596. Find the least common multiple of the denominators of the fractions, 11, §, 17, 48, 71⁄2

2. 9, 15, 15, 4, 4, 12, 25. Strike out one 15 and two 4's.

3. 2, 3, 5, 7, 5, 14, 10, 12, 24

4. 2, 3, 5, 6, 8, 10, 15, 16, 80

5. 20, 30, 40, 50

6. 2, 3, 4, 6, 8, 12, 16, 24

7. 24, 12, 5, 3, 10, 18

8. 11, 3, 7, 77, 33

9. 18, 5, 9, 40, 16

10. 10, 12, 15, 21

ADDITION AND SUBTRACTION OF FRACTIONS.

598. In adding or subtracting fractions, they must be reduced to a common denominator. The least common denominator is

the least common multiple of the denominators.

In the following examples, determine the least common denominator by inspection, if possible.

599. Add:

1. 84, 51, 31

2. 45, 201, 83, 9

3. 321, 193, 61, 811
4. 21, 20, 3, 12, 5
5. 81, 455, 217, 41, 21

16

6. 7. 8. 10. 20. 28

23

7. 631, 3, 21, 5, 77 8. 4, 78, 84, 6170, 10% 9. 5, 18, 31, 71, 81 10. 1710000%, 6%, 1850, 180

603. Oral Problems.

1. A person traveling from New York to Albany (140 miles apart) has gone 93 miles. How much farther has he to go?

2. There are 196 pounds of flour in a barrel. How many pounds in bbl.?

3. How many fourths in 24?

4. Reduce to lowest terms.

5. Change 100 to a mixed number.

6. Add,, and 1.

7. From a chest of tea containing 45 lb., 14g lb. are sold. How many pounds remain?

8. From of a dollar take 10 cents.

9. How many cents in ++ of a dollar?

10. A farmer has 60 acres of pasture and 20% acres of woodland. How many acres in both?

11. The circumference of a circle is about 34 times its diameter. If the diameter is 8 feet, about what is the circumference?

12. Mary is 12 years and 7 months old; Jane is 3 years and 11 months older. How old is Jane?

13.

In a year

and a half William will be 7 years 2 months old. How old is he now?

14. What number multiplied by 3 equals 231?

15. What number between 7 and 12 is a prime number?

16. A boy received 9 marks in arithmetic, 8 in penmanship,

and 7 in reading. What was his average mark?

17. of a class consists of boys. How many girls in the class if it contains 49 pupils?

18. If July 1 falls upon Tuesday, what will be the date of the third Tuesday of July?

19. If July 1 falls upon Thursday, upon what day will the first of August fall?

20. A man bought 20 lb. of sugar; he sold 10 lb. at one time and 6 lb. at another. How much had he left?

21. If 3 qt. 1 pt. oil cost 7 cents, what will 1 gal. 1 qt. cost?

22. How much will have to be paid for 7 cows at $50 each, and 4 horses at $150 each?

23. how many hundredths?

=

24. What are the two factors of 87?

25. Find the G. C. L. of 36 and 54.

604. Slate Problems.

1. A merchant sold one firkin of butter at 19 per lb., a second at 20¢ per lb., a third at 163 per lb. What was the average price per lb., each firkin containing 56 lb. ?

2. If eggs are sold at the rate of 21 for 25 cents, how much will be paid for 5 dozen?

3. If a train travels 45 miles per hour, how far will it go from half-past 9 in the morning to a quarter of 7 in the evening?

4. To the sum of 63 and 19 add their difference, and find how often the greater number is contained in this total.

5. A mechanic has deposited in the savings bank $35 per month for 11 months, and $20 the twelfth month. His expenses have averaged $3 each day of the year. What are his daily wages for the 300 days he has worked?

containing 271⁄2 yd.,

6. A merchant sold 4 pieces of cloth 26 yd., 29 yd., and 28 yd., respectively. How much did he receive for the cloth at 96 cents per yard?

7. Reduce 182 to lowest terms.

8. A man has 85 bu. of peanuts. He puts them into bags holding bu. How many bags does he fill?

9. A 160-acre farm consists of 5 fields. The first contains 17.38 acres, the second 29.4 acres, the third 35.073 acres, the fourth 25.875 acres. How many acres are there in the fifth field?

10. How many seconds in 7 hours 15 minutes?

11. Find the total cost of 2 doz. rockets at $7.50 per gross, 3 dozen Roman candles at $9.60 per gross, and 24 doz. pin wheels at $1.35 per gross. (1 gross 12 doz.)

=

12. From a piece of silk that contained 28 yd., there were sold 21 yd., 61 yd., and 13 yd. Find the value of the remainder at $1.20 per yd.

13. Three pieces of cloth bought at $2 per yard cost $150. The first piece measures 234 yd., the second measures 30 yd. How many yards in the third piece?

14. Three lots of tea were sold for $330. The second contained twice as much as the first, and the third three times as much as the first. The third lot contained 330 pounds. Find the selling price of the tea per pound.

15. What part of a person's income remains after he spends , and of it?

16. A boy loses of his marbles, and he gives away of them. If he has 17 marbles left, how many had he at first?

17. A cask of molasses contained 80 gallons. One-fourth of it leaked out. If the molasses cost 60 cents per gallon, what price must be charged for the remainder so that there will be no loss.

18. A dealer sells 14 gross, 37 gross, 411 gross, 91 gross, and 8 gross of lead pencils at 36 cents per dozen. How much does he receive for all?

19. There are four towns, A, B, C, and D, on a certain railroad running east and west. A is 41 miles west of C; D is 391 miles east of B; B is 221⁄2 miles west of C. How many miles from A to D? Make a diagram.

20. If 12 dozen rockets cost $5.75, what will 15 dozen cost?