Three Forms, One Fraction

Pick a fraction — say 3/8 — and write it in three forms. Double everything: 6/16. Triple everything: 9/24. All three point to the same slice of a whole, just cut at different grains.

Now flip it. Start from a messy fraction — 45/60 — and reduce. Divide top and bottom by 5: 9/12. Divide by 3: 3/4. The greatest common factor of 45 and 60 is 15, so one step of ÷15 also reaches 3/4. Both routes land in the same place because reduction is multiplication by 1 in reverse.

Run this drill five minutes a day for a week, and you will see 2/3 in 24/36 at a glance.