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# Operations on Rational Numbers

 A rational number can be represented in the form of a/b, where a and b are integers, and b is not zero a/b is called a fraction, where a is the numerator of the fraction and b is the denominator of the fraction. Two fraction are said to be equivalent if they have the same value but different forms. For example, 2/3, 4/6, -6/-9. We denote two equivalent fractions by writing an equal sign between them, 2/3 = 4/6 = -6/-9 Two fractions are equivalent, if their cross products are equal.     Addition and subtraction of fractions    The least common denominator, or LCD Example 1: Solution The denominators are factored as : 15 = 3 × 5 and 6 = 2 × 3 The prime factors are 3, 5, 2, and therefore the LCD of the fractions is 3 × 5 × 2 = 30 Example 2: Solution Writing the denominators in factored form, 18 = 3 × 3 × 2 = 32 × 2 and 27 = 3 × 3 × 3 = 33 so that, the LCD of the fractions is 33 × 2 = 54 Multiplication and Division of Fractions  