Pride of place
Two fractions have been placed on a number line. Where should another fraction be placed?
Age
11 to 14
Challenge level
Problem
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?
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer:
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Using a common denominator
$$\frac15 \qquad \frac14 \qquad \frac13\\
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\frac{12}{60} \qquad \frac{15}{60} \qquad \frac{20}{60}$$ The distance from $\dfrac{12}{60}$ to $\dfrac{20}{60}$ is $\dfrac 8{60}$
There are $16$ intervals on the diagram so two make $\dfrac1{60}$
The distance from $\dfrac{12}{60}$ to $\dfrac{15}{60}$ is $\dfrac 3{60}$ so go along $6$ intervals
Finding the size of the intervals
The difference between $\frac{1}{3}$ and $\frac{1}{5}$ is $\frac{1}{3}-\frac{1}{5}= \frac{2}{15}$.
This section of the number line is divided into $16$ intervals, each of length $\frac{2}{15}\div 16 = \frac{1}{120}$.
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 $\frac{1}{5}$.