Fraction Adding and Subtracting

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Student: When I add fractions that have the same denominator, such as 1/5 + 2/5, I know that the answer is 3/5. But what do I do when the denominators are different?

Mentor: The first thing is to find the lowest common denominator, the smallest number that both denominators divide into evenly. If I am adding 3/4 + 1/6, what is the lowest common denominator?

Student: Well, it looks to me like it would be 12. Both 4 and 6 can divide into 12.

Mentor: Exactly! So you rewrite the problem to look like this:

Instead of 3/4 + 1/6, write it as:

something/12 + something/12. Then you will see what the correct answer is.

To find out the "somethings", start with the first fraction. If you are changing the denominator in the fraction 3/4 to "something"/12, you multiplied 4 by 3 to get 12. So multiply the numerator by 3 also. That gives us 9/12.

Student: OK, now I'll try the second fraction, 1/6. If I change the denominator to 12, I multiplied 6 by 2 to get 12. So I will multiply the numerator (1) by 2, which is 2. So that gives me a fraction of 2/12.

Mentor: Right so far. We just made the problem easier to solve by converting it this way:

3/4 + 1/6 became 9/12 + 2/12

Student: That's much easier to solve. 9 + 2 = 11, so the answer would be 11/12.

Mentor: Yes! It works the same way for subtraction. Try this problem: 4/5 - 4/15.

Student: Let's see. The lowest common denominator is 15, because both 5 and 15 divide evenly into it.

So I can rewrite the problem:

4/5 - 4/15


something/15 - something/15

I'll start with the first fraction. I multiplied the denominator 5 by 3 to get 15, so I will also multiply the numerator, 4, by 3. That will make the fraction 12/15.

The second fraction is very easy. The denominator is already 15 (15 divides into 15 one time), so I will multiply the numerator by one, giving me a fraction of 4/15. My subtraction problem now looks like:

12/15 - 4/15

And the answer is 8/15.

Mentor: Very good! You learn fast.

Can you solve this problem 2/3 - 4/9?

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