Common Denominator

Before we begin to add or subtract fractions, we must first understand the meaning of common denominator and how it is found. A common denominator means that the denominators in two or more fractions are the same. The first step to adding and subtracting fractions is to make sure that the denominators are the same. If they are not, we must find their common denominator. This can be done by finding the least common denominator or by multipliying one denominator by the other. To find the LCD, we start by listing the multiplies of our denominators.
I will use the numbers 1/3 and 1/12
3 : 3, 6, 9, 12
12:  12, 24, 36
I then look at these numbers and find the smallest number that they have in common. In this case it is 12, so my common denominator would be 12.

The question that I am to answer is: "How will you explain to your students that when you add or subtract fractions you must have a common denominator but you do not need one with multiplication or divison?"
I think I would simply say that you can't add or subtract two things that are not the same. For example, you can not add an apple and an orange. If you do you will still have 1 apple and 1 orange. You have to have the same type of fruit to be able to add or subtract from them.

I was looking at it all WRONG!

Fractions scare me. I can't explain why, they just do. They rank right up there with graphs on my mathematical fear chart. I can now say those fears have been put to rest. I have learned to view the correct way to add, subtract, multiply, and divide fractions. The biggest lesson came to me when we began to review multiplication of fractions. Mixed number operations to be exact. I was wrong at first glance. If I were given a multiplication problem with mixed numbers, 2 1/7 x 3 2/5, I would have looked at it from two different angles. The first method would be incorrect, and lead me to an incorrect answer. I would have taken the 2 and multiplied it by the 3 to give me 6. Then I would have multiplied the 1/7 x 2/5. WHAT WAS I THINKING? The second way I would have gone about this problem would have been to change it to an improper fraction. This would have given me the correct answer, but it is not the correct way to view this problem. It all made sense once Mrs. Truelove said these magic words (and I parapharse) "If you had 27 x 32 you would not multiply the 7 by the 2 and the 2 x 3 to get your answer." BINGO!! It clicked. I need to distribute my numbers. Once I complete this process and find my answer, I can then go back and change my numbers into an improper fraction to check my answer.
Example of the problem mentioned in the post:
2 1/7 x 3 2/5
2(3 + 2/5) + 1/7(3 + 2/5) (distribute)
6 + 4/5 + 3/7 + 2/35 (now it looks familiar/ we need to find the LCD which is 35)
6 + 28/35 + 15/35 + 2/35 (add)
6 45/35 = 7 10/35 (reduce) = 7 2/7


Change to improper fraction:
2 1/7 x 3 2/5
15/7 x 17/5 (from here you can cross cancel)
51/7 = 7 2/7


I have checked my answer and found it to be correct.

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