Fractional units

A whole chikki is cut into 6 equal parts in two different ways: once into little squares, once into triangles. The pieces come out in different shapes, but each one is 1/6 of the chikki. Equal parts of the same whole are the same size, whatever their shape.

A piece's fractional unit comes from how many equal pieces make the whole. A piece we get by breaking the chikki into 3 equal pieces is 1/3 chikki. A piece we get by breaking it into 8 equal pieces is 1/8 chikki.

We can measure a bigger piece by counting fractional units in it. The book breaks a chikki into 2 pieces. The bigger piece has 3 pieces of 1/4 chikki in it, so the bigger piece is 3/4 chikki.

Take a paper strip one unit long.

• Fold it into 2 equal parts: each part is 1/2.
• Fold again: 4 equal parts, each 1/4. Then 2 times 1/4 = 2/4, 3 times 1/4 = 3/4 and 4 times 1/4 = 4/4, the whole strip.
• Fold once more and you get eighths: 8 times 1/8 = 8/8 = 1.

We usually read 3/4 as 'three quarters' or 'three upon four'. Reading it as '3 times 1/4' shows its size clearly: the fractional unit is 1/4, and there are 3 of them. That is why 5/4 does not mean '5 out of 4' (you cannot take 5 parts out of 4); it means 5 times 1/4. The top number is the numerator and the bottom number is the denominator: in 5/6, 5 is the numerator and 6 is the denominator.