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A Fraction C

One of my favorite movies is The Shawshank Redemption. The film is deeply compelling and allegory-rich. It is also 98 minutes long.

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers. (Source: www.calculator.net)

With respect to any Principal Prepayment on any Mortgage Loan and with respect to any Class of the Class A-1, Class A-2, Class A-3, Class A-4, Class A-AB, Class A-S, Class B, Class C and Class D Certificates, a fraction (a) whose numerator is the amount, if any, by which (i) the Pass-Through Rate on such Class of Certificates exceeds (ii) the discount rate used in accordance with the related Loan Documents in calculating the Yield Maintenance Charge with respect to such Principal Prepayment (or, if the Yield Maintenance Charge is a fixed percentage of the principal balance of the related Mortgage Loan, the yield rate applicable to any related yield maintenance charge or that is otherwise described in the related Loan Documents) and (b) whose denominator is the amount, if any, by which (i) the Mortgage Rate on such Mortgage Loan exceeds (ii) the discount rate used in accordance with the related Loan Documents in calculating the Yield Maintenance Charge with respect to such Principal Prepayment (or, if the Yield Maintenance Charge is a fixed percentage of the principal balance of the related Mortgage Loan, the yield rate applicable to any related yield maintenance charge or that is otherwise described in the related Loan Documents); provided, however, that under no circumstances shall the Base Interest Fraction be greater than one. If the discount rate referred to in the preceding sentence is greater than or equal to both of (x) the Mortgage Rate on the related Mortgage Loan and (y) the Pass-Through Rate described in the preceding sentence, then the Base Interest Fraction shall equal zero, and if such discount rate is greater than or equal to the Mortgage Rate on such Mortgage Loan, but less than the Pass-Through Rate described in the preceding sentence, then the Base Interest Fraction shall equal one.

a/b, where a and b are integers and b is not zero, is called the set of rational numbers and is represented by the symbol Q, which stands for quotient. A number is a rational number precisely when it can be written in that form (i.e., as a common fraction). However, the word fraction can also be used to describe mathematical expressions that are not rational numbers. Examples of these usages include algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as (Source: en.wikipedia.org)