### Consecutive Numbers

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

### Have You Got It?

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

### 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.