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Answer: $\frac15$
Working out how much is left after each stage
After A has eaten the fraction left is $\frac{1}{2}$.
B eats $\frac{1}{3}$ of this which leaves $\frac{1}{2} - (\frac{1}{2} \times \frac{1}{3}) = \frac{1}{2} - \frac{1}{6}= \frac{1}{3}$.
C eats $\frac{1}{4}$ which leaves $\frac{1}{3} - (\frac{1}{3} \times \frac{1}{4}) = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}$.
D eats $\frac{1}{5}$ which similarly leaves $\frac{1}{5}$.
Multiplying the fractions not eaten
A eats $\frac12$ and leaves $\frac12$
B eats $\frac13$ so leaves $\frac23$
And so on, so the fraction left at the end will be $\frac12\times\frac23\times\frac34\times\frac45=\frac15$ since most numerators cancel with the previous denominator.
Peanut Harvest
Age 11 to 14
ShortChallenge Level 
Answer: $\frac15$
Working out how much is left after each stage
After A has eaten the fraction left is $\frac{1}{2}$.
B eats $\frac{1}{3}$ of this which leaves $\frac{1}{2} - (\frac{1}{2} \times \frac{1}{3}) = \frac{1}{2} - \frac{1}{6}= \frac{1}{3}$.
C eats $\frac{1}{4}$ which leaves $\frac{1}{3} - (\frac{1}{3} \times \frac{1}{4}) = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}$.
D eats $\frac{1}{5}$ which similarly leaves $\frac{1}{5}$.
Multiplying the fractions not eaten
A eats $\frac12$ and leaves $\frac12$
B eats $\frac13$ so leaves $\frac23$
And so on, so the fraction left at the end will be $\frac12\times\frac23\times\frac34\times\frac45=\frac15$ since most numerators cancel with the previous denominator.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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