Fraction Comparison Reflection

You know how to compare fractions using cross products, LCD, and logical reasoning. When is it better to use one method over another?

Methods - Pros and Cons

Cross Products
Pro: It's a quick way to compare fractions, you only need to solve 2 equations.
Con: When the numbers get higher, it's harder to solve the equations.

LCD
Pro: Once you find the LCD, you just need to compare the numerators.
Con: If the LCD is really high, it's harder to find the new numerator.

Logical Reasoning
Pro: It requires no solving of equations!
Con: If the numerators are about the same, it's really hard to compare.


Examples

1) 5/7 or 6/8
For this question, I would use cross products because it's the quickest way to solve it. The numbers aren't huge and massive. Logical reasoning would not be a good method to use for this problem because the numerators are really close to each other. You could use LCD to solve this problem but that would take longer.

2) 21/35 or 46/70
For this question, I would use LCD because it's the easiest way to solve it. The LCD is pretty easy to find because 70 is a multiple of 35. Cross products would be another way to solve this problem but the numbers are really high which makes multiplying them harder. Logical reasoning would be hard to use because if you simplify the fractions, they both are more than 1/2.

3)3/82 or 32/35
For this question, I would use Logical reasoning because it's easy to use logical reasoning for this question. Also, you don't have to waste time doing unnecessary math. LCD and cross products would not be good methods because the numbers are really high.