Fractions as equal parts — Mathematics, 7–10 years
A fraction describes equal parts of one whole or a group. The bottom number tells how many equal parts there are, while the top number tells how many of them we mean.
Parts must be fair
If a sandwich is cut into four equal pieces, one piece is one quarter, written 1/4. The 4 says there are four equal parts; the 1 says we are talking about one of them. Unequal pieces are not four quarters.
Why use fractions?
People often need to share something when it cannot be divided into whole objects: half a pizza, three quarters of a litre or two of five equal tokens. Fractions let everyone describe the share precisely instead of saying only “some”.
Three eighths
A strip is divided into 8 equal sections, and 3 are coloured. The denominator is 8 because the whole has eight equal sections. The numerator is 3 because three sections are coloured, so the fraction is 3/8.
The larger denominator
It can seem that 1/8 is bigger than 1/4 because 8 is bigger than 4. But one whole cut into eight equal pieces gives smaller pieces than one cut into four. For unit fractions, more equal pieces means each piece is smaller.
Sharing and measuring
Fractions appear when a recipe needs 3/4 of a cup, a walk is 1/2 kilometre long or 2/5 of a group chooses a game. They describe real amounts, but only after we know what the whole is.
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