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Add the fractional parts as before, and if their sum be an improper fraction, reduce it to its equivalent whole or mixed number, and add the integral part with the whole numbers of the given mixed numbers.

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* When fractions are of different kinds, it will be necessary to reduce them to one name, before they can be added or subtracted,

SUBTRACTION OF FRACTIONS.

Case list.—To subtract a simple fraction from a simple fraction, having a common denominator.

Subtract the less numerator from the greater, under the difference place the denominator, and the fraction thus formed will be the difference required.

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Case 2d.—To subtract simple fractions from simple fractions, not having a common denominator. Reduce both fractions to a common denominator, and proceed as before.

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When the given fractions are compound, or complex, they must be reduced to simple fractions, with which proceed as

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Case 3d.—To subtract a fraction or a mixed number from a whole number.

Take the numerator from the denominator, and place the difference as a numerator, and under it put the denominator. and subtract one from the whole number, if the less quantity be a fraction but if it is a mixed number, one must be added to the integral part thereof, the sum subtract from the whole number, and the remainder with the fractional part annexed

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CAs E 4th.--To take mixed numbers from mixed numbers.

If the fractional parts have not a common denominator. reduce them to it, when if the numerator of the fraction belonging to the greater number exceed that belonging to the less, subtract the less from the greater, under which place the common denominator, which will give the remainder of the fractional part; the integers of the given quantities subtract as in whole numbers. But if the numerator of the fraction belonging to the less number, exceed the numerator of that belonging to the greater, subtract this numerator from its denominator and to this remainder add the numerator of fraction belonging to the greater number, which will be the numerator of the fractional part of the remainder, under which place the common denominator, add one to the integral part of the less quantity and subtract as before.

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4-> - - For a demonstration of the rules for adding and subtracting fractions, see John Walker's Philosophy of Arithmetic, pages 146 and 147.

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After having reduced the given fractions according to the former rules, mixed or whole numbers to improper fractions, and compound fractions to simple ones, &c. multiply the numerators together for a new numerator, and the denominators together for a new denominator; except when a mixed number is to be multiplied by a whole number, then the fractional part may be multiplied separately, and the result annexed or added to the product of the integers, as the case may require.

Note—A fraction is multiplied by a whole number, either by multiplying its numerator, or dividing its denominator thereby.

If, in the given quantities to be multiplied or divided, a numerator and denominator are alike, both may be wholly expunged, and where they have a common measure or divisor; . . ) the quotients after dividing the contrary terms thereby, will answer as well as, or better than, the original numbers.

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- Tor 40. 31's + 1} + 4 – 2," X 4 x 15 — 2,', When one or both of the fractional parts to be multiplied, are compound fractions or quantities, the continual product of the several numbers will be that required. (framples. Let 4 of + of + of 23 be multiplied by 3 of 3 of 4 #x+x #x3x}x}x + = "... Answer.

DIVISION OF FRACTIONS,

prepare the quantities by the foregoing rules, then invert the divisor, and proceed in every respect, as in Multiplication. Note.—A fraction is divided by a whole number, by an Operation the

eonverse to that of Multiplication, that is, by the multiplication of the denominator or division of the numerator by the given divisor.

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