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126 Rh CHAPTER XIV.

Complex Fractions. Mixed Expressions.

152. We now propose to consider some miscellaneous questions involving fractions of a more complicated kind than those already discussed. In the previous chapter, the numerator and denominator have been regarded as integers; but cases frequently occur in which the numerator or denominator of a fraction is itself fractional.

153. A Complex Fraction is one that has a fraction in the numerator, or in the denominator, or in both.

Thus -, -, - are Complex Fractions.

In the last of these types, the outside quantities, a and d, are sometimes referred to as the extremes, while the two middle quantities, b and c, are called the means.

154. By definition (Art. 148) - is the quotient resulting from the division of - by - ; and this by Art. 143 is