Page images
PDF
EPUB
[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small]

Reduce the fractions, if necessary, to equivalent fractions having a common denominator; then subtract the numerator of the subtrahend from that of the minuend, and write the result over the common denominator.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

89. To reduce a mixed quantity to an improper fraction.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

RULE.

Multiply the integral part by the denominator of the fraction; to the product add the numerator if the sign of the fraction is plus, and subtract it if the sign is minus, and under the result write the denominator.

NOTE. - By a change of the language, Examples 12-14 in Art. 87, and 11-13 in Art. 88, become examples under this case. Thus, Example 12, Art. 87, might be expressed as follows: Reduce

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

NOTE. — It must be remembered that the sign before the dividing line belongs to the fraction as a whole.

[merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

Ans.

[merged small][merged small][merged small][merged small][ocr errors][merged small]

NOTE. According to the same principle an integral quantity can be reduced to a fraction having any given denominator, by multiplying the quantity by the proposed denominator, and under the product writing the denominator.

[merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

12. Reduce 4 ax to a fraction whose denominator is

[blocks in formation]

90. To reduce an improper fraction to an integral or mixed quantity.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

As the value of a fraction is the quotient arising from dividing the numerator by the denominator (Art. 82), we perform the indicated division. Hence,

RULE.

Divide the numerator by the denominator; if there is any remainder, place it over the divisor, and annex the fraction so formed with its proper sign to the quotient.

2. Reduce

3. Reduce

quantity.

4. Reduce

[merged small][merged small][ocr errors][merged small][merged small][ocr errors]

4 ab 3 abx+ to an integral or mixed

a b

[merged small][merged small][merged small][merged small][merged small][ocr errors]

5. Reduce

quantity.

6. Reduce

[ocr errors]

tity.

6 y3

to an integral or mixed

[blocks in formation]

x2+ax+a3 to an integral or mixed quan

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

91. To multiply a fraction by an integral quantity.

[blocks in formation]
« PreviousContinue »