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Elementary Educators/Finding Equivalent Fractions (Mixed Numbers)


Hello and thank you for taking the time out to read my request. My child (4th grader) is having troubles with understanding how to find an equivalent fraction for mixed fractions. I showed her two examples and explained it to her but maybe my teaching method is not helpful. I also searched throughout the name to try and find other explanations but was unsuccessful. My aim is to find a different explanation that would possibly help her.

Here is an example of a problem she had for classwork practice:

3 12/10 = 4 (blank numerator)/10 = 4 (blank numerator)/5

The instructions that she got on solving this math problem was: To rename 3 12/10 to a mixed number with a proper fraction, start with 12/10. 12/10 = 10/10 + 2/10 = 1 2/10. Then add 1 2/10 to 3. This gives you 4 and how many tenths?

These instructions were confusing to her. I'd really appreciate it if you could possibly give a different and more simple explanation and example for her so that I can have her practice. If you need further information, please do not hesitate to contact me. I look forward to your response and thank you so much for your time.

Hello and thank you for your question.  I will try to help you so your daughter will understand fractions better.  I can see how she would be confused.  

Step 1.  Understand that an improper fraction has a numerator that is larger than the denominator.

Step 2.  Forget about the whole number right now.  Look at the fraction.  In the example 3 12/10, just concentrate on the 12/10.  

Step 3.  In the improper fraction 12/10 we now that the whole number 1 is 10/10.  If we take out the 10 from the numerator this leaves 2/10.

Step 4.  Add the 1 with the whole number from the original fraction. 1 + 3 = 4.  Now we have    4 2/10.

Step 5.  Reduce the fraction to the lowest terms.  2/10....use two's.  There is one 2 in the numerator and there is five two's in the denominator.  This gets us the fraction 1/5.

Step 6.  Put the reduced fraction with the whole number.  4 1/5.   3 12/10 = 4 1/5

Here is another example:

3 12/9 ......  leave the 3 alone for now.  Look at the fraction.  One would be 9/9.  Take out 9 from the numerator and that leaves us 3/9.

Add the 1 with the whole number from the original fraction.  1 + 3 =4.  So we get 4 3/9.

Now reduce the fraction.  3/9.  The common multiple is 3.  There is one 3 in the numerator and there is three 3's in the denominator.  So the reduced fraction would be 1/3.

Put the reduced fraction with the whole number and we get 4 3/9.   3 12/9 = 4 3/9

I hope this is understandable and clears up the confusion a little bit.  If not, please let me know and we can try something else.  Good luck!


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Kevin Kennaugh


I can answer questions from teachers, parents, students, and other interested parties. I can answer questions regarding classwork, curriculum, behavior, classroom management, homework, and other school related issues.


I have been an 3rd grade elementary teacher for the past 12 years. I also work with students in grades 1-4 on a daily basis.


B.S. Elementary Education M.S. Elementary Education/Technology Integration

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