Math ? Can I just do it my way? Proportions and x-multipliying...

[KathyBC]

We're doing questions like this one: If the ratio of birds to bees is 15 to 17 and there are 135 birds, how many bees are there?

 

The method taught is to x-multiply, then divide. Honestly, I always find it easier to divide the corresponding numbers first, then multiply to find the missing number. Is there any reason not to teach it this way instead?

[avilma]

In the end, when you are performing the arithmetic operations, there is no contradiction between the taught method and

what you want to do. According to the taught method the result is 135 x 17 / 15. To perform the operation you can do

the multiplication first and then the division, or you can first divide 135 / 15 = 9 first and then multiply 9 x 17 = 153.

Multiplication first is usually done by people why rely too much on the calculator.

 

The problem with your method is that you have to think all the time what are the corresponding numbers.

Because of course you have 2 choices, right, you could do 135/15 first and then multiply with 17,

or you could also do 17/15 first and then multiply with 135. They both give your the correct result but if

you are doing the operations by hand, doing 17/15 first results in way more work than necessary.

 

I would suggest to keep using the taught method since it is a very useful formula which

can be applied automatically after enough practice.

[Dana]

I think the more options you have, the better.

WIth proportions, I want students to understand WHY they do the cross-multiplication & division.

Proportions are just rational equations. The properties of solving linear equations work (so long as you don't end with a denominator of zero when substituting back).

 

So you can simplify each side first, and multiply both sides by any non-zero number.

You can do this in any order.

 

So solving 5/15 = x/7,

I might reduce 5/15 first, giving 1/3 = x/7.

Rather than cross-multiply here, to get x by itself, I just want to multiply by 7. Thus 7/3 = x.

This is the same as if I'd done 7(5) = 15(x), then divided by 15.

Note that if I write that out... [7*5] / 15 = x, I can still reduce the 5/15 by properties of fractions (divide by 1: cancel the 5/5).

 

So yes, your method is fine.

Sometimes one procedure is easier than others though. Thus having multiple approaches can be helpful. And, most importantly, showing why a procedure works is crucial.

[KathyBC]

Thanks for taking the time to reply. We'll use both methods, I think.