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How to Multiply Rationals

Rational expressions are fractional terms containing variables. Multiplying them is much like multiplying regular fractions, and need to be simplified and cross-multiplied to find the simplest solution. Rational expressions are often used in physics, chemistry, architecture, optics, electrical engineering and many other scientific fields.

Instructions

- 1
  Cross-cancel the factors in the rational expressions to simplify them. That is, factor the numerator of the first expression and the denominator of the second and factor the denominator of the first expression and the numerator of the second. For example, in the expression (7x² / 3) * (9 / 14x), the numerator of the first expression, 7x², and the denominator of the second expression, 14x, contain factors of each other. The 7 factors into 14 twice so the 7 cancels to 1 and the 14 reduces to 2, since 14 / 7 = 2. The x is a factor of x² and cancels to 1 and the x² reduces to x. Similarly, the 3 of the first denominator cancels to 1 and the 9 of the second numerator reduces to 3, since 9 / 3 = 3.
- 2
  Write out the simplified expression: (7x² / 3) * (9 / 14x) simplifies to (x / 1) * (3 / 2).
- 3
  Solve the simplified expression multiplying the numerators and multiplying the denominators. For example, the expression (x / 1) * (3 / 2) equates to (3x / 2).

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