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Adding Fraction With Different Denominator. Definition. Common Denominator – When the fractions in an addition problem do not have the same denominators, rewrite the problem so that each fraction has the same denominator.

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definition
Definition
  • Common Denominator – When the fractions in an addition problem do not have the same denominators, rewrite the problem so that each fraction has the same denominator.
  • Lowest Common Denominator – A common denominator is a number that can be divided evenly by all the denominators in a problem. The smallest number that can be divided evenly by all the denominators in a problem.
  • Sometimes the largest denominator is a problem is the lowest common denominator.
finding a common denominator
Finding a Common Denominator

Here are two ways of finding a common denominator when the largest denominator in addition problem doesn’t work.

  • Multiply the denominators together.
  • Go through the multiplication table of the largest denominator.
example 1
2/5 + 3/4 =

Multiply the denominators. 5 X 4 = 20. 20 is the lowest common denominator (LCD).

Raise each fraction to 20ths .

Add the new fractions.

Change the answer to a mixed number.

2/5 = 8/20

+ 3/4 =15/20

23/20 = 1 3/20

Example 1
example 2
2/3 + 5/6 + 3/4 =

Go through the multiplication table of the 6’.

6 x 1 = 6, which cannot be divided by 4.

6 x 2 = 12, which can be divided by 3 and 4.

Raise each fraction to 12ths.

Add the new fractions.

Change the answer to a mixed number and reduce.

2/3 = 8/12

5/6 =10/12

+3/4 = 9/12

27/12 = 2 3/12

= 2 1/4

Example2
practice
3/5 + 2/3 =

3/7 + 1/3 =

1/4 + 3/5 + 7/10=

2/3 + 4/9 + 5/6 =

4 3/5 + 6 ¾ =

6 5/12 + 7 3/8 =

Practice