I was taught to compare or order fractions by finding a common denominator. Or by finding the LCM. Or just turning them into decimals.
But here’s how I actually want to compare fractions now — using:
Number sense and the fraction 1/2
A common numerator
Perfect pinks (just go with me)
Compare 3/4 and 5/12
3/4 is greater than 1/2.
5/12 is less than 1/2.
So, 3/4 > 5/12.
Compare 1/5 and 2/7
1/5 is the same as 2/10.
And 2/10 is less than 2/7 (because pizza).
So, 1/5 < 2/7.
Compare 5/7 and 6/9
Let’s talk about pink.
A perfect pink is 1 part red, 2 parts white — a 1/2 ratio.
That’s our benchmark. That’s the “true pink.”
Anything greater than 1/2 is darker pink.
Anything less than 1/2 is lighter pink.
So, 5/7 is a dark pink.
To get to 6/9, I imagine adding something to 5/7 that results in 6/9:
5/7 + 1/2 = 6/9
If I add something lighter (1/2) to something darker (5/7), the result will be a lighter shade.
Therefore, 5/7 > 6/9.
(And if I add the same shade to itself, the color doesn’t change:
2/3 + 2/3 = 4/6 — same color.)
Compare 19/60 and 21/55
Both are light pinks — less than 1/2.
From 19/60 to 21/55:
We added 2 reds (numerator went up)
We removed 5 whites (denominator went down)
That’s a net gain in red. It’s darker.
So, 19/60 < 21/55
This kind of reasoning isn’t far from how batting averages work — adding more successful hits (numerators) while playing fewer games (denominators) can bump the average quickly.
So maybe fractions aren't so abstract.