### 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

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

### Hello Again

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

# Bouncing Ball

##### Age 11 to 14 Short Challenge Level:

Working out the height after each time it hits the ground
First time: $\frac{3}{5}$ of 125 cm = 125$\div$5$\times$3 = 25$\times$3 = 75 cm.

Second time: $\frac{3}{5}$ of 75 cm= 75$\div$5$\times$3 = 15$\times$3 = 45 cm.

Third time: $\frac{3}{5}$ of 45 cm= 45$\div$5$\times$3 = 9$\times$3 = 27 cm.

Working out the height after each time it hits the ground using 3s and 5s
125 = 5$\times$5$\times$5
First time: $\frac{3}{5}$ of 125 is 3$\times$5$\times$5

Second time: $\frac{3}{5}$ of 3$\times$5$\times$5 is 3$\times$3$\times$5

Third time: $\frac{3}{5}$ of 3$\times$3$\times$5 is 3$\times$3$\times$3 = 27 cm.

Using powers
Each time the ball hits the ground, it bounces to $\frac{3}{5}$ of the height from which it fell. So after each bounce, its height is multiplied by $\frac{3}{5}$.

So after 3 bounces, its height will be multiplied by $\left(\frac{3}{5}\right)^3=\frac{27}{125}$.

So after 3 bounces, its height will be $125\times\frac{27}{125}=27$ cm.

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