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?

Smallest Fraction

Age 11 to 14 Short Challenge Level:

Answer: $\dfrac{2\times3}{4\times6}$


Finding the value of each one
$\dfrac{2+3}{4+6}=\dfrac5{10}=\dfrac{1}{2}$

$\dfrac{2\div3}{4\div6}=\dfrac{\frac23}{\frac46}=\dfrac{\frac23}{\frac23}=1$
 
$\dfrac{23}{46}=\dfrac12\\$

$\dfrac{2-3}{4-6}=\dfrac{-1}{-2}=\dfrac12\\$

$\dfrac{2\times3}{4\times6}=\dfrac{6}{4\times6}=\dfrac14$

So $\dfrac{2\times3}{4\times6}$ is the smallest.


Preserving the ratio between the top and bottom numbers
All relate to $\frac24=\frac12$, numerator $:$ denominator $=1:2$

$\dfrac{2+3}{4+6}$
Numerator: $+2$
Denominator: $+4$ 
Operations are in the ratio $1:2$ so this fraction is still $\frac12$

$\dfrac{2\div3}{4\div6}$
Numerator: $\div3$
Denominator: $\div6$
Denominator gets smaller twice as quickly as numerator $\therefore$ fraction doubles in size

$\dfrac{23}{46}$, numerator $:$ denominator $=1:2$

$\dfrac{2-3}{4-6}$
Numerator: $-2$
Denominator: $-4$
Operations are in the ratio $1:2$ so this fraction is still $\frac12$

$\dfrac{2\times3}{4\times6}$
Numerator: $\times3$
Denominator: $\times6$
Denominator gets larger twice as quickly as numerator $\therefore$ fraction halves in size
$\therefore$ smallest


You can find more short problems, arranged by curriculum topic, in our short problems collection.