5. Find the least common denominator and add, }, , and. and 3%. Ans. 1.

146. When there are mixed numbers, instead of reducing them to improper fractions we may add the whole numbers and the fractional parts separately, and then add their sums.

1. Add 19, 63, and 4 together.

Whole numbers.

19+6+4=29.

64

OPERATION.

64

Fractional parts. }+3+3=188=18.

64

Hence, 29+1=3065, the sum.

2. Add 31, 65, 81%, and 65%.

CASE III.

147. When the fractions are of different denominations.

Then

Reduce the fractions to the same denomination. reduce all the fractions to a common denominator, after which add them as in Case I.

EXAMPLES.

1. Add of a £ to of a shilling.

Then,

of a £3 of 20=40 of a shilling.
40+5=240+15=255s.—3/5s.=14s. 2d.

Or, the of a shilling might have been reduced to the fraction of a £ thus,

of of a £=4 of a £.

4

Then, +2+31⁄2={} of a £: which being reduced, gives 14s. 2d.

2. Add of a yard to of an inch.

Ans.

Ans. 14s. 2d.

yd. or 14in.

of an hour

Ans. da. hr.

3. Add of a week, of a day, and together. 4. Add of a cwt., 857b., and 3 oz. together. Ans. 2qr. 23lb. 17oz.

146. How do you add when there are mixed numbers?
147. How do you add fractions of different denominations?

5. Add 1 miles, furlongs, and 30 rods together. Ans. 1m. 3fur. 13rd.

148. The value of each of the fractions may be found separately, and their several values then added.

EXAMPLES.

1. Add of a year, of a week, and of a day together.

2. Add of a yard, of a foot, and

gether.

11hr.

of a mile to

Ans. yd. ft. in. 3. Add of a cut., 42 of a lb., 13oz., and 1⁄2 of a cut.

67b. together.

Ans. 1cwt. 2qr. 177b. 13oz.

EXAMPLES IN ADDITION.

at

1. I bought 22 bushels of wheat at one time, 19 ancther, and 335 at another: how much did I buy in all ? Ans. 7520bu.

2. What is the sum of 263, 187, 193, 131, and 17? 3. A farmer owns three farms; the first contains 471 acres, the second 71418, and the third 1813: how many acres in all ? Ans. 136837 acres.

4. Bought of 3 of 5cwt. of sugar at one time; at another, of 5 of 6cwt.; at another, of of 8cwt.: how much did I buy in all? Ans. 2013cwt. 5. What is the value of of a ton, and of a cut. ? Ans. 12cwt. 1gr. 7lb. 13 oz. 6. How far is of a mile and of a furlong?

7. A man travelled 28 miles the first day, 33 the second day, and 29

he travel in all ?

miles the third day: how far did Ans. 90mi. 4fur. 15rd. 3ft. 114in.

148. How may fractions of different denominations be added by the second method?

8. Add 58 days and 52

the whole time.

minutes together, and give Ans. 5da. 20hr. 52m. 1515 sec. weight of cwt. 85lb. and Ans. 2qr. 16lb. 3oz. 8 dr. of a year, of a day, of

9. What is the entire 3,9oz.?

10. Find the value of

of an hour, and 3 of 24

2층

11. Bought 3 pieces of cloth; the first contained of 3 of of yards; the second of of 5; and the third of of what did they all contain?

Ans. 2yd. 2qr. 1na.

Ans. 3110.

Ans. 4181.

252

Ans.

12. Add together, 3, 13, and 18.
13. Add together, 2, 1, and 1.
14. Add together 382, 133, and 93.
15. Add together 62, 13, 17, and 132.

Ans. 16953

16. Add together of a week, of a day, and one

hour.
17. Add together 14cwt. 173lb. and 7 oz.

Ans.

Ans. 1cwt. 1qr. 7lb.7100%.

SUBTRACTION OF VULGAR FRACTIONS.

149. It has been shown that before fractions can be added together, they must be reduced to the same unit and to a common denominator. The same reductions must be made before subtraction.

SUBTRACTION of Vulgar Fractions is the process of finding the difference between two fractions.

CASE I.

150. When the fractions are of the same denomination and have a common denominator.

149. Can one-third of a shilling be subtracted from one-third of a £ without reduction? Can one-sixth of a shilling be subtracted from one-fifth of a shilling? What reductions are necessary before subtraction? What is subtraction?

150. How do you subtract fractions which have a common unit and the same denominator?

Subtract the less numerator from the greater and place the difference over the common denominator.

151. When the fractions are of the same denomination, but have different denominators.

Reduce mixed numbers to improper fractions, compound and complex fractions to simple ones, and all the fractions to a common denominator: then subtract them as in Case I.

EXAMPLES.

1. What is the difference between and ?

Here, -=-== answer.

2. What is the difference between 12 of

and 2? Ans.

3. What is the difference between 2 of a £, and

152. When the fractions are of different denominations.

151. How do you subtract fractions which have the same unit but different denominators? What is the difference between one-half and one-third?

152. How do you subtract fractions which are of different denominations?

Reduce the fractions to the same denomination: then reduce them to a common denominator, after which subtract as in Case I.

EXAMPLES.

1. What is the difference between } of a £ and } of a shilling?

30

60

- 60

of a shilling=} of 2=&% of a £. Then, -638-26-28 of a £=9s. 8d. 2. What is the difference between of a day and of a second? Ans. 11hr. 59m. 59 sec.

3. What is the difference between of a rod and of an inch? Ans. 10ft. 114in. 4. From 13 of a lb., Troy weight, take of an ounce. 5. What is the difference between of a hogshead, Ans. 16gal. 2qt. 1pt. 3gi.

6

and of a quart? 1

6. From of a £ take of a shilling. Ans.

7. From oz. take put.

8. From 4 cwt. take 4lb.

Ans. 11put. 3gr.

Ans. 4cwt. 3qr. 67b. 1oz. 931dr.

GENERAL EXAMPLES.

1. From of an ounce take of a put.

Ans. 6pwt. 15gr. 2. Take of a day and of of of an hour from

Ans.

3 weeks. 3. A man engaged to work 41 days, but was absent by indisposition 6 days: how many days did he work? Ans. 347 days. 4. What remains of a hogshead of vinegar if of it has leaked out? 5. A man has travelled 4mi. 1fur. 24rd.: how much farther must he go in order to make6 miles?

Ans.

Ans. 2mi. 2fur. 16rd.

Ans.

Ans. 7.

8. From of a degree take of a mile.

Ans.