### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

### Matching Fractions, Decimals and Percentages

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

# 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.