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how to compare fractions by finding common denominator

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In order to compare two fractions you must find a common denominator.  There is a variety of ways to do this but find the LCD is the most proper way to go.  Once the denominators are the same then you check the equivalent numerators and decide which is larger.  See example below.

2/3 and 3/4 are what is being compared.

find the LCD for 3 and 4 by listing the multiples of these nuimbers until you reach the smallest matching number.

3 - 3, 6, 9, 12, 15, 18, 21

4 - 4, 8, 12, 16, 20

12 is common in both so our LCD is 12

Now we must create our equivalent fractions

2/3 = ?/12  and  3/4 = ?/12

Ask yourself what you multiply by 3 to get 12.  Answer is 4 so muliply the top by the same number to get the equivalent fraction 8/12.  Do the same with 3/4.  What do I multiply 4 by to get 12.  Answer is 3 so muliply that factor of 3 to the numerators 3 and get 9.  The equivalent fraction of 3/4 is 9/12.

Now compare the equivalent fractions... 8/12 and 9/12.  Ask yourself which is larger 8 or 9 and use your symbol to show that relationship.

8/12 < 9/12