Comparing and ordering unit fractions
Maths · Key Stage 2 · The School
What a unit fraction is
A unit fraction has 1 on top. One half, one third, one quarter — all unit fractions. The bottom number tells you how many equal pieces the whole was cut into. A bigger bottom number means more pieces. And more pieces means each single piece is smaller. Every unit fraction shares this one shape: a 1 on top, and some other whole number underneath it.
A cake cut two ways
Picture one cake cut into 3 equal pieces, and an identical cake cut into 8 equal pieces. One piece from the first cake, a third, is a big slice. One piece from the second cake, an eighth, is a thin sliver. The cakes started the same size. Cutting into more pieces made each piece smaller. Holding that picture in your head is the fastest way to compare any two unit fractions.
The rule, stated plainly
For unit fractions, the bigger the bottom number, the smaller the fraction. One tenth is smaller than one fifth. One hundredth is smaller than one tenth. This feels backwards at first, because bigger numbers usually mean bigger amounts. Fractions are the one place that rule flips.
Ordering four fractions
Put one quarter, one half, one eighth and one third in order, smallest first. Look only at the bottom numbers: 8, 4, 3, 2. The biggest bottom number gives the smallest fraction. So the order is one eighth, one quarter, one third, one half. Checking against the cake picture confirms it: an eighth truly is the thinnest slice.