Comparing Fractions

Same Bottom Number #

Same-sized pieces — more pieces means larger.

When the pieces are the same size, more pieces means more

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Both bars are cut into 5, so every single piece is the same size. $\frac{3}{5}$3/5 is bigger than $\frac{2}{5}$2/5.

Same Top Number #

Same number of pieces — bigger pieces means larger.

Taking the same number of pieces, the one with bigger pieces is larger

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Both bars have 2 pieces colored — but the pieces are not the same size.

Fewer cuts means bigger pieces, so $\frac{2}{3}$2/3 is larger than $\frac{2}{5}$2/5.

More Than a Half #

Compare against a half to judge quickly.

Comparing anything to one half tells you a lot very quickly

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That dashed line marks exactly halfway along the bar.

Shade fifths one at a time until the shading crosses the dashed line: that is more than a half.

This coloring stops before the dashed line, so it is less than half.

$\frac{2}{4}$2/4 ends right on the line: exactly a half. Double the top and you get the bottom.

Ordering Fractions #

Three tools that order almost any fractions.

Three tools together will order almost any fractions you meet

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Tool one: on the wall these are cuts of one whole, and $\frac{1}{4}$1/4 is plainly the shortest.

Tool two, the half check: on the line $\frac{1}{4}$1/4 falls short of a half, $\frac{3}{5}$3/5 and $\frac{7}{8}$7/8 pass it.

Tool three: the half check ties $\frac{3}{5}$3/5 with $\frac{7}{8}$7/8, so read the line: $\frac{1}{4}$1/4, $\frac{3}{5}$3/5, $\frac{7}{8}$7/8.