Compound fractions must be reduced to simple ones, and mixed numbers to improper fractions, and they may then be multiplied as before. Hence it appears, that a fraction may be multiplied by a whole number by dividing the denominator by that number, when this division can take place. DIVISION. 37. To divide one fraction by another, or to determine how often one is contained in the other, invert the numerator and denominator of the divisor, and proceed as in multiplication. For, from the nature of division, the divisor multiplied by the quotient must produce the dividend: therefore 517 3 4 X quotient =; let these equal quantities be multiplied by the same quantity, and the products must be equal; 21 = as was found by 35 20 35 but = 1; therefore the quotient the rule. And the same method of proof is applicable to all cases. Compound fractions must be reduced to simple ones, and mixed numbers to improper fractions, before the rule can be applied. [38. It will often happen in practice that fractions present themselves which require the application, not of one single rule only, as of Addition, or Subtraction, or Multiplication, &c., but of several rules in one operation. Thus, Ex. 1. Required to find the single fraction which is equivalent to Compound fractions must be reduced to simple ones, and mixed numbers to improper fractions, and they may then be multiplied as before. Hence it appears, that a fraction may be multiplied by a whole number by dividing the denominator by that number, when this division can take place. DIVISION. 37. To divide one fraction by another, or to determine how often one is contained in the other, invert the numerator and denominator of the divisor, and proceed as in multiplication. For, from the nature of division, the divisor multiplied by the quotient must produce the dividend: therefore 7 by the same quantity and the products must be equal; the rule. And the same method of proof is applicable to all cases. Compound fractions must be reduced to simple ones, and mixed numbers to improper fractions, before the rule can be applied. [38. It will often happen in practice that fractions present themselves which require the application, not of one single rule only, as of Addition, or Subtraction, or Multiplication, &c., but of several rules in one operation. Thus, Ex. 1. Required to find the single fraction which is equivalent to 39. In order to lessen the trouble which in many cases attends the use of vulgar fractions, decimal fractions have been introduced, which differ from the former in this respect, that their denominators are always 10 or some power of 10, as 100, 1000, 10000, &c. and instead of writing the denominator under the numerator, it is expressed by pointing off from the right of the numerator as many figures as there are cyphers in the denominator; |