# Which Fraction Is Bigger?

##### Age 16 to 18

Challenge Level

*This resource is from Underground Mathematics**.*

Warm-up

Which is bigger, $\frac{2}{5}$ or $\frac{1}{3}$?

How do you know?

Is there more than one way of convincing yourself that one is bigger than the other?

What if you had the fractions $\frac{2x}{5}$ and $\frac{x}{3}$? Would your answer be the same?

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Main problem

Here are some more pairs of fractions for you to try.

If you are working with others you may wish to tackle examples separately and then compare approaches and conclusions.

You may like to print and cut out the pairs of fractions on cards, so that they may be attempted in any order.

- $\dfrac{4x}{7}$ and $\dfrac{9}{14}$

- $\dfrac{5}{9}$ and $\dfrac{2x}{12}$

- $\dfrac{3x}{4}+1$ and $\dfrac{x}{4}+3$

- $\dfrac{8(1-x)}{5}$ and $\dfrac{x}{6}$

- $\dfrac{8}{2x}$ and $\dfrac{4x}{16}$

**This is an Underground Mathematics resource.**
*Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.*
*Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.*