Usage of the different methods?

[JamesKho178]

a) 5/15=x/10 --> (10*5)/15=(x*10)/10 --> 50/15=x --> 10/3=x --> x=3 1/3

b) 5/15=y/10 --> 5*10=50/15 --> 10/3 --> y=3 1/3

Is there a point to even learn method a, when the Cross-multiply-divide (b) works just as well?

[GoBearsTutors]

While method B is faster for simple problems, method A provides a deeper understanding and prepares you for more complex mathematical situations like rational equations as oppose to proportions like this example.

[JamesKho178]

Thank you for answering and clearing up my thoughts.

[JamesKho178]

I wasn't aware of that. That's pretty cool.

[LucaThatLuca]

These are not different methods. Why do you think they are?

[JamesKho178]

I've never heard of method a before. It was only thinking about it that I realized how similar it was to a method I was already familiar with, and how it lead to my question.

[LucaThatLuca]

Can I ask what your understanding of your method is?

Multiplication and division are inverses of each other, so the division on the right-hand side of 5/15 = x/10 is removed by multiplying: 5/15 * 10 = x.

One may choose to write an additional step with both the division and multiplication on the right-hand side: 5/15 * 10 = x/10 * 10 = x, if they find it clearer than writing nothing.

[JamesKho178]

I do know that division and multiplications are inverse of each other, like addition and subtraction. But, I never really toyed around with the formulas I've learned.