How to Divide Fractions Into Lowest Terms

Simplify the Fraction 3/4

• 1

  Determine the factors of the numerator. Factors are numbers that, when multiplied together, equal that number. The factors of the numerator "3" are 1 and 3. There are no other whole numbers that equal 3 when they are multiplied together. Therefore, 1 and 3 are the only factors of the numerator 3.

• 2

  Determine the factors of the denominator, "4." The factors of 4 are 1, 2 and 4 because 1 times 4 equals 4, and 2 times 2 equals 4. There are no other whole numbers that, when multiplied together, equal 4. Therefore, the factors of 4 are 1, 2 and 4.

• 3

  Find the common factors between the numerator and the denominator. In other words, compare the factors to see which numbers are factors of both the numerator and the denominator. For 3/4, the only common factor is the number 1.

• 4

  Choose the greatest common factor (GCF). For the fraction 3/4, the number 1 is the only common factor. Therefore, it is also the GCF.

• 5

  Divide both the numerator and the denominator by their greatest common factor. When you divide 3 by 1 you still get 3. Divide 4 by 1 and you still get 4. Neither number can be reduced any further. Therefore, 3/4 is already in its lowest terms.

Simplify the Fraction 10/12

• 6

  Follow the example in Section 1. Find all the factors of the numerator 10. The factors of 10 are 1, 2, 5 and 10, because 1 times 10 equals 10, and 2 times 5 equals 10. No other whole numbers, when multiplied by another whole number, equal 10. Therefore, there are no other factors of the number 10.

• 7

  Find all the factors of the number 12. The factors of 12 are 1, 2, 3, 4, 6 and 12, because each of these numbers can be multiplied by another whole number to equal 12.

• 8

  Study the factors of 10 and 12 and determine which factors are common to both numbers. The numbers 1 and 2 are the only common factors for 10 and 12. The other factors can be evenly divided into either 10 or 12, but not both.

• 9

  Determine the greatest common factor (GCF) for the numbers 10 and 12. Since the common factors of 10 and 12 are 1 and 2 -- and 2 is greater than 1 -- the number 2 is the GCF.

• 10

  Divide the numerator and the denominator by the greatest common factor, 2. Ten divided by 2 equals 5, and 12 divided by 2 equals 6. Therefore, simplifying the fraction 10/12, or reducing it to its lowest terms, it becomes 5/6.