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'Rod Fractions' printed from http://nrich.maths.org/

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What fraction of the orange rod is the yellow rod?

Orange and yellow


Use this picture to help you. Note that it only uses orange and yellow rods.

One orange equals two yellow


Now use the interactivity below to build similar pictures that will help you to answer the following problems:

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Using as many brown and red rods as you like, but no rods of any other colours, work out what fraction the red rod is of the brown one.

Brown and red


Using as many blue and dark green rods as you like, but no rods of any other colours, work out what fraction the dark green rod is of the blue one.

Blue and dark green


Using as many pink and orange rods as you like, but no rods of any other colours, work out what fraction the pink rod is of the orange one.

Pink and orange


Using as many pale green and orange rods as you like, but no rods of any other colours, work out what fraction the pale green rod is of the orange one.

Orange and pale green


Pick two other rods of different colours. Given an unlimited supply of rods of each colour, work out what fraction the shorter rod is of the longer one.

Given an unlimited supply of any two differently coloured rods, can you find a general rule to work out what fraction the shorter rod is of the longer one?

Why does your rule work?