SECTION XVII.

ADDITION OF VULGAR FRACTIONS.

CASE I.

To add fractions that have a common denominator.

1. What part of an apple is

2. What part of a dollar is 3. What part of a shilling is

and ? and ? and ? and? and? and ? and? 12, 12, and 131⁄2?

10

4. What part of an orange is and ? and ? § and ? 5. Add 12, 12, 72, and 12 together.

3

5

In this question, we add the numerators, and divide their sum by the denominator.

RULE.

Write the sum of the numerators over the common denom

inator, and reduce the fraction if necessary.

6 9

6. Add 7, 17, 17, 14, 14, and 19 together.
7. Add,, 11, 1, and 18 together.

13

8. Add 47, 17, 19, 19, and 17 together.

יד

19

29 49
879
29

14

9. Add 1,1,4, and 111 together. 10. Add 619 491 567, and together.

631 631 631

631

11. Add 41, 41, 988, and 780 together.

and together.

Ans. 2133. Ans. 2123

83

777 1000

CASE II

To add fractions that have not a common denominator. 1. What is the sum of 7, 12, 1, and 13 ?

4×2×3×2×5=240 common denominator.

Having found a common denominator by Case VIII., we proceed as in the last Case.

8 30X 7=210 12 20x 5 = 100 16 15X11=165 20 12 × 13 = 156

RULE.

Let the pupil examine the second method of reducing fractions to a common denominator in Case VIII., Sec. XVI.

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.

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 112, 153, 125, and 17% ?

15. What is the sum of 119, 195, and 235? 16. What is the sum of 183, 271%, and 49 ? 17. What is the sum of 213, 183, and 265 ?

Ans. 54399.

Ans. 96. Ans. 6613.

18. What is the sum of 173, 14, and 134? Ans. 451⁄2· 19. What is the sum of 163, 87, 93, 31, and 17?

Ans. 40.

20. What is the sum of 37111, 61418, and 81 ?

21. Add 4 of 18, and 1 of 3 of 6

Ans. 106837.

22. Add of 18, and

of 1 of 74

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

Place the sum of the denominators over their product.

1. Add to.

EXAMPLE.

4-5 9

Answer.

4 X 5 20

2. Add to, to, to, to, to, to, too. 3. Add to, to, to, to, to, to, to . 4. Add to, to, to, to, to, to 5. Add to, o to, to 4, 1% to 1, To to, to TO

to,

6. Add
7. Add to,
8. Add to,

9. Add

to,

to, to 1, to, to, to, to .
to ‡, to, to, to, to, to
to,to,to,to,to 1, † 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
=20

= 12% Ans.

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

to, to,&to, to, to r

12. Add
13. Add to,

tor,

to fr,

to f, fr to f, fi to fr, fi to 5.

6

8

I

14. Add to, to, to f, is to 15, 13 to fr, is to 1.

15. Add

16. Add

to T, fo to f, fo to fe, fo to fr, fo to . to 3, 7 to 1, 7 to 1,to,to 75, to 17. Add to,&to, &to, &to, & to, & to 21. 18. Add 1 to 18, 11 to 19, 11 to 18, 18 to 18, 19 to 19.

19. Add 1 to 11, 11 to 11, 11 to 11, 12 to 16, 11 to 14.

159

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

CASE IV.

To add compound numbers.

1. Add of a £. to of a £.

Value of of a £.

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£. +11£. = 14£. 1£. 7s. 1d. 25qr. Ans.

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? × 2b=180=5b£.

f £. + 7 £. + 3% £. = 3:18 £. = 0£. 17s. 10d. 131qr. Ans.

150

NOTE.- The pupil should solve the following questions by both pro

cesses.

yard.

of a furlong, and of a

22

Ans. 5fur. 16rd. Oft. 3in. 1149bar.

How

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

How far did he

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. travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 4 in. of a gallon of wine to of a hhd.

Äns. 6gal. Oqt. 1pt. 11gi.
Ans. 2d. 9h. 1 m.

8. Add

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

of a week to of a day.

of a square foot to a foot square. Ans. 1 foot.

Ans. 12rd. Oft. 5in.

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 g be taken from § what will be left?

3. If be taken from what will be left?

4. What portion of a dollar will be left, if be taken from?

5. Subtract

from

11-5=6. Ans.