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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.

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ADDITION AND SUBTRACTION OF FRACTIONS.

79

ADDITION AND SUBTRACTION OF

FRACTIONS. Add

Ans. 248 1, 3, 4, 5,

Ans. 131 2. , }, to, and itt:

Ans. 37 3. }, }, in

Ans. 2116 4. 4, 5, 4, and H.

Ans. 48 5. 13, and 31.

Ans. 1014. 6. 21, 34, and 51.

Ans. 1117. 7. 11, 2}, 34, and 41.

Ans. 47. 8. 4 of $; } of 4, and 1 of 4. 9. $,$, and is

Ans. 14.

Ans. 1347 10. 21, 43, and 77. 11. From take f.

Ans. H. 12. From take D.

Ans. .

Ans. 46 13. From take f.

Ans. He 14. From is take

Ans. 15. From I take a

Ans. 57. 16. What is 121 – 71?

Ans. 54. 17. What is 10% - 47? 18. What is 21% 101?

Ans. 10% 19. What is 254 – 121 ?

Ans. 1241 20. What is 364 - 214 ?

Ans. 15211

Ans. 4844. 21. What is 757 - 261? 22. What is 1 of 11 - off?

Ans. 13 23. What is 3 of 3 - 4 of z?

Ans. 33

Ans. 11 24. What is 4 of 54 - of 34 ? 25. What is off - of ?

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

Ans. 374

27. What is the difference between 1 of 2 and } of 3?

Ans. ta. What is the difference between 28. 1 of 12 and 4 of 164 ?

Ans. 29. of 204 and 1 of 36 ?

Ans. 145. 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 its by 5.

Ans. 4. Multiply is by 6.

Ans.. 5. Multiply } of 8 by 1 of 10.

Ans. 4. 6. Multiply } of 61 by of 57.

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

Ans. 6473 8. Multiply 61, 51, 31 and of 53. Ans. 2697& 9. Multiply $, , , of 23, and 4 of 51. Ans. tab. 10. Multiply 3, 5, 4, 3, and 11:

Ans. 11. Multiply 31, 54, 65, $ of fi, 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,

26. i

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19. Divide H by Thai

Ans. 6. 20. Divide Td4 by 128•

Ans. 9. 21. Divide 1} by i.

Ans. 155 22. Divide $47 by to

Ans. 3131 23. Divide { of of of 4 by 1 of t1 of %. Ans. 17. Reduce to a simple fraction, 24. Ans. 8.

Ans. ill.

23 25. Ans. *

27.

Ans. 1.

1 * $ X% 28.

Ans. 10. Xt 29.

Ans. 좋을

$+$. 1-4. 30.

Ans. 1934. 1-17 +7 x

Ans. tit. } 1:1 +*$ 32. kxf ******* *********. Ans. 32. 33. 37* = 25$

Ans. 6 34. 2014 • 3071.

Ans. 1346 35. doo 1000.

Ans. Toodoo

18

308

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.

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