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Second Method. OPERATION. 7 x12 x 16 x 20 =26880

Let the pupil exam5 X 8 X 16 X 20 = 12800

ine the second method 11 X 8 X 12 X 20= 21120

of reducing fractions X 8 X 12 x 16 = 19968

to a common denomi80768

nator in Case VIII.,

Sec. XVI. 8 x 12 x 16 x 20 – 30720 = 2270

[Ans. RULE. — Reduce mixed numbers to improper fractions, and compound fractions to simple fractions; then reduce all the fractions to a common denominator, and the sum of their numerators written over the common denominator will be the answer required. 2. Add 1, 3, 14, and g together.

Ans. 243. 3. Add 1 , 5, and together.

Ans. 121. 4. Add I, , 1, and together.

Ans. 2138. 5. Add BT , 166, and { together.

Ans. 1. 6. Add I, 17, 18, and my together. Ans. 318. 7. Add 1, 1, , 1, 4, and 7 together. Ans. 113. 8. Add , 4, and 53 together.

Ans. 6349. 9. Add tri da, and 931 together.

Ans. 931 10. Add , , and 4 together.

Ans. 61. 11. Add , 71, and 8 together.

Ans. 177. 12. Add ;, 37, and 53 together.

Ans. 9112. 13. Add 63, 73, and 4g together.

Ans. 1835.

NOTE. - If the quantity be a mixed number, the better way is to add their fractional parts separately, as in the following example. 14. What is the sum of 11%, 15%, 12 , and 175 ?

OPERATION.
4)4 8 12 6 4x3x2= 24
3)1 2 3 6

114 16 X 3
2)1 2 1 2

3 x 7 = 21

12 52 x 5= 10 1 1 1 1

4 x 5= 20 Ans. = 577

24=27

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15. What is the sum of 114, 195, and 233 ? Ans. 549.. 16. What is the sum of 184, 277, and 491 ? Ans. 96. 17. What is the sum of 21%, 18%, and 26%? Ans. 6613.

18. What is the sum of 17, 141, and 134 ? Ans. 45136 19. What is the sum of 167, 87, 93, 31, and 13?

Ans. 4045 20. What is the sum of 37111, 61428, and 814?

Ans. 106837. 21. Add 4 of 1871, and 11 of 4 of 6 together.

Ans. 126.1. 22.. Add f of 18, and I of 11 of 741 together.

Ans. 1331. 23. Add 4 of 154, and 8 of 1077 together. Ans. 93). 24. Add f of 2 of 2804 to 2004 Ans. 670. 25. Add 4, 25,945and fill together. Ans. 341385884.

4 257091 92998325

CASE III.
To add any two fractions, whose numerators are a unit.
RULE. -- Place the sum of the denominators over their product.

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Note. - The truth of this rule is evident from the fact, that this process reduces the fractions to a common denominator, and then adds the numerators.

If the numerators of the given fractions be alike, and more than a unit, multiply the sum of the denominators by one of the numerators for a new numerator, then multiply the denominators together for a new denominator.

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CASE IV.

To add compound numbers. 1. Add 7 of a £. to & of a £. Value of 7 of a £. = 10s. 9d. 01qr. This question is perValue of of a £. = 16s. 4d. 1 &qr. formed by finding the 1£. 7s. 1d. 254-qr. values of Iz of £.

* and 11 of a £. by Case XI., Sec. XVI. The fractions and are added by Case II. of Addition of Fractions. The following questions are performed in the same manner.

The above question may be performed by first adding the fractions of the pounds together, and then finding their value by Case XI. ; thus :

OPERATION. 73£. tf£. = 14. = 1£. 7s. 1d. 2*r. Ans. 2. Add together of a £., 4 of a £., and of a shilling.

OPERATION.

£. 8. d. gr. of a £. = 8 10 24 of a £ =0 8 6 33 of a s. = 0 0 4 31

0 17 10 13% The above question may be solved by first reducing of a shilling to the fraction of a pound by Case IX., Sec. XVI.

Moons

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Section XVIII.
SUBTRACTION OF VULGAR FRACTIONS.

CASE I.
To subtract fractions that have a common denominator.
1. If be taken from what will be left ?
2. If z be taken from what will be left?
3. If to be taken from To what will be left?

4. What portion of a dollar will be left, if be taken from 1? 5. Subtract from 11

11-5=6. = 1 Ans.

RULE. — Subtract the less numerator from the greater, and under the remainder write the common denominator, and reduce the fraction if necessary.

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6. Subtract from 14.

Ans. 17 7. Subtract from 13.

Ans. is. 8. Subtract from

Ans. 4. 9. Subtract 17 from 4.

Ans. 10. Subtract 18 from . 11. Subtract 4 from 9.

Ans. 13. 12. Subtract 16 from o

Ans. It 13. Subtract 11 from 11%.

Ans. Tóm: 14. Subtract do from 20.

Ans. 1. 15. Subtract 4 from .

Ans. 1 16. Subtract from

Ans. 17. Subtract 100 from 166.

Ans. Zo 18. Subtract 32 from 1928

Ans. Po 19. Subtract 1487 from 100 .

Ans. ਤੰਗ
CASE II.
To subtract fractions whose denominators are unlike.
1. Subtract 4 from H.

OPERATION.
Common denominator 77

In this ques117 x 10 = 70

tion, we find the 711 x 4=

common denom

inator, 77, by 26 = Ans. multiplying the

two denominators, 7 and 11; and then obtain the numerators, as in Case VIII., Sec. XVI.; the difference of which we write over the common denominator. 2. From I take i.

Ans. 15.
OPERATION,
4)16 12

4X4 X3= 48 common denominator.
4 3

163 x 11 = 33
124 x 5= 20

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