one more proportional math problem help?

Question

Instead of equating cross products, a student solves x/7 = 5/3 by multiplying on both sides by the least common denominator, 21. Is this approach a good one? Why or Why Not?

Answer 1

if you use the common denominator method ,
you get

3x/21 = 35/21

therefore 3x = 35

x = 35/3

if you cross multiply you will get the exact same thing, but in other cases its not feasible to find the LCD and solve that way. Its not a good approach since you will end up with large fractions.
lets say for example

x/2773 = 1893/3926

The least common denominator for this thing would just be a waste of ink

Answer 2

It is the right approach.
x/7=5/3 3x/21=35/21 thus 3x=35 or x=35:3
or you can do it in another way
x/7=5/3 thus x=5/3 x 7 x=35:3
Finding the least common denominator is essential in adding, subtracting and comparing fractions, but is not essential in multiplication and division of fractions.

Answer 3

They are the same solution...just different ways of understanding it...it is a good solution if it makes it possible for the student to understand the method. We still have 3x=35 and the solution is x=35/3.
Yes the approach is a good one and after performing the method for a few different problems the student should start to see that the two methocs are the same.

Answer 4

The approach is fine, you end up getting the same anwser.
I wouldn't even cross multiply though, just multiply 7 on both sides.

Answer 5

Yes. As is readily seen, this generates your cross-products.
x/7 = 5/3
21*x/7 = 21*5/3
3x = 7*5

...and there you have it. Using LCD actually saves steps if it is some fraction of the product of denominators.

Answer 6

I have a better way that you can try. Let the variable left alone one side;
x/7=5/3
x=35/3
The solution is 35/3 or 11.67

Answer 7

Multiplying both sides by 21 is ok, but I think it is more time consuming. Use the method that suits you.