# Help me explain this fraction algorithm

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2/3 x 12 for example (fraction x a whole number). Conceptually my son understands why it is 24/3 and it makes perfect sense then to him just simplify it to 8 wholes but unfortunately ALEXS taught him (not to well I might add) to change the problem to 2/3 x 12/1 and to cross out the 3 and write 1 and cross out the 12 and write 4 and then to multiply the top across and the and the bottom across to get 8.

Is there a better way to explain this algorithm better than my thought here? Lay out 12 sets of 2/3s, ask him to focus on just 1/3 out of each set (12) and ask how many wholes can you make with just those 12 and the answer is obviously 4. Ask him to look at how many thirds is left with is 12 which is another obvious 4 wholes-then go back to the alogorithm to multiply the 2/1 x 4/1 = 8. Then we do several of these types of problems with the fraction strips and test the algorithm to see if it works every time.

This is my common sense way to teach why this algorithm works-BUT I am not a math teacher and want to run this by someone more experienced. I assume this algorithm is essential to teach and that it lays the foundation for something down the road. I have always taught math conceptually with Right Start-but I am solo on teaching the why of this algorithm.

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Take a look at visualfractions.com. It might help :)

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2/3 x 12 for example (fraction x a whole number). Conceptually my son understands why it is 24/3 and it makes perfect sense then to him just simplify it to 8 wholes but unfortunately ALEXS taught him (not to well I might add) to change the problem to 2/3 x 12/1 and to cross out the 3 and write 1 and cross out the 12 and write 4 and then to multiply the top across and the and the bottom across to get 8.

Is there a better way to explain this algorithm better than my thought here? Lay out 12 sets of 2/3s, ask him to focus on just 1/3 out of each set (12) and ask how many wholes can you make with just those 12 and the answer is obviously 4. Ask him to look at how many thirds is left with is 12 which is another obvious 4 wholes-then go back to the alogorithm to multiply the 2/1 x 4/1 = 8. Then we do several of these types of problems with the fraction strips and test the algorithm to see if it works every time.

This is my common sense way to teach why this algorithm works-BUT I am not a math teacher and want to run this by someone more experienced. I assume this algorithm is essential to teach and that it lays the foundation for something down the road. I have always taught math conceptually with Right Start-but I am solo on teaching the why of this algorithm.

I'm in a hurry, so I will be honest and say I didn't read your entire explanation. :tongue_smilie:;)

Very simply, fractions are taking wholes and dividing into parts. So with 3/4 x 12, you want to take the number 12 and divide it into 4ths (which is why cross reducing works). How many of those fractional 1/4s do you want? 3.

So......12 divided into 4ths means that each factional group has 3 and 3 of those groups = 9.

I told you I was in a hurry, so I just realized your example was 2/3 x 12, not 3/4, but it is the same thing.

take 12 and divide into thirds....each group is 4 (why cross reduction works) and take 2 of those groups of 4 and end up with 8.

Does that help at all?

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2/3 x 12 for example (fraction x a whole number). Conceptually my son understands why it is 24/3 and it makes perfect sense then to him just simplify it to 8 wholes but unfortunately ALEXS taught him (not to well I might add) to change the problem to 2/3 x 12/1 and to cross out the 3 and write 1 and cross out the 12 and write 4 and then to multiply the top across and the and the bottom across to get 8.

Is there a better way to explain this algorithm better than my thought here? Lay out 12 sets of 2/3s, ask him to focus on just 1/3 out of each set (12) and ask how many wholes can you make with just those 12 and the answer is obviously 4. Ask him to look at how many thirds is left with is 12 which is another obvious 4 wholes-then go back to the alogorithm to multiply the 2/1 x 4/1 = 8. Then we do several of these types of problems with the fraction strips and test the algorithm to see if it works every time.

This is my common sense way to teach why this algorithm works-BUT I am not a math teacher and want to run this by someone more experienced. I assume this algorithm is essential to teach and that it lays the foundation for something down the road. I have always taught math conceptually with Right Start-but I am solo on teaching the why of this algorithm.

You're probably fine for that type of fraction problem.

The procedure shown in ALEXS isn't the most useful for a problem like 2/3 x 12 or even 3/4 x 108 (e.g., where you can easily divide 108 into 4 equal groups, and since you need 3 groups of fourths, multiply by 3). However, it will be important to know that procedure as you approach algebra, since you're reducing fractions by crossing out common factors.

It might be easier to explain the longer algorithm with fraction problems like 2/3 x 9/10, where you have to do this:

2 x 9

3x10

...and then you can see how the algorithm would be more of a shortcut.

HTH!

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2/3 x 12 for example (fraction x a whole number). Conceptually my son understands why it is 24/3 and it makes perfect sense then to him just simplify it to 8 wholes but unfortunately ALEXS taught him (not to well I might add) to change the problem to 2/3 x 12/1 and to cross out the 3 and write 1 and cross out the 12 and write 4 and then to multiply the top across and the and the bottom across to get 8.

Explain the concept of factor & cancel. It is important that a student understands the need to factor first. Watch this Khan Academy video.

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