PRIN. 1.- When the dividend and divisor have a common denominator, divide the numerator of the dividend by the numerator of the divisor.

Prin. 2.-Any fraction having unity for its numerator, is contained in unity as many times as there are units in its denominator; if the fraction has 2 for its numerator, it is contained one-half as many times; if it has 3 for its numerator, one-third as many times; etc.

PRIN. 3.-Two fractions, each having unity for its
numerator, are divided by making the denominator of
the divisor the dividend, and that of the dividend the
divisor, regarding these numbers as integers and per-
forming the division.
For, 1:1= 2; 1:$=3; 1:1= 4; 1:= 5.

4:1=4; 1:}=0; 1:1=8; 1:1 = 10.
1:1=1; 1:$= = 11; 1:1== 2;

*:}== 21.
PRIN. 4.-If the dividend is increased, the quotient
is increased just as many times; if the dividend is
diminished, the quotient is diminished in like manner.

COR.-To divide any number, either integral or fractional, by a fraction, invert the divisor and then multiply the dividend by it.

=

ADDITION AND SUBTRACTION OF FRACTIONS.

179

ADDITION AND SUBTRACTION OF

FRACTIONS.

Add
1. , 1, $, .

Ans. 248. 2. }, k, po, and it

Ans. 1;}. 3. , b, t.

Ans. 37

Ans. 2146 4. }, }, #, and . 5. 15, and 37.

Ans. 485

Ans. 1016. 6. 21, 34, and 5%.

Ans. 1117 7. 11, 23, 31, and 44. 8. 1 of, of 4, and 7 of 4.

Ans. 47 9. &, $, and

Ans. 141.

Ans. 1317 10. 23, 4, and 7.

Ans. H. 11. From take f. 12. From take .

Ans. .

Ans. 18 13. From I take 14. From is take :

Ans. Vous

Ans. 15. From 1 take 16. What is 121

Ans. 57. 17. What is 108 - 41 ? %

Ans. 51. 18. What is 21% - 104 ?

Ans. 109. 19. What is 254 - 121?

Ans. 124 20. What is 364 - 214?

?

Ans. 1521 21. What is 754 - 26} ?

Ans. 484 22. What is 1 of 1 - $ off ?

Ans. 135 23. What is 3 of - 4 of 1? 1 1 P2

Ans. 345. 24. What is 1 of 54 - of 34 ?

Ans. 11 25. What is off - 1 of 1 ?

Ans. 37 26. What is the difference between of off and of of 1 ?

Ans. 3724

5 22.

23 49

27. What is the difference between 1 of 2 and } of 31?

Ans. e. What is the difference between 28. of 12 and 1 of 164 ?

Ans. 29. of 204 and of 361 ? f

Ans. 173. 30. What is the difference between two fractions whose numerators are each 1 and whose denominators are 5 and y?

Ans.

REM.—The numerator will be the difference and the denominator the product of the denominators.

MULTIPLICATION AND DIVISION OF

FRACTIONS.

1. Multiply by 3.

Ans. 2. Multiply 1 by 4.

Ans. 1. 3. Multiply by 5.

Ans. 4. Multiply is by 6.

Ans.

Ans. 4. 5. Multiply } of 8 by 1 of 10. 6. Multiply } of 61 by of 57.

Ans. 6 P. 7. Multiply of of 5 by of 45.

Ans. 6473 8. Multiply 61, 57, 3 and of 5. Ans. 2697469. Multiply 4, 4, 11, 4 of 23, and 4 of 51. Ans. 16 10. Multiply $, %, 4, 5, and fr.

Ans. 11. Multiply 31, 55, 6%, 1 of it, and 74. Ans. 35%. 12. Divide y by f.

Ans. 241. 13. Divide 9 by

Ans. 24. 14. Divide 30 by 23.

Ans. 12. 15. Divide by 1.

Ans. 11. 16. Divide to by

Ans. 11. 17. Divide j by ic.

Ans. 2. 18. Divide by 15.

Ans. 3,

T

14

11:

18

321

19. Divide it by the

Ans. 6. 20. Divide the by 128

Ans. 93. 21. Divide i by .

Ans. 151 22. Divide 47 by to

Ans. 3134 23. Divide { of of } of 4 by $ of t1 of 13. Ans. 17. Reduce to a simple fraction, 24. Ans. S.

26.
15.

Ans.
25

.

** 11. Ans. ft.

27.

x 8.

25. Ans. $.

1 x $ X 28.

Ans. 10. * X}

等 29.

Ans. R. 플을 1+ i. $-$

主 30. •

Ans. 1934. -iis +3

Te 31. j * *.*:. x

Ans. Ti :1-4x

x 2 32. { xfxxxf 4x*x x x *. Ans. 32. 33. 374 = 25$.

Ans. 15%. 34. 2014 - 307.

Ans. 1846 35. ndoo • 1000.

Ans. Toodooo

3 5

NUMERATION, ADDITION AND SUBTRACTION

OF DECIMALS.

Write in figures,
1. Twelve and five tenths.
2. Five hundredths.
3. Five thousandths.
4. Five hundred, and five hundredths.

5. Five thousand, and five thousandths.
6. Fifty thousand, and five ten-thousandths.
7. Three hundred and seventy-five thousandths.

8. Two thousand three hundred and seventy-five tenthousandths.

9. Thirty-two thousand three hundred and seventyfive hundred-thousandths.

10. Two hundred and seventy-five hundred-thousandths.

11. Seventy-five hundred-thousandths.
12. Five hundred thousandths.
Read the following:
13. .01, 2.07, 11.11, 13.0013, 50.501, .0016.
14. 33.00033, 119.019, 3.000003, 4.00044.
Add the following numbers:

1. Fifty-five thousand, and twelve thousandths; twentyone hundred, and twenty-one hundredths; fifty-two, and two hundred and seventy-five thousandths.

Ans. 57152.497. 2. Twenty-one, and twenty-one hundredths; two hundred and ten, and two hundred and ten thousandths ; three thousand four hundred and fifty-one, and three thousand four hundred and fifty-one ten-thousand ths.

Ans. 3682.7651. 3. Forty-four, and four tenths; four hundred, and four hundredths; four thousand, and four thousandths; forty thousand, and four ten-thousandths; four hundred thousand, and four hundred thousandths; four million, and four millionths.

Ans. 4444444.444444. 4. From four million, and four millionths take four thousand, and four thousandths. Ans. 3995999.996004.