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Use the same starting size
Take two identical chocolate bars. Split each bar into five equal pieces.
You get three pieces from one bar. A friend gets two pieces from the other. Your share is bigger because the pieces are the same size and you have one more.
We write those shares as 3/5 and 2/5. When the bottom numbers match and the wholes are the same size, compare the top numbers.
Try it yourself
Draw two strips of equal length. Divide one into two equal parts and the other into four. Shade one part of each strip. Which shaded piece is longer?
One half is larger even though two is smaller than four. With one selected part in each fraction, a larger denominator means the whole was split into more, smaller pieces. The bottom number is not a score where higher always wins.
Compare using matching pieces
Which is bigger: 2/3 or 3/4? The pieces are different sizes, so counting two pieces against three is not enough.
Draw two identical strips, each divided into twelve small equal pieces.
On the first strip, one third covers four small pieces. Two thirds cover eight. Colour those eight pieces.
On the second strip, one quarter covers three small pieces. Three quarters cover nine. Colour those nine pieces.
Compare the coloured amounts. Nine small pieces cover more than eight.
So 3/4 is bigger than 2/3. We changed how we divided the strips, not the amounts we were comparing.
Is it more or less than half?
Halfway is a useful place to start. Draw a strip with eight equal pieces. Four pieces cover half of it.
Three pieces do not reach halfway, so 3/8 is less than 1/2.
Five pieces go past halfway, so 5/8 is more than 1/2.
You do not need a new calculation each time. First ask where the coloured amount sits on the strip.
