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Reducing fractions, simplify, and reduce to the lowest terms all refer to eliminating common factors between the numerator and the denominator.
2/4 = ½
18/72 = ¼
30/45 = 2/3
All of the above fractions have been reduced or simplified to its lowest terms. The most efficient way to do this is to
1. Find the greatest common factor (GCF) between the numerator and the denominator. (If necessary, refer to article, GCF by Listing Factors or GCF and LCM by Prime Factorization in the related article section below)
2. Divide both the numerator and denominator by the GCF.
Example 1: Simplify 2/4
Step 1) 2/4 --- GCF = 2
Step 2) Divide the numerator, 2, by 2
Step 3) Divide the denominator, 4, by 2
Answer: 2/4 = ½
Example 2: Reduce 18/72
Step 1) 18/72 GCF = 18
Step 2) Divide the numerator, 18, by 18
Step 3) Divide the denominator, 72, by 18
Answer: 18/72 = ¼
Example 3: Reduce 30/45 to the lowest terms
Step 1 30/45 .GCF = 15
Step 2 Divide the numerator, 30, by 15
Step 3) Divide the denominator, 45, by 15
Answer: 30/45 = 2/3
How do you know if the fraction requires reducing?
A fraction requires reducing when the numerator and denominator have at least one common factor other than 1. For example 2/4, the factors for 2: 1, 2. the factors for 4: 1, 2, 4. What factors do they have in common? 1 and 2. Therefore, divide the numerator and denominator by 2, and the result is ½.
Can I divide the fraction by any common factor besides the GCF?
Yes, but remember as long as the numerator and denominator of a fraction have a factor in common, it has not been reduced to its lowest terms.
If you divide a fraction by its GCF, then it is reduced to its lowest terms in one step. Otherwise, reducing fractions can take several steps.
For example, lets take another look at 30/45.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
Common factors: 1, 3, 5, 15
Divide the numerator and denominator of 30/45 by the common factor 5. The result is 6/ 9. It was reduced, but 30/45 was not reduced to its lowest terms. Why? The numerator, 6, and the denominator, 9, still have a common factor. In other words, 3 x 2 = 6, and 3 x 3 = 9. The common factor is 3 which is also in the above list. So, to simplify, use the common factor, 3, to divide the numerator and the denominator. Thus 6/9 = 2/3. Examine the fraction 2/3. Do 2 and 3 have any common factors? No. Thus, 30/45 = 2/3 has been reduced or simplified to its lowest terms. In summary, 30/45 = 2/3. Since the GCF was not used, it took two steps to get to the lowest terms.
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