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Sum Equals Product

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

Rod Fractions

Age 7 to 14 Challenge Level:

What fraction is the yellow rod of the orange rod? 
 


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

 

You might like to use the interactivity further down this page to help you answer the following problems:

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.



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

 
 

Can you find any other pairs of rods so that the length of the shorter rod compared with the longer rod is a fraction with 1 as its numerator? 





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?

You may like to explore this by using the pairs of colours suggested below as starting points.

Dark green and blue:

 

Pink and orange:

 

Light green and orange:

 

Why does your rule work?

Now, looking back at the different pairs of rods you have explored, can you find a way to express the longer rod as a fraction of the shorter rod?