Adding unlike fractions

                In adding unlike fractions we discuss addition of unlike fractions.

To add unlike fractions first, we have to convert unlike fractions to like fractions. Then we can add the numerators and find the sum.

To convert unlike fractions as like fractions,

  • first we need to find the LCD of the denominators.
  • Next we need to convert each fraction to have the common denominator
  • Now we have to add the numerators of the new fractions.
  • If possible we have to bring to the lowest term(simplify).
  • Now we are going to see examples of the topic adding unlike fractions.

Examples for adding unlike fractions

    Example 1: 
    Add 2/3 + 2/5 + 3/15
    Now we have to find LCD of those denominators of the given fractions. The LCD of 3,5 and 15 is 15.

    Now we have to make the denominator of the fraction 2/5 as 15. For that we have to multiply this fraction 2/3 by 5/5. So we will get 10/15. Now we have to change the denominator of the fraction 2/5 as 15. For that we have to multiply the fraction 2/5 by 3/3. So that we will get 6/15.

  • converting 3/15 has the same LCD.
  • So 2/3 + 2/5 + 3/15 = 10/15 + 6/15 + 3/15 = (10+6+3)/15 = 19/15
  • Simplifying 19/15 we will get 1 4/15.



    Example 2: 
  • Add 2/7 + 5/14 + 9/21
    Now we have to find LCD of those denominators of the given fractions. The LCD of 7,14 and 21 is 42.Now we have to make the denominator of the first fraction 2/7 as 42. For that we have to multiply this fraction 2/7 by 6/6. So we will get 14/42.Next we have to change the denominator of the second fraction 5/14 as 42. For that we have to multiply the fraction 5/14 by 3/3. So that we will get 15/42. Now we have to change the denominator of the third fraction 9/21 as 42. For that we have to multiply the fraction 9/21 by 2/2. So that we will get 18/42.
  • So 2/7 + 5/14 + 9/21 = 14/42 + 15/42 + 18/42 = (14+15+18)/42 = 47/42
  • Simplifying 47/42 we will get 1 5/42.

Students follow the examples step by step and try to do the problems in the worksheet using the method discussed in the examples. If you have any doubt you can Contact us through mail, we will help you to solve the problems. 

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