Comparing Fractions
I was taught to find a common denominator when comparing or ordering fractions. Find the LCM. Even change them into decimals.
Instead, I want to compare fractions in these three ways:
Using number sense and the fraction 1/2
Finding a common numerator
Thinking of them as perfect pinks or not
Compare 3/4 and 5/12.
3/4 is more than 1/2, and 5/12 is less than 1/2, hence 3/4 > 5/12.
Compare 1/5 and 2/7.
1/5 is the same as 2/10, and 2/10 is smaller than 2/7 because pizza.
Compare 5/7 and 6/9.
A perfect pink color is made from 1 part red and 2 parts white, expressed as 1/2. I have a visual sense of this color, this red/white ratio of 1/2. Anything greater than 1/2 is dark pink, and anything less is light pink.
So 5/7 is darker, and to get to the color of 6/9, I’d need to do this: 5/7 + 1/2 = 6/9. If I’m adding something less dark than what I’d started with, then I’m going to dilute the color, so 6/9 is less dark than 5/7. I conclude 5/7 > 6/9.
Of course if I add the exact same color to itself, then there should be no change: 2/3 + 2/3 = 4/6.
Compare 19/60 and 21/55.
19/60 is light pink, so is 21/55. To get from 19 to 21, I’d need to add 2 reds, and to get from 60 to 55, I’d take away 5 whites. The net effect is more red, making 21/55 darker, or 19/60 < 21/55.
This is not unlike how batting averages work.
