### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

### Circle Packing

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...

### Round and Round

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

# Fractions and Percentages Card Game

##### Age 11 to 16Challenge Level

Chris described a method for finding the percentages as amounts of money:

To find out a percentage out of a number you can divide the number by $100$ or $10.$ [Say] you divide the percentage by $10.$ After that you find out what the number divided by $10$ and the percentage by $10$ and you times it.
Eg. $40\%$ of $£11.20,$ $11.20\div10 = 1.12.$
You divide $40$ by $10$ which equals $4.$
$1.12x4= £4.48.$ Therefore  $40\%$ of $£11.20$ equals $£4.48$

Mark from International School of the Hague described a method for the fractions:

First I figured out what the fractioned numbers were by converting them to decimals. I did this by converting the denominators to a hundred. Then I [multiplied] the decimals by the currency that was on the same card and then I had different currencies that were equal to each other. I selected these and finished.

Sienna from Greenacre Public School in Australia described a way to speed up the matching:

However, there is a way to make to make this process faster. For example, $25\%$ of $4,$ you could assume that it would be less than a half of it. This would make the other options much more limited.

Erik from International School of the Hague described another way to speed up the matching:

The easiest way of doing this exercise is doing the easiest ones first. Also, you really need to know your fractions of a number, and percentages of a number really well for this exercise. If you do the easiest ones first, you have less space so you can find the answers to the harder ones easier, and if you leave the hardest flashcard to the last, you will automatically know the answer.