Denominator

Common Denominator

When the denominators of two or more fractions are the same, they are known as the common denominators. The least common denominator (LCD) is the smallest number that can be a common denominator for a given set of fractions. Addition and subtraction of fractions and comparing two or more fractions is possible only if the fractions have common denominators. For example, if we need to add 3/8 + 1/8. Since the denominators are the same, they are like fractions and can be instantly added up and the result will be 3/8 + 1/8 = 4/8 = 1/2.

Like fractions are the fractions that have the same denominators. Example: 5/15, 3/15, 17/15, and 31/15. Unlike fractions are the fractions which have different denominators. Example: 2/7, 9/11, 3/13, and 39/46. Let us see some examples here to add and subtract fractions with common denominators.

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  2/2 + 3/2 = (2+3)/2 = 5/2
  
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  6/7 - 2/7 = (6-2)/7 = 4/7
  

For different denominators, we need to convert the given unlike fractions to like fractions by changing the fractions to equivalent fractions having the same denominator. This can be done by finding the Least Common Multiple (LCM) of the denominators, which is known as LCD (Least Common Denominator). Let us understand this with the help of an
Solution:

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  Step 1: Since the given fractions are unlike fractions, we will find the LCM of the denominators 2 and 3. The LCM of 2 and 3 is 6.
  
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  Step 2: Now, we will multiply the first fraction 1/2 with 3/3, this will result in an equivalent fraction 3/6. Similarly, we will multiply the second fraction 1/3 with 2/2, this will result in 2/6.
  
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  Step 3: This step will convert both the fractions to like fractions, that is, 3/6 and 2/6.
  
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  Step 4: Now, that the denominators are the same, we can add the numerators while the denominator will remain the same, that is, 3/6 + 2/6 = 5/6. Therefore, the sum of 1/2 + 1/3 = 5/6.
  

Important Notes

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  A denominator must be an integer.
  
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  A denominator can never be zero because zero parts can never make up a whole.
  
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  The term denominator is widely used in the concepts of rational numbers, ratios and proportions, and division concepts.
  

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