You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Have You Got It?

Can you explain the strategy for winning this game with any target?

problem icon

Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Adding Tricky Fractions

Age 11 to 14 Short Challenge Level:

Answer: 1


Change the order of the fractions in the sum so that fractions whose denominators share more factors are added first: $$\begin{align}&\tfrac{1}{7}+\tfrac{1}{8}+\tfrac{1}{9}+\tfrac{1}{10}+\tfrac{1}{11}+\tfrac{1}{12}+\tfrac{1}{14}+\tfrac{1}{15}+\tfrac{1}{18}+\tfrac{1}{22}+\tfrac{1}{24}+\tfrac{1}{28}+\tfrac{1}{33}\\

&=\hspace{2mm}\tfrac{1}{7}\hspace{1mm}+\tfrac{1}{14}+\tfrac{1}{28}\hspace{2.5mm}+\hspace{3.5mm}\tfrac{1}{8}\hspace{1mm}+\tfrac{1}{12}+\tfrac{1}{24}\hspace{2.5mm}+\hspace{4.5mm}\tfrac{1}{9}\hspace{1mm}+\tfrac{1}{18}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{1}{10}+\tfrac{1}{15}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{1}{11}+\tfrac{1}{22}+\tfrac{1}{33}\\

&=\hspace{1.7mm}\tfrac{4}{28}+\tfrac{2}{28}+\tfrac{1}{28}\hspace{2.2mm}+\hspace{2.5mm}\tfrac{3}{24}+\tfrac{2}{24}+\tfrac{1}{24}\hspace{2.5mm}+\hspace{3.1mm}\tfrac{2}{18}+\tfrac{1}{18}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{3}{30}+\tfrac{2}{30}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{6}{66}+\tfrac{3}{66}+\tfrac{2}{66}\\

&=\hspace{13.2mm}\tfrac{7}{28}\hspace{14mm}+\hspace{14.25mm}\tfrac{6}{24}\hspace{14.25mm}+\hspace{8.5mm}\tfrac{3}{18}\hspace{9mm}+\hspace{8.5mm}\tfrac{5}{30}\hspace{8.5mm}+\hspace{13mm}\tfrac{11}{66}\\

&=\hspace{14.3mm}\tfrac{1}{4}\hspace{14.4mm}+\hspace{15.3mm}\tfrac{1}{4}\hspace{15.3mm}+\hspace{9.4mm}\tfrac{1}{6}\hspace{9.3mm}+\hspace{10.3mm}\tfrac{1}{6}\hspace{9.4mm}+\hspace{13.3mm}\tfrac{1}{6}\\
&=\hspace{3mm}1\end{align}$$
You can find more short problems, arranged by curriculum topic, in our short problems collection.