7141
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2011-02-01T00:00:01
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<mdoxml version="1.0"><p>The fractions $\frac{1}{3}$ and $\frac{1}{5}$ have been placed on the number-line shown. At which position should the fraction $\frac{1}{4}$ be placed?<br></br>
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<mdo:image alt="" height="134" src="47%202010.PNG" width="431"></mdo:image><br></br>
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If you liked this problem, <a href="http://nrich.maths.org/34&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas. <br></br>
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The difference between $\frac{1}{3}$ and $\frac{1}{5}$
is $\frac{1}{3}-\frac{1}{5}= \frac{2}{15}$.<br></br>
<br></br>
This section of the number line is divided into $16$
intervals, each of length $\frac{2}{15}\div 16 =
\frac{1}{120}$. <br></br>
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The difference between $\frac{1}{4}$ and $\frac{1}{5}$
is $\frac{1}{4}-\frac{1}{5}= \frac{1}{20}= \frac{6}{120}$, and
hence $\frac{1}{4}$is six smaller intervals
from $\frac{1}{5}$. <br></br>
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<mdo:image width="431" height="134" alt="" src="47%202010a.PNG"></mdo:image><br></br></mdoxml>
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