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How to Reduce Large Fractions to Their Lowest Terms

A large fraction is reduced to its lowest terms by finding an equivalent fraction that expresses the terms in the numerator and denominator in their completed factored forms. This involves finding the greatest common factor of both the numerator and denominator which is the largest number that is a factor of both of these terms. Reducing a fraction is also known as simplifying a fraction, because the fraction is being reduced into its simplest form.

Instructions

- 1
  Find the greatest common factor of the numerator and denominator by first factoring each term. For example, for the fraction (2,940 / 3,150) first factor 2,940. Since 2,940 is an even number, its lowest factor is 2. Divide the number by 2 to obtain: 2,940 / 2 = 1,470.
- 2
  Divide the new number by its lowest factor. Once again, the lowest factor is 2 since 1,470 is even. So, 1,470 / 2 = 735.
- 3
  Continue finding the lowest factor of the current number until you reach prime numbers. For example, since 735 is divisible by 3 the next number is: 735 / 3 = 245. Then 245 is divisible by 5 so: 245 / 5 = 49, then 49 / 7 = 7. Since 7 is a prime number factorization ends. So, the factorization of 2,940 = 2 * 2 * 3 * 5 * 7 * 7.
- 4
  Factor the denominator in the same way as for the numerator. For example, using the same method on 3,150 you find the factorization is 3,150 = 2 * 3 * 3 * 5 * 5 * 7.
- 5
  Multiply the common factors between the two numbers together. For example, the common factors between 2,940 and 3,150 are 2, 3, 5 and 7. Multiplying them together finds: 2 * 3 * 5 * 7 = 210. This is the greatest common factor.
- 6
  Divide the numerator and denominator by the greatest common factor to obtain the fraction's lowest terms. In this example, 2,940 / 210 = 14. And 3,150 / 210 = 15. So the fraction reduced to its lowest terms is 14 / 15.

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