More fraction bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Problem

Look at these different coloured bars.

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Various equal width bars. Black: 48 squares long, representing the number 2. The following are bar names, along with their lengths: P 36. Q 42. T 40. V 28. R 30. U 24. S 32.

You might like to download a printable version of them here.

Put the bars in size order - can you do it without cutting them out?

Now focus on this bar:

 

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Black bar from before, representing the number 2 with 48 little squares.

 

This bar represents two wholes, or the number 2. You might find it easier to think of it as two bars which are each 'one whole' that have been stuck together.

We are thinking about all the other coloured bars as fractions of this bar, so we are thinking about them as fractions of 2.

For example, look at Bar S below:

 

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Bar S drawn underneath the black bar.

 

Drawing lines helps us measure it against the black bar:

 

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Lines are added in thirds along the black bar, to help compare its length to that of Bar S.

 

What fraction of the black bar is Bar S?

Go through each of the other coloured bars and compare them to the black bar. What fraction of 2 is each bar?

Write down your ideas for each bar. For example, you could write:

Bar S is two thirds of the black bar.

or

Bar S represents $\frac{2}{3}$ of 2.

or

Bar S is 1$\frac{1}{3}$.

Can you work out how we came up with these three ideas?

When you've worked out what fraction of 2 each bar represents, have a go at the next challenge here.