Need math help with common denominator to add two fractions

Mathematics
Tutor: None Selected Time limit: 1 Day

A friend asks "Why do I have to have a common denominator to add two fractions?” What would be your response?

Jan 6th, 2016

Thank you for the opportunity to help you with your question!

Give the friend an analogy like follows;

If you had 3 oranges and 2 other oranges to be shared to  4 children and 6 adults respectively. The fraction of orange held by each child would be 3/4 while the fraction of orange held by adults would be 2/6 or 1/3. Now to add these two fractions 3/4 and 2/6 we would need the least common multiple of the denominators 4 and 6 which is 12.

The reason for this is because adding 3/4 and 2/6 gives a single fraction of the orange held by one adult and one child. Therefore, the denominator of this single fraction needs to represent a number proportional to the number of children and adults relative to the numerator. Since the number of children and adults is universal to both the children and adults, hence the denominator should be equal to both cases and the numerators multiplied by the factor in which the respective denominators were multiplied.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jan 6th, 2016

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