18. What is the sum of 172, 14, and 132? 19. What is the sum of 163, 87, 93, 31, and

Ans. 45126· 17 ? Ans. 40

20. What is the sum of 3711, 61418, and 81 ?

21. Add of 18, and 11 of 3 of 6

Ans. 106837.

together.

Ans. 13

To add any two fractions, whose numerators are a unit.

RULE.

Place the sum of the denominators over their product.

1. Add to t

EXAMPLE.

4-5 9

Answer.

4 X 5=20

2. Add to, to, to, to 1,1 to 1,1 to 1,1 to 1. to, to, to }, to, to, to, to 4.

3. Add
4. Add to, to, to, to,
5. Add to, o to, o to, o to, o to

to, to

, to to 4.

6. Add to,

7. Add to, to, to . 8. Add to, to, to, to, to, to, to . 9. Add to, to,to,to,to,to 4, § to §.

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.

10. Add to §.

4+5=9x3=27

4 x 5 20

=1 Ans.

11. Add to, to, to, to , to, to, to .

tor, to, & to, to, to, to .

12. Add
13. Add to,

6

to fr, to fs, fr to f, fi to fr, fr to 1.

8

8

14. Add to, to, to 3, 3 to 5, stof,

I

8.

13
9

8

to f.

15. Add to I, fo to 14, 10 to 16, 10 to 17, fo to 19. 16. Add to, too, to, to, to fa, to 17. Add to, to ; & to fs, & to fr,&to, & to 21. 18. Add 1 to 18, 19 to 19, 11 to 18, 19 to 18%, 19 to 19. to 11, 11 to 11, 11 to 11, 11 to 1, 11 to 14.

19. Add

15,

NOTE.-The preceding rule may be found very useful, because all similar questions may be readily performed mentally.

XI., Sec. XVI. The fractions

formed by finding the values of of a £. and of a £. by Case 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:

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

and then adding it to the other numbers, and finding their value by Case XI., Sec. XVI. Thus :

of a shilling=×=180 = £.

#£. +7 £. + £. = 3; 13 £. = 0£. 17s. 10d. 13qr. Ans.

150

NOTE. The pupil should solve the following questions by both

cesses.

pro

yard.

9

of a furlong, and of a

22 136 143

Ans. 5fur. 16rd. Oft. 3in. 1128bar.

of an acre, How

6. A. has three house-lots; the first contains the second of an acre, and the third 12 of an acre. many acres do they all contain ?

Ans. 2A. 1R. 9p. 142ft. 873in. 7. A man travelled 183 miles the first day, 2311 miles the second day, and 19 miles the third day. How far did he travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 4 in. of a gallon of wine to of a hhd.

Ans. 6gal. Oqt. 1pt. 14gi.
Ans. 2d. 9h. 18m.

8. Add

9. Add

10. Add

of a week to of a day.
of a square foot to a foot square.

Ans. 1 foot.

11. Add 6 inches to 11rd. 16ft. 5in.

Ans. 12rd. Oft. 5in.

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

tors, 7 and 11; and then obtain the numerators, as in Case VIII., Sec. XVI.; the difference of which we write over the common denominator.

RULE.

·Reduce compound fractions to simple ones, and mixed ones to improper fractions; then, having found a common denominator, divide this by each of the denominators of the fraction, and multiply their quotients by their respective numerators. The difference of these products, placed over the common denominator, will give the answer required.