197. Rule for Addition of Fractions.-Reduce the frac tions to equivalent fractions having a common denominator; add their numerators, and write und r the sum the common denominator.

If there be mixed numbers or integers, add the fractions and integers separately, and uni! the results.

10. What is the sum of 31+ 2+ 3+ §?

11. A farmer has in one bin 31 bushels of wheat, in a second bin, 15% bushels, and in a third, 16 bushels. How many bushels has he in the three bins?

12. If you should spend 6 hours in study, 32% hours in play, and 11 hours in sleep, how many hours would you spend in all?

SECTION XVI.

SUBTRACTION OF FRACTIONS.

199.-1. John and his brother have of an apple. If John has g, what part of the apple has his brother? 2. Jane has of an orange; if she should give Susan , what part of the orange would she have left?

3. How many fifths are dess ? less ?

4. How, then, do you subtract one fraction from another when both have a common denominator?

5. If of an apple be taken from it, what part will remain ?

6. How much is 1 less ? 2 less? 3 less?

7. If a cord of wood cost

dollars, what is its cost?

of a dollar less than 6

less?

SOLUTION.-equals, and equals ; and less

8. How much is

9. A man worked

is f

of a day, and his son of a day. How much longer did the man work than his son? 10. How much is less? less ? less? 11. How do you prepare fractions having different denominators for subtraction?

12. If a man owning of a mill should sell of the mill, what part of it would he have left?

13. How many are 2 less? 5 less 2?

14. What number must be added to 33 to make 9?

200. Principle.-Fractions must express like parts, or have a common denominator, before they can be subtracted.

WRITTEN EXERCISES.

201.-1. What is the difference between and ?

mon denominator and finding the difference between their numerators, we have, the difference required.

2. Find the difference between and .

3. Find the difference between and .

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5. Find the difference between 14 and 6. 6. Find the difference between 283 and 914.

202. Rule for Subtraction of Fractions.-Reduce the fractions to equivalent fractions having a common denominator, and write the difference of the numerators over the common denominator.

If there be mixed numbers, subtract first the fractional part of the subtrahend, and then the integral part, and unite the results.

acres from a lot con

10. If a farmer should sell 24

taining 66 acres, how many acres would be left? 11. What is the difference between 851 and 831?

204. TEST QUESTIONS.—1. What is the principle in addition of fractions? How do you add when all the numbers are fractions? When there are fractions and mixed numbers or integers?

2. What is the principle in subtraction of fractions? How do you subtract when the minuend and subtrahend are fractions? When the minuend and subtrahend are mixed numbers?

SECTION XVII.

MULTIPLICATION OF FRACTIONS.

CASE I.

Fractions Multiplied by Integers.

205.-1. If you should give of a melon to each of 5 boys, how many sixths of a melon would they all have?

2. If you should give of a cake to each of 7 boys, how many thirds of a

cake would be required? How many cakes? 3. 7 times are how many times 1?

4. If 1 yard of cloth cost of a dollar, how many dollars will 8 yards cost?

SOLUTION. Since 1

yard of cloth cost of a

dollar, 8 yards must cost 8 times of a dollar, which are 40, or 30, equal to 63 dollars.

5. At of a dollar each, how many dollars will 9 hats cost?

6. If 1 pound of tea cost of a dollar, how many dollars will 7 pounds cost?

7. 7 times are how many times 1 ?

8. If a horse eat of a bushel of grain in 1 week, how many bushels will he eat in 10 weeks?

9. How many are 6 times ? 7 times §?

10. How many are 8 times? 5 times ?

11. If of an acre will pasture a cow, how many acres will pasture 12 cows?

12 times ?

12. How many are 11 times ? 13. If of a yard of cloth is of what is required for a suit of clothes, how many yards will be required for the suit?

by 11 gives 1,

14. If you can earn of a dollar in 1 day, how many dollars can you earn in 11 days? 15. Multiplying the numerator of or; dividing the denominator of in each case the fraction is multiplied by 11. How, then, may a fraction be multiplied by an integer?

16. Multiply by 8.2 by 7.

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17. How many are 5 times 6?

by 11 gives ;

by 5.

SOLUTION.-5 times 6 are 30, and 5 times are, or 2, which added to 30 gives 32, the answer required.

18. If 1 ton of coal cost 5 dollars, how many dollars will 7 tons cost?

19. If you can gather 63 quarts of berries in 1 day, how many quarts can you gather in 6 days?

20. At the rate of 33 miles in 1 hour, how far can you walk in 8 hours?

21. How much must be given for 11 pounds of tea, at 13 dollars a pound?

22. What will 5 yards of cloth cost, at 34 dollars a yard?

206. Principle.-Multiplying the numerator, or dividing the denominator, by any number, multiplies the fraction by that number.