 are 28 are 42 are 15 times are 15 are 30 are 45 are 16 times are 16 are 32 are 17 times are 17 are 34 are 51 are 18 times are 18 are 36 are 54 are 19 times are 19 are 38 are 57 are 20 times are 20 are 40 are 60 are 21 times are 21 are 42 are 63 are 84 are 105 are 126 22 times are 22 are 44 are 66 are 88 are 110 are 132 23 times are 23 are 46 are 69 are 92 are 24 times are 24 are 48 72 are 96 are 25 times are 25 75 are 100 are

are 50

are
are

50

115 are 138 120 are 144 125 are 150